Lusas Modeller User Manual

Fixing Mesh Problems

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Chapter 5 ModelAttributesAttribute datasets are used to describe the properties of the model. Attributes areassigned on a feature basis and hence are not lost when the geometry is edited, or thefeature is re-meshed at a different density. Attribute assignments are inherited whenfeatures are copied and are retained when features are moved. The LUSAS attributetypes are:

General

q Mesh describes the element type and discretisation on the geometry. Seepage 92.

q Geometric specifies any relevant geometrical information that is notinherent in the feature geometry, for example section properties or thickness.See page 117.

q Material defines the behaviour of the element material, including linear,plasticity, creep and damage effects. See page 118.

q Support specifies how the structure is restrained. Applicable to structural,pore water and thermal analyses. See page 145.

q Loading specifies how the structure is loaded. See page 148.

Specific

q Local Coordinate provides a transformation for loads and supports, andan alternative to the global coordinate system. See page 167.

q Composite defines the lay-up properties of composite materials in themodel. See page 171.

q Slideline slidelines control the interaction of disconnected meshes. Seepage 173.

q Constraint Equations provides the ability to constrain the mesh todeform in certain pre-defined ways. See page 179.

Chapter 5 Model Attributes

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q Thermal Surface defines thermal surfaces, which are required formodelling thermal effects. See page 183.

q Retained Freedoms specifies the master nodes used in a Guyanreduction or superelement analysis. See page 187.

q Damping defines the damping properties for use in dynamic analyses. Seepage 188.

q Birth and Death allows elements to be added (birth) and removed(death) throughout an analysis, e.g. in a tunnelling process or a stagedconstruction. See page 189.

q Equivalencing allows nodes which are close to each other but ondifferent features to be merged into one according to defined tolerances. Seepage 193.

q Search Area restricts discrete (point and patch) loads to only apply overcertain areas of the model. See page 195.

Manipulating AttributesAttributes are defined from the Attributes menu. Defined attribute datasets arearranged in the Attribute panel of the Treeview and can be assigned to selectedfeatures by dragging them onto the model, by using the shortcut menu, (RH mousebutton), or by setting them as a default.

1. Attributes are definedusing the Attributes Menu.

2. Defined attributes are displayed inthe Treeview.3. To assign an attribute to features,select the features with the mouse,then drag the attribute onto the model.

4. Manipulate the attributes using theshortcut menu (right mouse button).

Attributes are manipulated using the shortcut menu in the Treeview , with thefollowing commands:

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q Rename Attributes can be given meaningful names, for example, 'Steel' todescribe a material, or 'Plate - Four Divisions' to describe a Line mesh.

q Delete Existing datasets may be deleted, provided they are not assigned tofeatures.

q Edit Attribute dataset may be edited. If the name is changed by editing adataset a new dataset is created and the original dataset is left unchanged.

q Select users Selects the features that have the current attribute assignment.

q Visualise users Visualises the current attribute assignment. See VisualisingAttributes below.

q Assign Assigns the current attribute to any features selected on the model.LUSAS only assigns attributes to features that are valid. Some attributesrequire further information in order to be assigned, in these cases, a dialog isdisplayed. Assigning an attribute to a feature overwrites any previousassignment of that attribute type.

q Deassign Deassigns the current attribute. Choose from all assignments or theselected features only.

Set default AssignmentCertain attributes, (mesh, geometric properties and material properties), can beassigned automatically to all newly created features. For this to happen they mustfirst be set as default, by right-clicking the attribute dataset in the Treeview , thenchoosing Set default from the shortcut menu.

This is useful for models with similar materials or thickness throughout, or wherethe same element is to be applied to all features. Attributes that are set as default aredisplayed with a red box around them in the Treeview.

Visualising AttributesAttribute assignments can be visualised using three methods:

q Attributes layer The Attributes layer is a window layer in the Treeview and is normally added in the initial start-up. The Attributes layer propertiesdefine the styles by which assigned attributes are visualised.

The attributes layer properties may be edited directly, by double-clicking thelayer in the Treeview , or attributes can be visualised individually byselecting an attribute dataset in the Treeview , clicking the right mousebutton to choose Visualise Users from the shortcut menu. This is the easiestway to visualise a single attribute.

q Contour layer (materials/geometry/loading only) Allows the model to becontoured with material, geometric or loading attribute assignments.


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(With nothing selected), click the right mouse button in the graphics area.Choose Contours from the shortcut menu. Double-click the contour layer inthe Treeview to display the properties and select either Loading (model),Geometry (model) or Materials (model).

q Colour by attribute (From the Geometry layer ). Colours the geometryaccording to which attributes are assigned to which features. A key isgenerated to identify the colours.

See also Composites for visualising composites and materials.

Drawing Attribute LabelsLabels are a window layer in the Treeview . To display attribute labels:

1. With nothing selected, click the right mouse button in the graphics area. ChooseLabels from the shortcut menu.

2. Labels are not displayed for attributes by default. Double-click the Labels layer inthe Treeview to display the Properties.

3. Switch on labels for the attribute type. Scroll through the labels list if necessary.

Meshing a Model

What is Meshing?LUSAS models are defined in terms of geometric features which must be sub-dividedinto finite elements for solution. This process is called meshing, and mesh datasetscontain information about:

q Element Type Specifies the element type to be used in a Line, Surface orVolume mesh dataset may be selected either by describing the genericelement type, or naming the specific LUSAS element.

q Element Discretisation Controls the density of the mesh, by specifying theelement length or the number of mesh divisions, spacing values and ratios.

q Mesh type Controls the mesh type e.g. regular or irregular, transition orgrid.

Mesh datasets are defined from the Attributes menu for a particular geometry typei.e. Line, Surface or Volume. They are then assigned to the required features.Various techniques exist for meshing different types of models, these are describedbelow.

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Mesh TypesThere are various mesh patterns which can be achieved using LUSAS. These are:

q Regular meshes only used on regular or analytical Surfaces, andregular Volumes. Regular meshing uses two discretisation techniques, gridand transition. Any element shape may be selected for regular meshing.LUSAS will automatically insert triangular elements in the appropriatepositions of a triangular surface for a regular or a transition mesh.

Regular grid mesh Non-uniform Line spacing

q Transition or Grid if the number of mesh divisions on opposite sides ofa surface are equal a grid will be generated, otherwise transition patterns (oran irregular mesh) will have to be used. Transition meshes do not produceresults which are as good as those from grid meshes or irregular meshes,therefore transition meshes will only be used if specified in the mesh dataset.

q Irregular used for Surfaces and irregular swept Volumes. A Surface meshconsists of triangular elements or a quadrilateral and triangular mixturefollowing no set pattern, and may be used on regular or irregular surfaces. AVolume mesh consists of pentahedral or a hexahedral and pentahedralmixture of elements following no set pattern.

Regular transition mesh Irregular mesh

q Extruded irregular mesh used for Volumes which have been swept from anirregular Surface. See below.

q Interface Meshes Applicable to joint and composite interface elements only.


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Techniques for Meshing a ModelThe simplest way to mesh a model might be to define a dataset for a particularfeature type containing the element type and discretisation, for example a Surfacemesh could be used for a 3D shell model, or a Line mesh for a frame model. Twoother methods exist allowing greater control over the mesh distribution. These are:

q Boundary and Surface discretisation Useful for Surface andVolume meshing.

q Background grid method Useful for creating a graduated elementmesh.

q Meshing Volumes

Default Number of Mesh Divisions If the discretisation has not been specified inthe mesh dataset, or using a Line mesh of element type ‘none’, then the feature willbe sub-divided according to the default number of mesh divisions. This may bespecified in File > Model Properties > Meshing tab.

Tip. Fixing Mesh Problems A group can be created containing all the features thatfailed to mesh.

Boundary discretisationIn the case of Surface or Volume meshing, the boundary divisions may either bespecified in the Surface or Volume mesh dataset, or they can by defined using Linemeshes of element type ‘None’. In many realistic problems, where several Surfaces(or Volumes) exist, using Line meshes may be the most convenient way to define themesh. The spacing can be specified using either element length or number ofdivisions. LUSAS provides several Line meshes of type ‘None’ by default, withdifferent numbers of divisions.

Regular Surface Meshing

Techniques for Meshing a Model

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Irregular Surface Meshing

The applied boundarydiscretisation (top) produces theirregular mesh pattern on theSurface (bottom).

Surface DiscretisationApplicable to Volume meshes. The Volume discretisation is specified in the Surfacemeshes defining the Volume.

Using a Point Mesh and a Background GridA background grid is a collection of triangular or tetrahedral shapes which are usedto specify the element edge length when meshing surfaces automatically. A Line orSurface mesh is used to define the element type and the background grid defines thediscretisation, (applicable to Lines and Surfaces). Can be used to create a gradedelement edge length, but mostly used for an adaptive analysis (remeshing).

A background grid is defined from the Utilities menu. When a background grid hasbeen defined, the background grid layer is added to the current window.

Graded Element Mesh on SurfaceBackground Grid Point Mesh Spacing a Point mesh, defining the element edgelength can be assigned to any Point used to define a Background Grid. The elementedge lengths in the vicinity of these Point mesh assignments can then be controlled.Finer control is available using more Points in the Background Grid definition.

If a graded element edge length is required on a Surface when meshed, then this canbe specified using a Background Grid. The procedure is as follows:


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Define thebackground gridas a series oftriangular ortetrahedral shapescompletelyencompassing theSurfaces to bemeshed. This maybe specifiedexplicitly byspecifying Pointnumbers at eachvertex orgenerated automatically. If the background grid is generated automatically,tetrahedral shapes will always be used. The example on the right shows an irregularSurface bounded by a background grid. The Background Grid is used when theSurface mesh dataset containing the element information is assigned.

The element edge length may then be graded by assigning different spacingparameters to various Points in the Background Grid definition. In addition, theBackground Grid may be used to control the overall Surface mesh discretisation andadditional Line mesh assignments can be used to control the mesh on specific edges.

Define a Point mesh dataset setting the spacing parameter to the required elementedge length. Any mesh distortion required may be entered as stretching parameters.Note the Attributes > Mesh > Define/Edit by Description method must be used todefine Point meshes. Assign the point mesh dataset to the points defining thebackground grid using Attributes > Mesh > Assign to Features. Repeat this processwith different spacing parameters to grade the mesh with as much control asrequired.

Constant MeshSpacingSame spacingparameters (Pointmeshes) are assignedto all Points inbackground grid.

Meshing Volumes

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Varied Mesh SpacingDifferent spacingparameters (Pointmeshes) are assignedto the top Points(spacing=7) and thebottom Points(spacing=1) in thebackground grid.

Meshing VolumesVolumes are meshed using regular and limited transition mesh patterns. Onlyregular volumes, defined by 4, 5 or 6 Surfaces forming tetrahedral, pentahedral orhexahedral bodies, or certain irregular swept Volumes, can be meshed in LUSAS.

Tetrahedral VolumesTetrahedral Elements Pentahedral/Tetrahedral

Elements

Pentahedral VolumesPentahedral Elements Hexahedral/Pentahedral

Elements


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Hexahedral VolumesPentahedral Elements Hexahedral Elements Hexahedral/Pentahedral

Elements

Mesh DiscretisationThe mesh density may be controlled by:

q Boundary Discretisation taking the Volume mesh density from themesh discretisation on the Lines defining the Surfaces of the Volume.

q Surface Discretisation taking the Volume mesh density from thespecified Surface discretisation defining the Volume.

q Volume Discretisation specifying the Volume discretisationexplicitly in the Volume mesh dataset.

Regular, Irregular or Transition GridIn order to generate a regular grid mesh pattern the number of mesh divisions onopposite faces of the volume must match. If they do not match then transitionpatterns will be used. A transition mesh may only be used in one direction throughthe volume. LUSAS will automatically insert pentahedral/tetrahedral elements in theappropriate positions of a transition mesh.

Tip. The Volume mesh may be graduated by using non-uniform spacing in theLine mesh assignments on the boundary Lines.

Meshing Volumes

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Extruded Irregular MeshVolumes defined by sweeping anirregular Surface may now be meshedby extruding the irregular Surfacemesh. The interconnecting linesbetween the irregular end Surfacesmust all be straight Lines, or allminor or major arcs with a commonaxis of rotation. The side Surfacesmust all be defined by 4 Lines andLUSAS meshes them with a regulargrid of quadrilateral faces. Theirregular end Surfaces must not shareany common boundary lines thereforewedge-shaped Volumes cannot bemeshed as extruded irregular Volumes.

Composite Material AssignmentWhen a Volume feature with a composite material assignment is meshed LUSASwill move the nodes so that they lie on the composite layer boundaries. This ensuresan exact number of layers in each element.

MESH ADJUSTEDAUTOMATICALLY TO LAY ONINTERLAMINA BOUNDARIESWHEN > 1 THROUGH DEPTH


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Case Study. Meshing Volumes by Extruding Irregular Surfaces

It is possible to mesh an irregular volume if it has been formed by extruding anirregular surface i.e. by sweeping the irregular surface.

1. Define an irregular Surface with more than 4 sides.2. Define a Volume by sweeping the irregular surface.3. Define a Volume mesh and leave the number of divisions blank; this will ensure

an equal number of divisions on the swept edges.4. Assign the Volume mesh to the Volume.5. Draw the mesh.

Case Study. Connecting Shells and Solids

Solid and shell elements may be connected but the procedure is not asstraightforward as it as first appears. Solids and shells have different sets of nodalfreedoms and the rotational freedom present in the shells can only be passed throughto the solid elements by extending the shell around the side of the solid, thus passingthrough the rotation via combined translational effects. This form of connectionstops rotation relative to a solid which only has translational degrees of freedom.

The following case study outlines the general method of fixing shells to solids.

1. Define the Surfaces and Volumes.2. Assign suitable meshes, for example HX8 elements for the solid and QSI4

elements for the shells.3. Mesh a Surface that forms part of the solid with shell elements. The surface

should share a common edge with the shell Surface that is being fixed to the solidpart of the model. Do not forget to assign material and geometric properties tothe surface attached to the solid. The properties can be relatively weak incomparison to the main shell properties, or indeed to the solid as the shell ispresent purely to pass forces and moments through to the underlying solidelements. It is advisable to make a connection such as this reasonably distantfrom the main area of interest as it may affect the quality of the results locally.

Meshing Surfaces

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Beam Shell ConnectivityExtend the beams alongthe edge of the shellindicated by thick lines.

Beam Solid ConnectivityExtend the beams alongthe edge of the solidelements indicated bythick lines. Torsion isrestrained using out ofplane beams.

Shell Solid ConnectivityExtend the shells over aportion of the solidsindicated by dark shadedarea.

Beams to be attached

Overlappingbeams

Beams to be attached

Overlappingbeams

Shells to

be attached

Overlappingshells

End Releases for Beam ElementsRotational freedoms at the ends of a Line can bemade free to rotate by using an element with momentrelease end conditions.

See the Element Reference Manual for moreinformation on these element types.

When defining a Line mesh dataset, with a validelement selected click on the End Release button.Options are available to free rotations about element local y and z axes (θy and θz).

Releasing beam element end rotational freedoms could be used as an alternative tousing a joint element between beam elements, for example when defining a Pinwhich is free to rotate.

Meshing Surfaces

Mesh DiscretisationRegular meshing is used to generate a set pattern of elements on Surfaces andVolumes. Only surfaces which are regular (defined by 3 or 4 lines) can be meshedusing a regular mesh pattern. The meshing pattern may be chosen as:

y

x

2

1


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q Grid only in order togenerate a regular gridmesh pattern the number ofmesh divisions on oppositesides of the Surface must match. The examples shown here mesh triangularand quadrilateral Surfaces using both triangular and quadrilateral elements.Note that for a triangular Surface the apex is defined opposite the first Line inthe Surface definition and therefore, the second and third Lines in thedefinition must have the same number of divisions assigned.

The Surface mesh may begraded using mesh spacingparameters in null elementLine meshes assigned to theboundary Lines. In the examples shown here mesh spacing has been used tozoom the same number of elements as above into the apex of the triangle andone corner of the rectangle.

The mesh discretisation for regular meshing can be controlled using one of twomethods. These are:

q Surface Mesh Dataset specifying the surface discretisation explicitlyin the Surface mesh dataset. This is useful only for small problems with fewSurfaces and is not recommended.

Irregular Surface MeshingIrregular meshing is used to generate elements on any arbitrary surface. The meshdensity can be controlled in a number of ways. These are:

q Element Length specifying the required approximate element edgelength. Two Surface mesh parameters are used in irregular meshing only. Anoptional default mesh size, will be applied to a whole Surface if a Surface hasno background grid assignment. A mesh quality parameter determines thegreatest deviation allowed in element size from either the size interpolatedfrom the background grid or from the default mesh size. This method has atendency to produce a more uniform mesh as the element size within aSurface is controlled more closely than when just the boundary sizes arespecified.

Element Selection

About LUSAS ElementsThe LUSAS Element Library contains over 100 element types. The elements areclassified into groups according to their function. The LUSAS element groups are

Line Element Selection

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listed below. Refer to the Element Reference Manual for further details. For fulldetails of the element formulations refer to the LUSAS Theory Manual.

q Bar Elementsq Beam Elementsq 2D Continuum Elementsq 3D Continuum Elementsq Plate Elements

q Shell Elementsq Membrane Elementsq Joint Elementsq Thermal Elements

Line Element SelectionThe following table lists the elements available for Line meshing by type and byname. The first column matches the option list in the Line mesh dialog box.

Element Typesq ’None’ Element - One of the generic element types is ‘none’. This type

generates no structural elements on the line, the mesh dataset will be usedpurely to control the line discretisation.

q Bar - Bar elements transfer axial force but have no bending or rotationalstiffness.

q Thin Beam - Thin beam elements behave as a bar, but will also supportmoment transfer. This formulation of beam neglects shear deformations.

q Thick Beam - Thick beam elements support shear effects.

q Thick Beam (Nonlinear)q Engineering Grillage - Engineering grillage beam elements in 2D only, with

constant shear force along the length, constant torsion and linear bendingmoment variation. Shear deformations are included.

q Ribbed Plate Beam - Ribbed plate beam elements are straight, eccentricbeam elements with shear effects.

q Cross-section Beam - Cross-section beams are curved, thin beam elementswith user-specified quadrilateral cross-section. Shear deformations areneglected.

q Semiloof Beam - Semiloof thin beam elements are for use with semiloof shellelements.

q Axisymmetric Membrane - The axisymmetric membrane element is theaxisymmetric equivalent of a shell element. Modelled as a line over a unitradian segment.

q Joint - Joint elements are used to connect two or more nodes by springs, withtranslational and rotational stiffness. They may have an associated mass anddamping.


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q Thermal Bar - Thermal bar elements are isoparametric bars for use in a fieldanalysis.

q Axisymmetric Thermal Membrane - The axisymmetric thermal membraneelement has a formulation that applies over a unit radian segment.

q Thermal Link - The thermal link element is a straight conductive,convective or radiative link element for field analyses.

Generic Element Types2D

2 noded2D

3 noded3D

2 noded3D

3 noded

’None’ ElementBarThin BeamThick BeamThick Beam (Nonlinear)Engineering GrillageRibbed Plate BeamCross-section BeamSemiloof BeamAxisymmetric MembraneJoint (no rotational stiffness)Joint (for beams)Joint (for grillages)Joint (for ribbed plates)Joint (for axisymmetric solids)Joint (for axisymmetric shells)Thermal BarAxisymmetric Thermal MembraneThermal Link

-BAR2-BEAM-GRILBRP2--BXM2JNT3JPH3JF3JRP3JAX3JXS3BFD2BFX2LFD2

-BAR3BM3----BMX3-BXM3------BFD3BFX3-

-BRS2-BMS3BTS3-----JNT4JSH4----BFD2BFX2LFS2

-BRS3BS4----BSX4BSL4-------BFD3BFX3-

Notes

q Elements in italic text are only available with the LUSAS +Plus option.q Quadratic elements are curved with a mid-side node.q Rotational freedoms at the ends of a Line can be made free to rotate by using

an element with moment release end conditions.q No check is made at this stage as to whether the element type is valid for the

analysis being performed, however the LUSAS Solver will stop the analysis ifthe element is unsuitable.

q This list is a guide as to which elements to use. Not all elements are listedhere. See the Element Library for full details.

Surface Element Selection

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Surface Element SelectionThe following table lists the elements available for surface meshing by type and byname. The first column matches the option list in the Surface mesh dialog box.

Generic Element TypesTriangle3 noded

Quadrilateral4 noded

Triangle6 noded

Quadrilateral8 noded

Plane StressPlane StrainAxisymmetric SolidThin PlateThick PlateRibbed PlateThin ShellThick ShellMembraneFourierPlane Field (Thermal)Axisymmetric Solid FieldExplicit Dynamic - Plane StressExplicit Dynamic - Plane StrainExplicit Dynamic -Axisymmetric

TPM3TPN3TAX3TF3TTF6TRP3TS3TTS3TSM3TAX3FTFD3TXF3TPM3ETPN3ETAX3E

QPM4MQPN4MQAX4MQF4QSC4RPI4QSI4QTS4SMI4QAX4FQFD4QXF4QPM4EQPN4EQAX4E

TPM6TPN6TAX6-TTF6-TSL6TTS6-TAX6FTFD6TXF3---

QPM8QPN8QAX8-QTF8-QSL8QTS8-QAX8FQFD8QXF8---

Notes

q Elements in italic text are only available with the LUSAS +Plus option.q No check is made at this stage as to whether the element type is valid for the


q This list is a guide as to which elements to use. Not all elements are listedhere. See the Element Library for full details.

Volume Element SelectionThe following table lists the elements available for volume meshing by type and byname. The first column matches the option list in the Line mesh dialog box.

Tetrahedral Pentahedral


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Generic Element Types 4 noded 10 noded 6 noded 12 noded 15 noded

StressThermalExplicit DynamicComposite

TH4TF4TH4E-

TH10TF10--

PN6PF6PN6E-

-PNC12C

PN15PF15

HexahedralGeneric Element Types 8 noded 16 noded 20 noded

StressThermalExplicit DynamicComposite

HX8MHF8HX8E-

-HX16C

HX20HF20

Notesq Elements in italic text are only available with the LUSAS +Plus option.q No check is made at this stage as to whether the element type is valid for the


Joint/Interface Element MeshesJoint elements are used to connect two or more nodes by springs, with translationaland rotational stiffness. They may have initial gaps, contact properties, an associatedmass and damping, and other nonlinear behaviour.

Interface elements are used for modelling interface delamination in compositematerials.

Joint and Interface elements may be inserted between corresponding nodes andfeatures by using interface meshes.

Using Joint MeshesJoint elements are defined in either a Line or Surface mesh dataset. In a 2D analysisthe Line joint mesh is assigned to Line features and in a 3D analysis the Surfacejoint mesh is assigned to Surface features. There are two methods of assigning jointmesh datasets:

q Single Joint (Lines only) Joint meshes are assigned directly to theLine(s) that join two structures. This method is more suitable for defining oneor two joints since a Line feature must be defined for every joint required.

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q Joint Mesh Interface (Lines and Surfaces) Uses a master andslave connection to tie two Lines (2D) or two Surfaces (3D) together with ajoint mesh.

Modelling a single Joint ElementTo model a single joint element between two Points.

1. Create a Line joining the two Points.2. Define a Line mesh dataset with the chosen joint element.3. Assign the Line mesh to the Line between the two Points.

Modelling a Joint Mesh InterfaceTo define a joint mesh interface between two Lines or two Surfaces:

1. Add the slave feature to selection memory,2. Assign the joint mesh to the master feature.As the same mesh dataset is assigned to both master and slave features, a meshpattern is created between the two, with the number of divisions in the meshdetermining the divisions along the interface edge.

Joint elements are automatically created joining all nodes on the master and slavefeatures. Joint elements cannot be created between two Points using the interfacemesh technique.

Joint Local Axis DirectionThe joint local axis direction is defined when the Line mesh is assigned. Threeoptions are available:

q Global axis (default).q A Point in selection memory.q Local coordinate dataset, if at least one has been defined.

Example. Interface Mesh (2D)In this example a Line jointmesh with 6 divisions isassigned to Line 1 with Line2 as the slave. Joints arecreated automatically to tiethe Lines together with aninterface joint mesh.

Note. The LUSAS Unmerge facility allows coincident features to be created froma single feature and also allows a feature to be set as Unmergable, so it will not be

L2

S1

S2

L1


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accidentally merged back with another coincident feature. See Merging andUnmerging for more details.

Example. Cylindrical Interface Mesh (3D)In this example, aSurface joint meshis assigned toSurfaces betweentwo concentriccylinders.Cylindrical axesare defined for thejoint propertiesusing a localcoordinate set. Joint local x axes will then coincide with the cylinder radial direction.

Joint Material and Geometric PropertiesJoint properties are assigned to the master feature.

q Joint Geometric Properties For joints with rotational degrees of freedom aneccentricity must be specified using the Attributes > Geometric menu.

q Joint Material Properties Joint meshes also require joint properties to beassigned to them, defined from the Attributes > Material menu.

Composite Delamination using Interface ElementsInterface elements may be used at planes of potential delamination to modelinterlaminar failure, and crack initiation and propagation.

If the strength exceeds the strength threshold value in the opening or shearingdirections the material properties of the interface element are reduced linearly asdefined by the material parameters and complete failure is assumed to have occurredwhen the fracture energy is exceeded. No initial crack is inserted so the interfaceelements can be placed in the model at potential delamination areas where they liedormant until failure occurs.

Fracture ModesThree fracture modes exist: open, shear, and orthogonal shear for 3D models. Thenumber of fracture modes corresponds to dimension of the model. (INT6 = 2, INT16= 3). The diagram below illustrates the three modes.

P1 P2

P3

qr

Cylindrical LocalCordinate Set (P1,P2,P3)used on Assignment toalign Joint Properties

Master

Slave

Joint

Composite Delamination using Interface Elements

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Mode 1 - Open Mode 2 - Shear Mode 3 - Shear (orthogonal tomode 2)

Interface ElementsThe interface elements, INT6 and INT16, are used to model composite delaminationin an incremental nonlinear analysis. These elements have no geometric propertiesand are assumed to have no thickness.

Interface elements are selected from within Line or Surface mesh datasets using theAttribute, Mesh menu. The mesh datasets are then assigned to the requiredgeometry.

Interface Material PropertiesThe interface material properties are defined from the Attribute, Material,Specialised menu then assigned to the same geometry.

Strength

Initial failure strength

Area = Fracture energy (G)

Softening

Elastic

Failure

Opening distanceRelativedisplacement


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Material Parametersq Fracture energy Measured values for each fracture mode depending on the

material being used, i.e. carbon fibre, glass fibre.

q Initiation Stress The tension threshold /interface strength is the stress atwhich delamination is initiated. This should be a good estimate of the actualdelamination tensile strength but, for many problems the precise value haslittle effect on the computed response. If convergence difficulties arise it maybe necessary to reduce the threshold values to obtain a solution.

q Relative displacement The maximum relative displacement is used to definethe stiffness of the interface before failure. Provided it is sufficiently small tosimulate an initially very stiff interface it will have little effect.

Coupling Modelq Coupled/mixed interface damage Recommended method.

q Uncoupled /reversible Unloading is reversible along the loading path.

q Uncoupled /origin Unloading is directly towards the origin ignoring theloading path.

Notes on Delamination Analysesq It is recommended that the arc length procedure is adopted with the option to

select the root with the lowest residual norm, when defining the transientcontrol [option 261].

q It is recommended that fine integration [option 18] is selected for the parentelements from the Model Properties, Solution tab.

q The nonlinear convergence criteria should be selected to converge on theresidual norm.

q Continue Solution if more than one Negative Pivot Occurs [option 62] shouldbe selected (from the Model properties, Solution tab) to continue if more thanone negative pivot is encountered and option 252 should be used to suppresspivot warning messages from the solution process.

q The non symmetric solver is selected automatically when mixed modedelamination is specified.

q Although the solution is largely independent of the mesh discretisation, toavoid convergence difficulties it is recommended that a least 2 elements areplaced in the process zone.

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Adaptive Analysis (Remeshing)Adaptive analysis allows a LUSAS model to be remeshed based on the solution froma previous analysis. The remeshing procedure uses the background grid meshingapproach and bases the mesh spacing on nodal error values.

The procedure involves creating a background grid from the current mesh using aspecified results entity as a measure of the error at each node. The error is calculatedfrom the difference in the nodal values common to a node from the average value atthe same node. The discontinuity in the chosen results parameter at the nodes,quantified by the error, is then used to define the required mesh spacing at the Pointsdefining the background grid.

The existing mesh is adjusted by increasing or decreasing the mesh spacing at aPoint. If the discontinuity error at a node is less than a user specified value then theelements in the region of that node will become larger, conversely at nodes witherrors above the acceptable limit the elements will become smaller.

Performing an Adaptive AnalysisThe adaptive process is not automatic and should be controlled using a parametriccommand file. The model must be tabulated and the LUSAS analysis run to obtainthe next set of results and hence the next model mesh. At this stage adaptivity islimited to a Surface mesh implementation only.

If a valid results type is active, a command dialog is opened allowing the resultscolumn to be selected using an options list.

Having created a model and solved it, the results must be read into LUSAS on top ofthe model. The adaptive process is controlled using three steps, which must beexecuted in the following order:

1. From Surface Mesh generates a background grid from the mesh on theSurfaces specified. If specified Surfaces lie in a common plane a background gridof triangles is created, otherwise tetrahedral features enclosing the Surfaces arecreated. A new Point feature for the background grid is created at each cornernode of elements meshed in the specified Surfaces.

2. Mesh Spacing from Results specifies the required mesh spacing bygenerating Point mesh datasets that define the mesh spacing for the backgroundgrid created from the Surface mesh in 1 above. Mesh spacing parameters areestablished by examining the discontinuity of the chosen results parameter(including calculator column results) between elements sharing a common node.This value is termed the Discontinuity Error. Point mesh datasets are thenautomatically assigned to the correct Point features defining the background grid.This command causes adaptive error results to be created in a results column. See


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the section titled Discontinuity Error later for more details. The followingcommand options are available:

• Background Grid Number specifies the number of thebackground grid created using this command.

• Results Column to Process specifies the results column to beused as an error estimate for calculating new mesh spacing parameters.Shear and principal stresses have been excluded from the adaptivityresults column selection as these stress types cannot be used to calculate asensible mean nodal value.

• Element Size Reducing Scaling Factor specifies a scalingfactor to control the amount by which an element size is reduced duringthe adaptive process. See the section titled Discontinuity Error below formore details.

• Element Size Increasing Scaling Factor specifies a scalingfactor to control the amount by which an element size is increased duringthe adaptive process. See the section titled Discontinuity Error below formore details.

3. Assign to Defining Features assigns the new background grid or gridsspecified to the Surfaces from which each was created. Any command thatredraws the mesh will cause an updated mesh to be created using the newspacing parameters.

As the adaptive process proceeds and the number of remeshing cycles increases,redundant Point features, and background grid and Point mesh datasets will start tobe accumulated. This data may be deleted with the existing commands using theALL entry for the parameter list, allowing LUSAS to check for redundancy.

Discontinuity ErrorThe discontinuity error at a node is given by:

( MaxNode - Mean ) / Mean * 100%

Where MaxNode represents the maximum result from any element defined by a node,and Mean represents the mean result from all the elements contributing to that node.The discontinuity error may be contoured using PostView > Nodal Results > PlotContours and printed using PostView > Nodal Results > Print Adaptive in asimilar manner to existing results columns. The results column header is Eadp.

Element re-sizing is controlled using two relationships. For values of discontinuityerror greater than the specified acceptable limit:

SizeNew = SizeOld / [ 1 + (DErr * ScaleRed) ]

For values of discontinuity error less than the specified acceptable limit:


113

SizeNew = SizeOld [ 1 + ScaleInc * (AErr - DErr) ]

Where DErr is the calculated discontinuity error, AErr is the acceptable error set inthe Utilities > Background Grid > Options dialog (default=1%), ScaleRed is theelement size reducing scaling factor and ScaleInc is the element size increasingscaling factor.

Excluding FeaturesUsing the menu commands Geometry > Feature type > Exclude/Include featuresmay be excluded from the adaptive process so that the mesh on those featuresremains fixed. Features may be excluded from the discontinuity error calculations tostop the elements gathering around point loads where there can be artificially highstress concentrations.

Nodes excluded from the adaptive process can be printed to the text window usingMeshView > Show Nodes Excluded from Adaptivity.

Element Size ControlFrom the Meshing tab (Adaptivity button) of the model properties global elementparameters can be set to stop elements becoming too large or too small or to stop theelements changing size by a large percentage between solutions. Options are asfollows:

q Minimum and Maximum Element Size sets the minimum andmaximum allowable element size in model units (initially unset). See notebelow.

q Maximum Element % Change sets the maximum allowablepercentage change in element size (default=50%).

q Error % Cut-off sets the acceptable limit of percentage discontinuityerror, below which the element size is not changed (default=1%). Theadaptivity error results are stored in the Eadp column.

q Minimum Result sets the percentage of the absolute maximum resultsvalue below which there is no change in mesh size (default = 0%). This valueis useful to remove large areas of fairly constant stress from the solution,where the stress level is well below the peak values in the areas of interest.

The maximum and minimum element sizes are initially unset. LUSAS sets theparameters when the model is scaled, or when the adaptivity convergence parametersare calculated. In both cases the overall model dimensions are used to calculatemaximum and minimum element sizes, but only if these parameters are unset. Onceset these values will remain unchanged. LUSAS sets the parameters using thefollowing formulae:


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Elem(max) = DMINSZ * Current model size

Elem(min) = DMAXSZ * Current model size

Where Elem(max) and Elem(min) represent maximum and minimum elementsizes respectively, and DMINSZ and DMAXSZ are system variables with default sizes0.010 and 0.50 respectively.

Convergence ControlA check of the current level of convergence of the adaptive process can be madeusing the command line command show adaptive change. These parameters aredesigned to provide a measure of the converged state of the adaptive process and areideal for using adaptive meshing in a parametric command file. Having retrieved theconvergence values, the parametric file can stop or continue with anotherremesh/solution cycle. Valid convergence parameters are as follows:

q Maximum Change in Element Size (chgesz) Maximumpercentage change in mesh spacing. This value is initialised to 100%.

q Change in Strain Energy (chgstr) Percentage change in strainenergy between solutions of the problem. This value is initialised to 100%.

Within a parametric these real number parameters can be accessed via their internalLUSAS names using the function m$mysvbs. The function usage is shown in theexample below:

real csiz, cnrg

...

csiz = m$mysvbs(chgesz)

cnrg = m$mysvbs(chgstr)

printf("Change in element size: %s", csiz)

printf("Change in strain energy: %s", cnrg)

if ( csiz < 2.0 && cnrg < 5.0 ) then

{

goto exit

}

...

exit:

Files. The adaptive process lends itself to execution via the command file facility.An example set of command files that can be used to analyse a simple plate withhole have been included with the release kit. Command files csadapt1.cmd,


115

csadapt2.cmd and csadapt3.cmd are included in the tutorial directory. They shouldbe used with reference to the following case study.

Case Study. Plate with a Hole Adaptive Mesh Improvement

This case study makes reference to the command files csadapt1.cmd, csadapt2.cmdand csadapt3.cmd.

1. Using Files > Command File > Open, run the command file csadapt1.cmd.This will define a single irregular Surface model and tabulate a LUSAS data fileplate_1.dat and save a model database plate_1.mdl.

2. Run LUSAS using the generated data file plate_1.dat. A results database is thencreated.

3. Run the command file csadapt2.cmd. This file uses the model file and resultsfile from the analysis to regenerate an improved mesh based on the errorscalculated in the x direction direct stress results. After remeshing, the model issaved as plate_2.mdl and a second data file plate_2.dat is tabulated.

4. After running the Solver a second time to create results file plate_2.mys, run thecommand file csadapt3.cmd. This creates a further level of mesh refinement.The meshes for each level of adaptive meshing are shown in the accompanyingdiagrams following this case study.


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Plate 1Original mesh.

Plate 21st mesh iteration.

Plate 32nd mesh iteration.

MeshOriginalmesh refinedin 2 stages.

Contour Plotshowing xdirectionstress used foradaptivity.

Error PlotAs mesh isrefined, errorsreduce andlocalise.

Tip. The post-processing command files in the case study above can be merged byincluding parametric variables to refer to the model and results files read in and thedata file and model names saved. In this way a single post-processing command filecould be used instead.

Geometric Properties

117

Geometric Properties

GeneralGeometric properties are used to describe geometric attributes which have not beendefined by the feature geometry. For example below. The properties required areelement dependent and are defined for an element family. The dataset is thenassigned to the required Line, Surface or Joint feature. If a geometric property of atype incompatible with the mesh is assigned to a feature a warning will be issuedwhen the model is tabulated.

Bar/Link Grillage Thin/ThickBeam Elements Structuresmodelled using bar or beam elementsrequire section properties to bedefined, for example, thickness, sheararea and eccentricity.

Plate/Membrane/ShellElements Structuresmodelled using shell elementsrequire their thickness to bedefined, and eccentricbehaviour can also be specifiedfor certain element types.

Using Geometric PropertiesGeometric properties are defined as attribute datasets from the Attribute Menu. Ageometric property dataset may be nominated as the default assignment,which is then automatically assigned to all Lines and Surfaces subsequently created.

Notes on Use

q Geometric properties are not required for plane strain, axisymmetric or solidelements.

q The geometric properties are specified in generic form for all elements andonly the properties required for the intended element need be specified. For

x

y

z

Nodal Line

Beam Local(Element) Axes

Eccentricity (e)

BeamCentre-Line

Thickness (T)

Nodal Line

Nodal Line

Thickness (T)

Eccentricity (e)

Local Surface(Element) Axes

Plate Centre-Line


118

example eccentricity is ignored by semi-loof shells which do not use it and soit may be entered as zero in the property dialog.

q Geometric properties can be varied over a given feature by using a Variationdataset. See Variations for more details.

q For more details on the properties required for specific elements refer to theLUSAS Element Library.

Material PropertiesEvery part of an FE model must be assigned a material property dataset. LUSASmaterial datasets are defined from the Attributes > Materials menu. Note that notall elements accept all material property types. Refer to the LUSAS Element Libraryfor full details of valid element/material combinations.

Linear and Nonlinear Material Propertiesq Isotropic/Orthotropic Defines linear elastic or nonlinear material

properties with options for plasticity, hardening, creep, damage, viscosity andtwo-phase materials.

q Anisotropic Different material properties are specified in arbitrary (non-orthotropic) directions by direct specification of the modulus matrix.

q Rigidities Allows direct specification of the material rigidity matrix.

Specialised Material Propertiesq Thermal Applicable to thermal elements only. Whenever thermal elements

have been used in a model thermal material properties should be defined andassigned to the relevant parts of the model. Thermal material propertiesinclude thermal conductivity, specific heat, enthalpy. Sub-types are Isotropicand Orthotropic.

q Joint Linear and nonlinear joint material models for contact and impactanalyses using joint elements.

q Interface Material models for use with the composite delamination interfaceelements. These elements enable composite delaminations to be modelledusing an incremental nonlinear analysis.

q Rubber Defines materials with hyper-elastic or rubber-like mechanicalbehaviour.

q Crushing A volumetric crushing model such as would be used for crushablefoam-filled composite structures.

Notes

q Material property datasets can be formed into a composite lay-up using thecomposite attribute facility.

Isotropic/Orthotropic Material Definition

119

q Once assigned to geometry material directions can be visualised using theAttributes layer .

q Rubber, crushing, and plastic material datasets cannot be combined.

Isotropic/Orthotropic Material DefinitionIsotropic and orthotropic material datasets can be used to specify the followingmaterial properties:

q Elasticity Linear elastic material properties including Young’s modulus,Poisson’s ratio, mass density, (orthotropic angle). Optional thermal anddynamic properties.

Note that not all elements accept all the orthotropic models. Refer to theLUSAS Element Library for full details of valid element/materialcombinations. Orthotropic models are Plane stress, Plane strain, Thick,Sheet, Axisymmetric, Solid.

q Plasticity Used to model ductile yielding of nonlinear elasto-plastic materialssuch as metals, concrete, soils/rocks/sand.

q Hardening Used to model a nonlinear hardening curve data. Hardening isdefined as part of the plastic properties. Isotropic, Kinematic and Granularsub-types are available. Isotropic hardening can be input in three ways.

q Creep Used to model the inelastic behaviour that occurs when therelationship between stress and strain is time dependent.

q Damage Used to model the initiation and growth of cavities and micro-cracks.

q Viscosity Used to model viscoelastic behaviour. Coupling of the viscoelasticwith nonlinear elasto-plastic materials enables hysteresis effects to bemodelled.

q Two-phase Required when performing an analysis in which two-phaseelements are used to define the drained and undrained state for soil.

Plastic Material Models - IsotropicThe following are Isotropic models available from the Attributes > Material >Isotropic dialog, after clicking the Plastic check box.

q Stress Resultant (Model 29) May be used for certain beams and shells. Themodel is formulated directly with the beam or shell stress resultants plusgeometric properties, therefore it is computationally cheaper.

q Tresca (Model 61) Represents ductile behaviour of materials which exhibitlittle volumetric strain (for example, metals). Incorporates isotropichardening.


120

q Optimised implicit von Mises (Model 75) Represents ductile behaviour ofmaterials which exhibit little volumetric strain (for example, metals).Especially for explicit dynamics.

q Stress Potential (von Mises model) Nonlinear material properties applicableto a general multi-axial stress state requiring the specification of yield stressesin each direction of the stress space. Incorporates hardening, yield stress andHeat fraction.

q Mohr-Coulomb (Model 63) Represents ductile behaviour of materials whichexhibit volumetric plastic strain (for example, granular materials such asconcrete, rock and soils). Incorporates isotropic hardening.

q Drucker-Prager (Model 64) Represents ductile behaviour of materialswhich exhibit volumetric plastic strain (for example, granular materials suchas concrete, rock and soils). Incorporates isotropic hardening.

q Concrete Cracking Represents the nonlinear material effects associatedwith the three dimensional cracking of concrete.

Plastic Material Models - OrthotropicThe Stress Potential Hill and Hoffman models are available from the Attributes >Material > Orthotropic dialog, click the Plastic check box.

The stress potential model defines nonlinear material properties applicable to ageneral multi-axial stress state requiring the specification of yield stresses in eachdirection of the stress space. Incorporates hardening, yield stress and Heat fraction.Hoffmann is a pressure dependent material model allowing for different propertiesin tension and compression.

Stress Resultant Material ModelThe model is formulated directly with the beam or shell stress resultants plusgeometric properties, therefore it is computationally cheaper. Consult the LUSASElement Library the check which elements are valid for this material model.

Material Parametersq Yield stress The level of stress at which a material is said to start

unrecoverable or plastic behaviour.

q Section shape Match the section type to the element being used.

Notes1. The yield criteria, when used with beam elements, includes the effects of

nonlinear torsion. Note that the effect of torsion is to uniformly shrink the yieldsurface.

2. The stress-strain curve is elastic/perfectly plastic.


121

3. The fully plastic torsional moment is constant.4. Transverse shear distortions are neglected.5. Plastification is an abrupt process with the whole cross-section transformed from

an elastic to fully plastic stress state.6. Updated Lagrangian (Option 54) and Eulerian (Option 167) geometric

nonlinearities are not applicable with this model. The model, however, doessupport the total strain approach given by Total Lagrangian and Co-rotationalgeometric nonlinearities, Option 87 and Option 229, respectively. Geometricnonlinearity options are set from the Model properties.

Tresca Material Model (Model 61)Material Parameters

Uniaxial YieldStress

L1

σ yo

αα =tan -1C1

Equivalent PlasticStrain, εp

Hardening Curve Definition for the Tresca Yield Model

Yield stress The level of stress at which a material is said to start unrecoverable orplastic behaviour.

Heat fraction The fraction of plastic work that is converted into heat energy. Onlyapplicable to temperature dependent materials and coupled analyses where the heatproduced due to the rate of generation of plastic work is of interest. The value shouldbe between 0 and 1.


122

Optimised implicit von Mises Material ModelRepresents ductile behaviour of materials which exhibit little volumetric strain (forexample, metals). Especially for explicit dynamics.

Material Parametersq Yield stress The level of stress at which a material is said to start


q Heat fraction The fraction of plastic work that is converted into heat energy.Only applicable to temperature dependent materials and coupled analyseswhere the heat produced due to the rate of generation of plastic work is ofinterest. The value should be between 0 and 1.

Hardening (von Mises)

q Kinematic hardening Plasticity hardening formulation associated withtranslation, as opposed to expansion, of the yield surface.

In the optimised implicit model the direction of plastic flow is evaluated from thestress return path. The implicit method allows the proper definition of a tangentstiffness matrix which maintains the quadratic convergence of the Newton-Raphsoniteration scheme otherwise lost with the explicit method. This allows larger loadsteps to be taken with faster convergence. For most applications, the implicit methodshould be preferred to the explicit method.

The model incorporates linear isotropic and kinematic hardening.

Uniaxial YieldStress

L1

σ yo

α1

α = tan-1C


Nonlinear Hardening Curve for the von Mises Yield Model (Model 75)


123

Stress PotentialStress PotentialThe use of nonlinear material properties applicable to a general multi-axial stressstate requires the specification of yield stresses in each direction of the stress spacewhen defining the yield surface (see the LUSAS Theory Manual).

Notes

q The yield surface must be defined in full, irrespective of the type of analysisundertaken. This means that none of the stresses defining the yield surfacecan be set to zero. For example, in a plane stress analysis, the out of planedirect stress σσzz, must be given a value which physically represents the modelto be analysed.

q The stresses defining the yield surface in both tension and compression forthe Hoffman potential must be positive.

Material Propertiesq Yield stress The level of stress at which a material is said to start



Hardening PropertiesThere are three methods for defining nonlinear hardening. Hardening curves can bedefined in terms of either the hardening gradient, the plastic strain or the total strainas follows:

q Hardening gradient vs. Effective plastic strain Requiresspecification of gradient and limiting strain values for successive straight lineapproximations to the stress vs. effective plastic strain curve.

In this case hardening gradient data will be input as (C1, ep1), (C2, ep2) foreach straight line segment. LUSAS extrapolates the curve past the last specifiedpoint.


124

Sy

ep1 ep2

S1

S2

Stress

Plastic Strain

GradientC2 = s2-s1/ep2-ep1

GradientC1 = s1-sy/ep1

q Uniaxial yield stress vs. Effective plastic strain Requiresinput of coordinate points at the ends of straight line approximations to theuniaxial yield stress vs. effective plastic strain curve.

For the curve shown here the plastic properties will contain the yield stress (sy)and the hardening data will be input as (s1, ep1), (s2, ep2), etc. LUSASextrapolates the curve past the last specified point.

ee2

Sy

ep2 ep3

S1

S2

Stress

ep3

ee1

ep2

Elastic/PlasticStrain Boundary

CurveExtrapolation

Young'sModulus

EffectivePlastic Strain

ep1

q Uniaxial yield stress vs. Total Strain Requires input ofcoordinate points at the ends of straight line approximations to the stressstrain curve.

Linear properties specify the slope of the stress strain curve up to yield in termsof a Young's modulus. Plastic properties specify the yield stress (sy) and thehardening data is input as a series of coordinates, for example (s1, e1), (s2, e2),etc. LUSAS extrapolates the curve past the last specified point.


125

Sy

e2 e3

S1

S2

Stress

TotalStrain

CurveExtrapolation

Young'sModulus

Mohr-Coulomb Material ModelThe Mohr-Coulomb elasto-plastic model may be used to represent the ductilebehaviour of materials which exhibit volumetric plastic strain (for example, granularmaterials such as concrete, rock and soils). The model incorporates isotropichardening.

Material Propertiesq Initial Cohesion A material property of granular materials, such as soils or

rocks, describing the degree of granular bond and a measure of the shearstrength.

q Initial Friction angle A material property of granular materials, such ascohesive soils and rocks.


Notes

q The heat fraction coefficient represents the fraction of plastic work which isconverted to heat and takes a value between 0 and 1. For compatibility withpre LUSAS 12 data files specify Option -235.

q Setting the initial cohesion (C) to zero is not recommended as this couldcause numerical instability under certain loading conditions.


126

Cohesion

L1

Coα1=tan-1C11

α1


Cohesion Definition for the Mohr-Coulomb and Drucker-Prager Yield Models(Models 63 and 64)

L1

φo

α2=tan-1C21

α 2


Friction Angle Definition for the Mohr-Coulomb and Drucker-Prager Yield Models(Models 63 and 64)

Drucker-Prager Material ModelThe Drucker-Prager elasto-plastic model (see figures on page) may be used torepresent the ductile behaviour of materials which exhibit volumetric plastic strain

Creep Material Properties

127

(for example, granular materials such as concrete, rock and soils). The modelincorporates isotropic hardening.

Material Propertiesq Initial Cohesion A material property of granular materials, such as soils or

rocks, describing the degree of granular bond and a measure of the shearstrength. Setting the initial cohesion to zero is not recommended as this couldcause numerical instability under certain loading conditions.

q Initial Friction angle A material property of granular materials, such ascohesive soils and rocks.


Concrete Cracking ModelThe multi-crack model assumes that, at any one point in the material, there are adefined number of permissible cracking directions. The model assumes that thematerial can soften and eventually loose strength in positive loading.

q The softening follows an exponential curve defined by the tensile strength andthe strain at end of softening curve. To ensure the softening function is avalid shape the following restriction should be used:

strain at end of softening curve > 1.5 * tensile strength Young’s modulus

q Fracture energy per unit area (to fully open the crack) should be specified(instead of strain at end of softening curve) when defining a localised fracturerather than a distributed fracture.

Note. Either the Fracture energy per unit area or the Strain at end of softeningcurve should be defined. If both are specified then the Fracture energy per unitarea is ignored.

Creep Material PropertiesCreep is the inelastic behaviour that occurs when the relationship between stress andstrain is time dependent. The creep response is usually a function of the stress, strain,time and temperature history. Unlike time independent plasticity where a limited set ofyield criteria may be applied to many materials, the creep response differs greatly fordifferent materials.


128

Creep PropertiesThere are three uniaxial creep laws available in LUSAS and a time hardening form isavailable for all laws. The power creep law is also available in a strain hardeningform. Fully 3D creep strains are computed using the differential of the von Mises orHill stress potential. A user-definable creep interface is also available which allows aprogrammable uniaxial creep law. The required creep properties for each law are:

q Power law (time dependent / strain hardening) εcf ff q t= 12 3

q Exponential law εcf q f tq f qf e f te

f= −L

NMOQP +− −

1 52 3

461

q Eight parameter law εcf f f f f Tf q t f t f t e= + + −

1 4 62 3 5 7 8 /

q User-supplied & , ,εc f q t T= b g

where: εc = uniaxial creep strain &εc = rate of uniaxial equivalent creep strain q = (von Mises or Hill) equivalent deviatoric stress t = current time T = temperature (Kelvin)

Stress PotentialThe definition of creep properties requires that the shape of the yield surface isdefined. The stresses defining the yield surface are specified using the Stress Potentialmaterial model.

If a Stress Potential model is used in the Plastic definition then this will override theCreep stress potential and will apply to both the plastic properties and the creepproperties. The Creep stress potential is only required when defining linear materials.If a stress potential type is not specified then von Mises is set as default.

None of the stresses defining the stress potential may be set to zero. For example, in aplane stress analysis, the out of plane direct stress must be given a value whichphysically represents the model to be analysed.

User Supplied Creep PropertiesThe User creep property facility allows user supplied creep law routines to be usedfrom within LUSAS. This facility provides completely general access to the LUSASproperty data input and provides controlled access to the pre- and post-solutionconstitutive processing and nonlinear state variable output.

Creep Material Properties

129

Source code access is available to interface routines and object library access isavailable to the remainder of the LUSAS code to enable this facility to be utilised.Contact FEA for full details of this facility. Since user specification of a creep lawinvolves the external development of source FORTRAN code, as well as access toLUSAS code, this facility is aimed at the advanced LUSAS user.

Notes

q The user-supplied routine must return the increment in creep strain. Further, ifimplicit integration is to be used then the variation of the creep strainincrement with respect to the equivalent stress and also with respect to thecreep strain increment, must also be defined.

q If the function involves time dependent state variables they must be integratedin the user-supplied routine.

q If both plasticity and creep are defined for a material, the creep strains will beprocessed during the plastic strain update. Stresses in the user routine maytherefore exceed the yield stress.

q User-supplied creep laws may be used as part of a composite element materialassembly.

Creep Data in Rate FormCreep data is sometimes provided for the creep law in rate form. The time componentof the law must be integrated so that the law takes a total form before data input. Forexample the rate form of the Power law

εcn mAq t=

integrates to

εcn mA m q t= + +/ 1 1a f

The properties specified as input data then become

f A m1 1= +/ a f f n2 =

f m3 1= +

where A, n and m are temperature dependent constants.


130

Damage Material PropertiesDamage is assumed to occur in a material by the initiation and growth of cavities andmicro-cracks. The damage model allows parameters to be defined which control theinitiation of damage and post damage behaviour. In LUSAS a scalar damage variableis used in the degradation of the elastic modulus matrix. This means that the effect ofdamage is considered to be non-directional or isotropic. Two LUSAS damage modelsare available (Simo and Oliver) together with a facility for a user-supplied model.

A damage analysis can be carried out using any of the elastic material models and thefollowing nonlinear models:

q von Mises (models 72 and 77)q Hill (model 76)q Hoffman (model 78)

Creep material properties may be included in a damage analysis.

Damage PropertiesThe initial damage threshold, r0 , can be considered to carry out a similar function tothe initial yield stress in an analysis involving an elasto-plastic material. However, in adamage analysis, the value of the damage threshold influences the degradation of theelastic modulus matrix. A value for r0 may be obtained from:

rE

td

00

1 2=σ

b g /

where σtd is the uniaxial tensile stress at which damage commences and E0 is the

undamaged Young’s modulus. The damage criterion is enforced by computing theelastic complementary energy function as damage progresses:

β σ σTe tD re j1 2

0/

− ≤

where σ is the vector of stress components, De the elastic modulus matrix and rt the

current damage norm. The factor β is taken as 1 for the Simo damage model, while forthe Oliver model takes the value:

β θθ

η= +

−FHG

IKJ

1

where

θσ σ σ

σ σ σ=

< > + < > + < >+ +

1 2 3

1 2 3| | | | | |η

σσ

=c

dtd

Viscous Material Properties

131

Only positive values are considered for <σi>, any negative components are set tozero. The values σc

d and σtd represent the stresses that cause initial damage incompression and tension respectively (note that if σc

d = σtd , β=1). The damage

accumulation functions for each model are given by:

Simo: G rr A

rA B r rt

ttb g a f b g= −

−− −1

100exp

Oliver: G rr

rA

r

rtt t

b g = − −FHG

IKJ

LNMM

OQPP1 10 0exp

For no damage, G(rt)=0. The characteristic material parameters, A and B, wouldgenerally be obtained from experimental data. However, a means of computing A hasbeen postulated for the Oliver model:

AG E

I

f o

chtd

= −L

NMMM

O

QPPP

−

σe j21

1

2

where Gf is the fracture energy per unit area, Ich is a characteristic length of the finiteelement which can be approximated by the square root of the element area.

These damage models are explained in greater detail in the LUSAS Theory Manual.

Damage ratio (Oliver model only)The Damage ratio is the ratio of the stresses that cause initial damage in tension andcompression = σ σc

dtd/ . It is invoked if different stress levels cause initial damage in

tension and compression.

Viscous Material PropertiesViscoelasticity can be coupled with the linear elastic and non-linear plasticity,(isotropic or orthotropic), creep and damage models available in LUSAS. The modelrestricts the viscoelastic effects to the deviatoric component of the material response.This enables the viscoelastic material behaviour to be represented by a shear modulusGv and a decay constant β. Viscoelasticity imposed in this way acts like a spring-damper in parallel with the elastic-plastic, damage and creep response. Coupling ofthe viscoelastic and the existing nonlinear material behaviour enables hysteresiseffects to be modelled.


132

Notes

q It is assumed that the viscoelastic effects are restricted to the deviatoriccomponent of the material response. The deviatoric viscoelastic components ofstress are obtained using a stress relaxation function G(t), which is assumed tobe dependent on the viscoelastic shear modulus and the decay constant.

σ''

vt

t G t ss

sa f a f= −∂ε∂

∂z 20

G t G evta f = − β

q The viscoelastic shear modulus Gv can be related to the instantaneous shearmodulus, G0 , and long term shear modulus, G∞ , using G G Gv = − ∞0 .

q When viscoelastic properties are combined with isotropic elastic properties, theelastic modulus and Poisson’s ratio relate to the long term behaviour of thematerial, that is, E∞ and υ∞ .

q At each iteration, the current deviatoric viscoelastic stresses are added to thecurrent elastic stresses. The deviatoric viscoelastic stresses are updated using;

σ σβ

β∆β∆

' ''

v vt

v

t

t t t e Ge

t+ = +

−−

−

∆∆ε∆

a f a f e j2

1

where

• σ'v = deviatoric viscoelastic stresses

• Gv = viscoelastic shear modulus

• β = viscoelastic decay constant

• ∆t = current time step increment

• ∆ε' = incremental deviatoric strains

q When viscoelastic properties are coupled with a nonlinear material model it isassumed that the resulting viscoelastic stresses play no part in causing thematerial to yield and no part in any damage or creep calculations.Consequently the viscoelastic stresses are stored separately and deducted fromthe total stress vector at each iteration prior to any plasticity, creep or damagecomputations. Note that this applies to both implicit and explicit integration ofthe creep equations.

q Nonlinear Control must always be specified when viscoelastic properties areassigned. In addition Dynamic Control must also be specified to provide a timestep increment for use in the viscoelastic constitutive equations. If no timecontrol is used the viscoelastic properties will be ignored.

Two-Phase Material Properties

133

User Supplied Visco Elastic PropertiesThe user supplied visco elastic properties facility enables routines for implementing auser supplied viscoelastic model to be invoked from within LUSAS. This facilityprovides completely general access to the LUSAS property data input via this datasection and provides controlled access to the pre- and post-solution constitutiveprocessing and nonlinear state variable output via these user supplied routines.

Source code access is available to interface routines and object library access isavailable to the remainder of the LUSAS code to enable this facility to be utilised.Contact FEA for full details of this facility. Since user specification of a viscoelasticmodel involves the external development of a FORTRAN source code, as well asaccess to the LUSAS code, this facility is aimed at the advanced LUSAS user.

Notes

q Option 179 can be set for argument verification within the user routines.q The current viscoelastic stresses must be evaluated at each iteration and added

to the current Gauss point stresses. These viscoelastic stresses are subsequentlysubtracted at the next iteration, internally within LUSAS, before any plasticity,creep or damage calculations are performed.

Two-Phase Material PropertiesTwo-phase material properties are required when performing an analysis in whichtwo-phase elements are used to define a drained and undrained state for soil.

Notes

q Usually, the value of Bulk modulus of solid phase is quite large compared toBulk modulus of fluid phase and not readily available to the user. If Bulkmodulus of solid phase is input as 0, LUSAS assumes an incompressible solidphase. Bulk modulus of fluid phase is more obtainable, e.g. for water Bulkmodulus of fluid phase = 2200 Mpa [N1]

q Two-phase material properties can only be assigned to geotechnical elements,that is, TPN6P and QPN8P.

q When performing a linear consolidation analysis TRANSIENT CONTROLmust be specified. DYNAMIC or NONLINEAR CONTROL cannot be used.

q In an un-drained analysis two-phase material properties may be combined withany other material properties, and creep, damage and viscoelastic properties. Ina drained analysis only linear material properties may be used.


134

Rigidity Material DefinitionThe linear rigidity model is used to define the in-plane and bending rigidities fromprior explicit integration through the element thickness.

Note

q Angle of orthotropy is relative to the reference axis (degrees).q The element reference axes may be local or global (see Local Axes in the

LUSAS Element Library for the proposed element type). If the angle oforthotropy is set to zero, the anisotropy coincides with the reference axes.

Example 1. Membrane Behaviour

N

N

N

D D D

D D D

D D D

N

N

N

x

y

xy

x

y

xy

xo

yo

xyo

xo

yo

xyo

RS|

T|

UV|

W|=L

NMMM

O

QPPP

RS|

T|

UV|

W|−

RS|

T|

UV|

W|

RS||

T||

UV||

W||+

RS|

T|

UV|

W|1 2 4

2 3 5

4 5 6

εεε

εεε

where:

N are the membrane stress resultants (force per unit width).D membrane rigidities.e membrane strains.

and for isotropic behaviour, where t is the thickness:

D Dt

1 3 21= =

−

Εν

Dt

2 21=

−

νΕν

Dt

62 1

=+

Ενb g D D4 5 0= =

The initial strains due to a temperature rise T are:

εεεε

ααα

ot

xo

yo

xyo

T=

RS|

T|

UV|

W|+

RS|T|

UV|W|

1

2

3

Example 2. Thin Plate Flexural Behaviour

M

M

M

D D D

D D D

D D D

M

M

M

x

y

xy

x

y

xy

xo

yo

xyo

xo

yo

xyo

RS|

T|

UV|

W|=L

NMMM

O

QPPP

RS|

T|

UV|

W|−

RS|

T|

UV|

W|

RS||

T||

UV||

W||+

RS|

T|

UV|

W|1 2 4

2 3 5

4 5 6

ΨΨΨ

ΨΨΨ

where:

M are the flexural stress resultants (moments per unit width).D flexural rigidities.Ψ flexural strains given by:

Rigidity Material Definition

135

ΨΨΨ

x

y

xy

w

x

w

y

w

x y

RS|

T|

UV|

W|

R

S

||||

T

||||

U

V

||||

W

||||

=

-

-

-

2

2

2

∂∂∂

∂∂

∂ ∂

2

22

and for an isotropic plate for example, where t is the thickness:

D DEt

1 3

3

212 1= =

−( )ν D

Et2

3

212 1=

−

ν

ν( ) D

Et6

3

24 1=

+( )ν D4 = D5 = 0


ΨΨΨΨ

ot

xo

yo

xyo

T

z=

RS|

T|

UV|

W|=

RS|T|

UV|W|

∂∂

ααα

1

2

3

Example 3. Thick Plate Flexural Behaviour

M

M

M

S

S

M

M

M

S

x

y

xy

xz

yz

x

y

xy

xz

yz

xo

yo

xyo

xzo

yzo

xo

yo

xyo

xzo

R

S|||

T|||

U

V|||

W|||

=

L

N

MMMMMM

O

Q

PPPPPP

R

S|||

T|||

U

V|||

W|||

−

R

S|||

T|||

U

V|||

W|||

R

S|||

T|||

U

V|||

W|||

+

D D D D D

D D D D D

D D D D D

D D D D D

D D D D D

1 2 4 7 11

2 3 5 8 12

4 5 6 9 13

7 8 9 10 14

11 12 13 14 15

ΨΨΨΓΓ

ΨΨΨΓΓ Syzo

R

S|||

T|||

U

V|||

W|||

where:

M are the flexural stress resultants (moments per unit width).S shear stress resultants (shear force per unit width).D flexural and shear rigidities.Ψ flexural strains given by:

ΨΨΨ

x

y

xy

w

x

w

y

w

x y

RS|

T|

UV|

W|=

−

−

−

R

S

||||

T

||||

U

V

||||

W

||||

∂∂∂

∂∂

∂ ∂

2

2

2

2

22

Γ shear strains given by:


136

ΓΓ

xz

yz

w

x

u

zw

y

v

z

RSTUVW

=

∂∂

+∂∂

∂∂

+∂∂

RS||

T||

UV||

W||and for an isotropic plate for example:

D DEt

k10 15

2 1= =

+( )ν

D D D D D D D7 8 9 11 12 13 14 0= = = = = = =

where t is the plate thickness and k is a factor taken as 1.2 which provides the correctshear strain energy when the shear strain is assumed constant through the platethickness. D1 to D6 are the same as defined for the thin plate flexural behaviour (seeExample 2. Thin Plate Flexural Behaviour).


Ψ

ΨΨΨΓΓ

ot

ot

xo

yo

xyo

xzo

yzo

T

zT

ε∂∂

ααα

αα

RSTUVW =

R

S|||

T|||

U

V|||

W|||

=

R

S|||

T|||

U

V|||

W|||

+

R

S|||

T|||

U

V|||

W|||

1

2

3

4

5

0

0

0

0

0

Example 4. Shell Behaviour

N

N

N

M

M

M

D D D D D D

D D D D D D

D D D D D D

D D D D D D

D D D D D D

D D D D D D

x

y

xy

x

y

xy

x

y

xy

x

y

xy

xo

yo

xyo

xo

yo

xyo

R

S

||||

T

||||

U

V

||||

W

||||

=

L

N

MMMMMMMM

O

Q

PPPPPPPP

R

S

||||

T

||||

U

V

||||

W

||||

−

R

S

||1 2 4 7 11 16

2 3 5 8 12 17

4 5 6 9 13 18

7 8 9 10 14 19

11 12 13 14 15 20

16 17 18 19 20 21

εε

εε

ΓΨΨΨ

ΓΨΨΨ

||

T

||||

U

V

||||

W

||||

R

S

||||

T

||||

U

V

||||

W

||||

+

R

S

||||

T

||||

U

V

||||

W

||||

N

N

N

M

M

M

xo

yo

xyo

xo

yo

xyo

where:

N are the membrane stress resultants (forces per unit width).M are the flexural stress resultants (moments per unit width).D flexural and shear rigidities.ε membrane strains.Γ flexural strains.


Joint Material Properties

137

Ψ ΓΨΨΨ

ot

ot

xo

yo

xyo

xo

yo

xyo

TT

zε

εε

ααα ∂

∂ ααα

RSTUVW =

R

S

||||

T

||||

U

V

||||

W

||||

−

R

S

||||

T

||||

U

V

||||

W

||||

+

R

S

||||

T

||||

U

V

||||

W

||||

1

2

3

4

5

6

0

0

0

0

0

0

Joint Material PropertiesJoint material models are used in conjunction with joint elements to define thematerial properties for linear and nonlinear joint models. See Joint Element Meshesfor information about using joints. Six joint models are available:

Linear Joint Modelsq Spring stiffness only corresponding to each local freedom. These local

directions are defined for each joint element in the LUSAS Element Library.

q General Properties full joint properties of spring stiffness, mass, coefficientof linear expansion and damping factor.

Non-Linear Joint Modelsq Elasto-Plastic uniform tension and compression with isotropic hardening.

Equal tension and compression yield conditions are assumed.

q Elasto-Plastic General with isotropic hardening. Unequal tension andcompression yield conditions are assumed.

q Smooth Contact with an initial gap. See note below.

q Frictional Contact with an initial gap. See note below.


138

+Yield force K - elastic springstiffness

+κ strain hardeningstiffness

-κstrain hardening

stiffness

ε = δ2 - δ1

-Yield force

+ : tension- : compression

F

Elasto-Plastic Joint Models

Lift-offforce

K - contact springstiffness

κ - lift-off stiffness

ε = δ2 - δ1ψ = θ2 - θ1Gap

F

Smooth Contact

Joint Material Properties

139

εxx = δx2 - δx1

Gap

Fx

K - contactspring stiffness

Kcy or Kcz - contact springstiffness

γxy = δy2 - δy1or

γxz = δz2 - δz1

Fy or Fz

Fo

-Fo

Fo

Fx

µ - coeff. offriction

Frictional Contact

Notesq Initial gaps are measured in units of length for translational freedoms and in

radians for rotational freedoms.

q Smooth Contact: If an initial gap is used in a spring, then the positive localaxis for this spring must go from node 1 to 2. If nodes 1 and 2 are coincidentthe relative displacement of the nodes in a local direction (δ2 δ1) must benegative to close an initial gap in that direction.

q Frictional Contact: If an initial gap is used in a spring, then the positivelocal x axis for this spring must go from node 1 to 2. If nodes 1 and 2 arecoincident the relative displacement of the nodes in the local x direction (δx2δx1) must be negative to close an initial gap.


140

Rubber MaterialRubber materials maintain alinear relationship betweenstress and strain up to verylarge strains (typically 0.1 -0.2). The behaviour after theproportional limit isexceeded depends on thetype of rubber (see diagrambelow). Some kinds of softrubber continue to stretchenormously without failure.The material eventuallyoffers increasing resistanceto the load, however, and the stress-strain curve turns markedly upward prior tofailure. Rubber is, therefore, an exceptional material in that it remains elastic farbeyond the proportional limit.

Rubber materials are also practically incompressible, that is, they retain theiroriginal volume under deformation. This is equivalent to specifying a Poisson's ratioapproaching 0.5.

Rubber Material ModelsThe strain measure used in LUSAS to model rubber deformation is termed a stretchand is measured in general terms as:

λ = dnew/dold

where:

• dnew is the current length of a fibre

• dold is the original length of a fibreSeveral representations of the mechanical behaviour for hyper-elastic or rubber-likematerials can be used for practical applications. Within LUSAS, the usual way ofdefining hyper-elasticity, i.e. to associate the hyper-elastic material to the existenceof a strain energy function that represents this material, is employed. There arecurrently four rubber material models available:

q Ogdenq Mooney-Rivlinq Neo-Hookeanq Hencky

σ

ε

Hard Rubber

Soft Rubber

Rubber Material

141

The rubber constants (used for Ogden, Mooney-Rivlin and Neo-Hookean) areobtained from experimental testing or may be estimated from a stress-strain curve forthe material together with a subsequent curve fitting exercise.

The Neo-Hookean and Mooney-Rivlin material models can be regarded as specialcases of the more general Ogden material model. In LUSAS these models can bereformulated in terms of the Ogden model.

The strain energy functions used in these models includes both the deviatoric andvolumetric parts and are, therefore, suitable to analyse rubber materials where somedegree of compressibility is allowed. To enforce strict incompressibility (where thevolumetric ratio equals unity), the bulk modulus tends to infinity and the resultingstrain energy function only represents the deviatoric portion. This is particularlyuseful when the material is applied in plane stress problems where fullincompressibility is assumed. However, such an assumption cannot be used in planestrain or 3D analyses because numerical difficulties can occur if a very high bulkmodulus is used. In these cases, a small compressibility is mandatory but this shouldnot cause concern since only near-incompressibility needs to be ensured for most ofthe rubber-like materials.

Using Rubber MaterialRubber is applicable for use with the following element types at present:

q 2D Continuum QPM4M, QPN4Mq 3D Continuum HX8Mq 2D Membrane BXM2

Notes

1. For membrane and plane stress analyses, the bulk modulus is ignored becausethe formulation assumes full incompressibility. The bulk modulus has to bespecified if any other 2D or 3D continuum element is used.

2. Ogden, Mooney-Rivlin and Neo-Hookean material models must be run withgeometric nonlinearity using either the total Lagrangian formulation (formembrane elements) or the co-rotational formulation (for continuum elements).The Hencky material model is only available for continuum elements and mustbe run using the co-rotational formulation. The large strain formulation isrequired in order to include the incompressibility constraints into the materialdefinition.

3. Option 39 can be specified for smoothing of stresses. This is particularly usefulwhen the rubber model is used to analyse highly compressed plane strain or 3Dcontinuum problems where oscillatory stresses may result in a "patchwork quilt"stress pattern. This option averages the Gauss point stresses to obtain a meanvalue for the element.


142

4. When rubber materials are utilised, the value of det F or J (the volume ratio) isoutput at each Gauss point. The closeness of this value to 1.0 indicates the degreeof incompressibility of the rubber model used. For totally incompressiblematerials J=1.0. However, this is difficult to obtain due to numerical problemswhen a very high bulk modulus is introduced for plane strain and 3D analyses.

Subsequent selection of state variables for displaying will include the variablePL1 which corresponds to the volume ratio.

5. Rubber material models are not applicable for use with the axisymmetric solidelement QAX4M since this element does not support the co-rotational geometricnonlinear formulation. The use of total Lagrangian would not be advised as analternative.

6. There are no associated triangular, tetrahedral or pentahedral elements for usewith the rubber material models at present.

7. The rubber material models are inherently nonlinear and, hence, must be used inconjunction with the NONLINEAR CONTROL command.

8. The rubber material models may be used in conjunction with any of the otherLUSAS material models. However, it is not possible to combine rubber with anyother nonlinear material model within the same material dataset.

Volumetric Crushing MaterialMaterial behaviour can generally be described in terms of deviatoric and volumetricbehaviour which combine to give the overall material response. The crushable foammaterial model accounts for both of these responses. The model defines thevolumetric behaviour of the material by means of a piece-wise linear curve ofpressure versus the logarithm of relative volume. An example of such a curve isshown in the diagram below, where relative volume is denoted by V/V0.

Volumetric Crushing Material

143

Tension

pressure Compression

K - Bulk modulus

-ln (V/V0)

cut-offpressure

K - Bulk modulus

Pressure - Logarithm of Relative Volume Curve

From this figure, it can also be seen that the material model permits two differentunloading characteristics volumetrically.

q Unloading may be in a nonlinear elastic manner in which loading andunloading take place along the same nonlinear curve.

q Volumetric crushing may be included (by clicking in the Volumetriccrushing check box) in which case unloading takes place along a straight linedefined by the unloading/tensile bulk modulus K which is, in general,different from the initial compressive bulk modulus defined by the initialslope of the curve.

In both cases, however, there is a maximum (or cut-off) tensile stress, (cut-offpressure), that is employed to limit the amount of stress the material may sustain intension.

The deviatoric behaviour of the material is assumed to be elastic-perfectly plastic.The plasticity is governed by a yield criterion that is dependent upon the volumetricpressure (compared with the classical von Mises yield stress dependency onequivalent plastic strain) and is defined as:

τ20 1 2

2= − +a a p a p

where p is the volumetric pressure, τ is the deviatoric stress and a0, a1, a2 arepressure dependent yield stress constants. Note that, if a1 = a2 = 0 and a0 =(syld2)/3, then classical von Mises yield criterion is obtained.


144

pressure

τhyperbolic a2>0

parabolic a2=0

elliptic a2<0a0

Yield Surface Representation For Different Pressure Dependent Yield Stress Values

Notes

1. Bulk modulus used in tension and unloading (see 1st figure). The relationshipbetween the elastic bulk (or volumetric) modulus, K, and tensile modulus, E, isgiven by:

KE

=−3 1 2( )ν

2. Shear modulus The relationship between the elastic modulus values in shear, G,and tension, E, assuming small strain conditions, is given by:

GE

=+2 1( )ν

3. Heat fraction coefficient Represents the fraction of plastic work which isconverted to heat and takes a value between 0 and 1.

4. Cut-off pressure Should be negative (i.e. a tensile value).

5. Pressure dependent yield stresses (a0, a1, a2) (Should be positive). The yieldsurface defined is quadratic with respect to the pressure variable. Therefore it cantake on different conical forms (see 2nd figure), either elliptic (a2<0), parabolic(a2=0) or hyperbolic (a2>0). The parabolic form is comparable to the modifiedvon Mises material model while the elliptic form can be considered to be asimplification of critical state soil and clay material behaviour.

6. The volumetric crushing indicator effectively defines the unloading behaviour ofthe material. If there is no volumetric crushing, the same pressure-logarithm ofrelative volume curve is used in loading and unloading and if volumetric

Support Conditions

145

crushing takes place the alternative unloading/reloading curve is used (see 1stfigure).

7. Log relative volume Natural logarithm (loge, not log10) of relative volumecoordinate for ith point on the pressure-logarithm of relative volume curve (see1st figure)

8. The pressure-logarithm of relative volume curve is defined in the compressionregime hence logarithms of relative volume must all be zero or negative and thepressure coordinates must all be zero or positive.

Support ConditionsSupport conditions describe the way in which the model is supported or restrained. Asupport dataset contains information about the restraints applied to each degree offreedom. There are three valid support conditions:

q Free (F) the degree of freedom is completely free to move. This is thedefault.

q Restrained (R) the degree of freedom is completely restrained frommovement.

q Sprung (S) the degree of freedom is subjected to a specified spring stiffness.Spring stiffness values can be applied uniformly to All nodes meshed on theassigned feature or their values may vary over a feature by applying avariation. Alternatively, per unit length or per unit area values can beapplied.

Using Support ConditionsSupport datasets are defined from the Attributes menu (structural and thermalsupports have separate menus), then assigned to features. For a nonlinear analysis inwhich the support conditions change the load case can be specified on assignment.Support assignments for similar orders of feature are additive. Support assignmentson lower order features override those on higher order features.

Notesq Support conditions cannot be changed for different load cases in a linear

analysis.q Support conditions may only be modified between increments of a

transient/dynamic nonlinear problem subject to the following conditions:

• Only the support conditions on the respecified features will be modified.

• Features that have supports specified on a subsequent load case must havethem specified on load case 1. A dummy support (i.e. all variables free)may be used if necessary.


146

q Ensure that nodes are not free to rotatewhen attached to beam elements withfree ends. For example, node 1 in thediagram shown must be restrained against rotation as well as displacementotherwise the element will be free to rotate as a rigid body.

q Support conditions may be omitted for eigenvalue analyses provided a shift isused in the eigenvalue control.

q Prescribed displacement loading supersedes support conditions. If a springsupport is defined at a variable then any subsequent Prescribed displacementapplied to that variable is read as the spring stiffness.

Tips

q If the required support conditions do not lie in the global axes then a localcoordinate system may be assigned to the feature to transform the supports tolocal directions. Note that this may also transform any loads applied to thefeature.

q Supports may be modelled that act in tension, but not in compression by usingthem in conjunction with joints or interface meshes.

Visualising Support ConditionsSupport conditions can be visualised in three ways:

q Arrows Visualises restrained variables as straight arrows representingtranslational degrees of freedom, and circular arrows for rotational degrees offreedom. Sprung supports are visualised as spring representations. Hingefreedoms are not visualised.

q Symbols places a symbol on each supported node.

q Codes writes a code next to each supported node representing the type ofsupport assigned. The code uses R = restrain, F = free, S = sprung. Forexample, a code RRSFFF represents a six degree of freedom node that isrestrained in nodal X and Y directions, supported with a spring in nodal Zdirection and free in all three rotational freedoms.

R1 2

F

Support Conditions

147

Example: Translational Fixed and SpringSupportsThis 3D structure is restrained from anylateral movement at the base of all legs. Thesame points are also sprung vertically torepresent a non-rigid base support.

Example: Translational SupportsThis 2D structure is restrainedhorizontally and vertically at theleft edge with a single restraint inboth in-plane translationaldirections. This rigidly fixes thebody along the edge shown whileallowing the rest of the model tomove.

Example: Rotational SymmetryOnly the right half of this structure ismodelled but the full structure is representedby assuming symmetry at the centre-line.Symmetry assumes the same behaviour forboth sides of the model therefore atranslational restraint is applied to stopmovement across the symmetry boundaryand a rotational restraint is applied to forcezero rotation at the boundary also.

Example: Translational SymmetryThis quarter plate model usessymmetry restraints to effectivelymodel the whole plate. Supports arepositioned in order to prevent anymovement at lines of symmetry.


148

About LoadingLoading datasets describe the external influences to which the model is subjected.All load types in LUSAS are feature based, except for the discrete loads.

Feature based loadsFeature based loads are assigned to the model geometry and are effective over thewhole of the feature to which they are assigned.

q Structural Concentrated, body force, distributed, face, temperature,stress/strain, and beam loads.

q Prescribed used to specify initial values for displacement, velocity oracceleration at a node.

q Thermal describe temperature or heat input to a thermal analysis.

Some loads act in global directions, others in local element directions. The definedloading value will be assigned as a constant value to all of the nodes/elements in thefeature unless a variation is applied. Variations can be applied to all feature loadtypes except for Beam Distributed loads which have a variation built into thedefinition.

Tip. If the required loading directions of a global load do not lie in the global axesthen a local coordinate system may be assigned to the feature to transform the loadsto local coordinate directions.

Discrete loads (feature independent)Discrete loads are assigned to Points only in order to distribute a given loadingpattern over full or partial areas of the model, independent of the model geometry.Point and Patch loads are discrete loads, also known as general loads.

Further control over how the loads are applied is available using Search areadatasets.

Load AssignmentLoads are assigned in the same way as other attributes, by dragging the definedattribute dataset from the Treeview onto the selected features. However, LUSASuses different methods when applying discrete loads and feature based loads.

q Features based loads can be factored, or scaled using load curves.q Discrete loads possess variations as part of their definition.

Structural Loads

149

Note. Consult the LUSAS Element Library in order to check that the requiredloading is available for that particular element.

Structural LoadsFor information on which load types can be applied to which element types, see theLUSAS Element Library.

Concentrated Load (CL)A Concentrated Loaddefines concentrated forceand moment loads in global(or transformed nodal) axisdirections. Concentratedforce loads are applied to allnodes underlying the featureonto which the load datasetis assigned.

Concentrated loads aredefined relative to the nodalcoordinate system. If therequired loading directionsof a global load do not lie in the global axes then a local coordinate system may beassigned to the feature to transform the loads to local coordinate directions.

Concentrated Loads can be applied in cylindrical coordinates for Fourier elements bysetting the option on the Model Properties (Attributes tab), File menu.

Body Force (CBF)A Body Force defines anacceleration or force per unitvolume loading in globaldirections. A typicalexample of body forceloading is self weight, whichrequires the specification ofgravitational accelerationand mass density (in thematerial properties).

X

Y

Global Xon Line

X load on Point withTransformed Freedoms

Global Zon Line

Z

x

y

z


150

By default, Body Forces define accelerations, but an option on the Model Properties(Attributes tab), File menu, can be set so that Body Forces define a force per unitvolume.

Global Distributed Load (CL)Defines concentrated force or moment loads in global (or transformed nodal) axisdirections. Concentrated force loads are applied to all nodes underlying the featureonto which the load dataset is assigned. Nodal freedoms can be transformed usinglocal coordinate sets. The following sub-types are supported:

q Total applies nodal load values calculated according to contributions fromsurrounding elements and to element nodal weighting values, e.g. loads areweighted with ratios 1:4:1 at nodes along the edge of a quadratic shell in sucha way as to make the shell strain equally.

q Line (per unit length) applies nodal loads using the specified values per unitlength loads. Must be assigned to Line feature types.

q Surface (per unit area) applies nodal loads using the specified values perunit area loads. Must be assigned to Surface feature types.

Local Distributed Load (UDL)Defines a load per unit length or area for line or surface elements in the localelement directions. Typically, local distributed loading is applied to beam elementsand shell faces. An example of a local distributed is internal pressure loading. Forbeam elements, when the element type permits, uniformly Distributed Load will bewritten to the LUSAS data file as Beam Element Loading (ELDS).

Face Load (FLD)Defines face traction values andnormal loading applied in localelement face directions. Face loadsare applied to the edges of planeelements or the faces of solidelements. This type of loading isapplicable to 2D and 3D continuumelements, and certain shell,membrane and thermal elements.

In the example shown, a local ydirection structural face load isassigned to the Surface boundary

Structural Face Load(y=1.0)

ElementAxes

FaceAxes

L1

L2

L3

S1

Structural Loads

151

Lines. Note the direction of the axes of the local element faces.

Where a loaded Line or Surface feature is common to two or more higher orderfeatures, it is possible to specify to which higher order feature elements the load isassigned.

See the Element Reference Manual for details of element face directions.

Internal Beam Loads (ELDS)The Beam Distributed Loadis an element load. An orientationis defined, along with pairs ofdistances and values.

The Beam Point Load is anelement load. An orientation isdefined, as well as a series of distances along a line and point load values.

Stress and Strain (SSI, SSR)q Initial element Stresses/Strains defines an element initial stress/strain state

in local directions. Initial stresses and strains are applied as the first load case and subsequently

included into the incremental solution scheme for nonlinear problems. Initialstresses and strains are only applicable to numerically integrated elements.

q Residual element Stresses/Strains defines element residual stress/strain levelsin local directions.

Residual stresses (unlike initial stresses) are assumed to be in equilibriumwith the undeformed geometry and are not treated as a loadcase as such. Theyare considered as a starting position for stress for a nonlinear analysis. Failureto ensure that the residual stresses are in equilibrium will result in anincorrect solution.

Refer to the LUSAS Element Reference Manual for valid element types.

Temperature Load (TEMP, TMPE)Nodal (TEMP) or Element (TMPE) temperatures produce the LUSAS TEMPand TMPE load types respectively. These loads apply temperature differences on anodal and element basis. Temperature gradients in x, y and z directions may also beinput. This load type can be used in conjunction with temperature dependentmaterial properties to activate a different set of properties at a specified point in theanalysis. The thermal expansion coefficient is normally set to zero in this case. Note

Element LoadDisplay


152

that this type of field loading is only applicable to thermal bars and only applies tothe first iteration.

Notes for using Temperature Loads1. Nodaltemperatures apply to all elements connected to that node, except joints, in

which temperature loading is invoked using Option 119. Elemental Temperature is only applied to the node of the element specified.2. For step by step problems, the (initial) temperature values need only be specified

on the first load step.3. The Temperature load may be used to provide a temperature field for computing

initial material properties in a nonlinear analysis. To initialise the temperaturefield in a nonlinear field analysis, the temperature loading must be applied usinga manual loading increment.

4. To initialise the temperature field in a nonlinear field analysis, the temperatureloading must be applied using a manual load increment.

Case Study. Temperature Cross-Fall on a Slab

Nodal and element temperature values accept gradient values for some elementtypes. This gradient applies a differential thermal load across the top and bottomsurfaces of a Surface element. The effect of this gradient is to cause bending in thestructure. See the LUSAS Element Library for temperature load input variations onan element basis.

To model the situationshown in theaccompanying diagram,where the top surface ofthe slab is subjected to atemperature of 50degrees centigrade andthe bottom surface is at20 degrees centigrade,the z directiontemperature gradientdT/dz would be enteredas (50-20)/d. Forexample, where the thickness d is 0.5m, the slab mid-surface temperature T wouldbe entered as 35 degrees, and dT/dz would be entered as 60 degrees centigrade permetre.

Top Surface50 degrees C

depth

Plate/shellelements

Bottom Surface20 degrees C

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153

LUSAS will multiply the temperature gradient by the thermal coefficient ofexpansion specified in the material property dataset to calculate the thermal bendingstrain. A change in gradient can be modelled by specifying an initial gradient usingthe additional dT0/dz parameter.

This method will assume a linear temperature distribution through the depth of theslab. If a known nonlinear variation is required, solid elements must be used with avariation dataset defining the nonlinear through-thickness behaviour.

Prescribed LoadsFor information on which load types can be applied to which element types, see theLUSAS Element Library.

Prescribed DisplacementA PrescribedDisplacement defines anodal movement by either atotal or incrementalprescribed distance in global(or transformed) axisdirections. Variables whichare loaded with a non-zeroprescribed variable willautomatically be restrained inthe required direction.

This example shows two methods of applying prescribed displacement. Incrementalloading adds displacements to a previous increment, whereas total requires the fulldisplacement to be specified on each increment. Use total prescribed loading withload curve definition.

Notes

q LUSAS applies an automatic support condition to nodes with a Prescribeddisplacement assigned. This is required in order to restrained the node forsolving the force, stiffness, displacement equation.

q The number of prescribed variables must not exceed the number of freedomsfor any node.

q Total and Incremental displacements should not be used in the same analysisif load curves have been defined, and never applied to the same node. It isrecommended that total prescribed displacements are used with load curves

1.0

1.0

1.0

1.0

2.0

3.0

Incr

emen

tal

To

tal


154

q Rotational displacements should be specified in Radians.

Prescribed Velocity and AccelerationIn dynamic analyses, velocities and accelerations can be defined at a nodal variable.These values can be used to specify an initial starting condition or they may beprescribed for the whole analysis.

q A prescribed, or initial, velocity defines a velocity loading in globaldirections.

q A prescribed, or initial, acceleration defines an acceleration loading inglobal directions. If acceleration loads are required, the density must bespecified in the material properties. Initial accelerations are only valid forimplicit dynamic analyses.

Notes

q If the values are to be prescribed throughout the analysis load curves must beused, see Load Curve Definition.

q Initial velocities and accelerations should only be applied to the first loadcase.q In general, load curves should be used to prescribe velocities and

accelerations in an analysis. However, initial values may be defined withoutusing load curves if no other load type is controlled by a load curve.

q If velocities and accelerations are prescribed for the same variable at the samepoint in time in an analysis, the acceleration will overwrite the velocity and awarning will be output. An exception to this rule occurs for implicit dynamicanalyses where an initial velocity and acceleration may be used to define aninitial condition for the same variable.

q If initial conditions are to be applied, refer to Transient Dynamic Analysis fordetails on how to compute the data input required for the appropriateintegration scheme.

Thermal LoadsFor information on which load types can be applied to which element types, see theLUSAS Element Library.

Concentrated Flux (CL)A Concentrated Flux produces the LUSAS CL load type which in a fieldanalysis applies a rate of internal heat generation (Q). Positive Q defines heat input.

Concentrated fluxes are defined relative to the nodal coordinate system. If therequired loading directions of a global load do not lie in the global axes then a local

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155

coordinate system may be assigned to the feature to transform the loads to localcoordinate directions.

Prescribed Temperature (PDSP/TPDSP)Prescribes temperature.

q The incremental prescribed load type adds to any temperatures present froma previous increment.

q The total prescribed load type defines the total temperature at a given node ata specified increment.

By default temperature should be input in Kelvin, however, an option on the Modelproperties, Attributes tab, file menu allows temperature input to be specified inCelsius.

Environmental Loading (ENVT/TDET)Models external fluid temperature and associated convective and radiativecoefficients. If an element face does not have an environmental temperature assignedit is assumed to be perfectly insulated.

A temperature dependent environmental temperature models properties that varywith nodal temperature. This load dataset requires a reference temperature for eachset of properties.

Note. Defining temperature dependent properties turns a linear thermal fieldproblem into a nonlinear thermal problem.

Notes1. If heat transfer coefficients vary on a specified face the values will be interpolated

using the shape functions to the Gauss points.2. If a nonzero radiation heat transfer coefficient is specified, the problem is

nonlinear and Nonlinear Control must be used.3. By default temperature should be input in Kelvin, however, an option on the

Model properties, Attributes tab, file menu allows temperature input to bespecified in Celsius.

4. Load curves can be used to maintain or increment the environmental temperatureas a nonlinear analysis progresses.

5. Automatic load incrementation within the Nonlinear Control can be used toincrement ENVT loading.

6. If a zero element face node number is specified, then the environmental load willbe applied to all nodes on the face.


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Internal Heat Generation (CBF/RIHG)Defines the internal heat generation for an element. Positive loading values indicateheat generation and negative values indicate heat loss.

A temperature dependent internal heat defines the rate of internal heat generation.This load dataset requires a reference temperature for each set of properties.

Note. Defining temperature dependent properties turns a linear thermal fieldproblem into a nonlinear thermal problem.

Notesq Load curves can be used to maintain or increment the RIHG as a nonlinear

analysis progresses.q Automatic load incrementation under Nonlinear Control cannot be used with

RIHG loading.

Case Study. Temperature Dependent Loading

Temperature dependent environmental loading can be useful to modelexperimentally determined correlation for convective coefficients. For example, ifthe convective coefficient may be given by C [deltat] to the power one third where Cis a constant, deltat is the temperature difference between the surface and theenvironment. To specify this loading in LUSAS the user defines the convectivecoefficient at as many reference points as are required to give a good piece-wiselinear approximation of the function. Each reference temperature point is defined ina loading dataset and collectively these datasets define a single loading table. Theloading table is then assigned to the features as required.

1. Define a row of Surface features.

2. Use an incremental prescribed loading to fix the temperatures at one end of themodel.

3. Define a convective coefficient function using environmental loading(temperature dependent).

4. Assign the loading and solve.5. Since the problem is one-dimensional the solution may be checked to ensure that

the convection coefficient has been correctly interpolated.

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Discrete Loads

About Discrete LoadingDiscrete loads, (alsoknown as General loads),are defined in relation totheir own local coordinatesystem, the origin of whichis given by the coordinatesof the Point feature towhich the load is assigned.(Note. Discrete loads arealways assigned to Points).Discrete loads differ fromfeature-based loads in that they are not limited to application over whole features,and may be effective over full or partial areas of the model.

Discrete loads are useful for applying a load that does not correspond to the featuresunderlying the mesh. A patch may be spread or skewed across several features.LUSAS automatically calculates the nodal distribution of forces that is equivalent tothe total patch load. This example shows a typical set of point loads assigned to agrillage model. A single point, a group of 6 and a group of 16 point loads are shown.

The local coordinates of the points defining the patch are relative to the Point featureto which the patch load is assigned, i.e. a load definition is based on a localcoordinate system, the origin of which is given by the coordinates of the Point towhich the load is assigned. The Point feature does not have to lie in the Surface towhich the load will be applied as the patch load is projected onto the Surface in adirection normal to the patch definition.

Using Search Areas with Discrete LoadsA discrete load is distributed to the element nodes over which the patch lies. ASearch Area is a way of controlling the load distribution over these elements. If nosearch area is specified when assigning the patch, then all of the underlying elementswill be used.

While projecting the loads into the search area a check is made for multipleintersections of the load and the search area. Multiple intersections indicate anambiguity in the location of the load. This ambiguity may be resolved with a morespecific search area. The multiple intersection check slows down assembly of loadsand may be suppressed in the Attributes > Loading > Options dialog. If the multipleintersection check is suppressed, then the first intersection found will be used.


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Note. The distribution of load to the nodes follows the shape functions of theparticular element. In quadratic elements, this distribution can appear at firstunlikely. For example, a unit positive load at the centre of an 8-noded quadraticelement, results in negative 0.25 loads at the corners and positive 0.5 loads at themid-side nodes.

Discrete Load TypesA discrete load consists of coordinates defining the vertices (different to geometricPoints defining the model), load intensity and local x, y and z position. Anygeometric Points selected when the Discrete loading dialog is initiated are entered ascoordinates. Discrete load types available are Point load and Patch load:

q Point Load Defines ageneral set of discretepoint loads in 3Dspace. Each individualpoint load can have aseparate load value.

This example uses 16 distinct load values. The loads are applied to the modelas distinct point loads.

q Patch Load 2 or 3 points define a continuous line load in 3D space. 2 pointsgive a straight line load and 3 points give a curved line load. A set of 4 or 8points define a general patch load in 3D space. A patch consisting of 4 pointswill give a straight-sided patch, while 8 points define a patch with curvedsides.

The following examples show patch loads assigned to Point 1:

Example 1. A line load defined using a 2point line. The local origin of the line isassigned to Point 1.

Example 2. A curved line load. Thecurved load is defined using a 3 pointline. The local origin of the line isassigned to Point 1.

p1

p2

x1,y1

x2,y2

P1

x1,y1,p1 x2,y2,p2y

xP1

p1p2

p3

P1

y

x

x1,y1,p1

P1

x3,y3,p3

x2,y2,p2

x1,y1

x2,y2

x3,y3

P1 P1

y

x

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159

Example 3. A standard 4 point patchload. The local origin of the patch isassigned to Point 1.

Example 4. A fully curved 8 point patchload. The local origin of the patch isassigned to Point 1.

P1

P2P4

P3

x4,y4

x2,y2

x1,y1P1

x4,y4,p4

x1,y1,p1

x3,y3,p3

x2,y2,p2

y

xP1

P1

P3P7

P5

P2

P4P6

P7

P1

x2,y2

x1,y1

x3,y3

x8,y8

x7,y7

x5,y5,p5

x1,y1,p1 x3,y3,p3x2,y2,p2

x6,y6,p6x7,y7,p7

x4,y4,p4x8,y8,p8y

xP1

Defining Discrete Loads

Coordinates and magnitudePoint coordinates The coordinates defining the discrete loads. Any Points selectedbefore initiating the Discrete load dialog, are entered as point coordinates in thediscrete load dialog.

q For a point load multiple points can be defined on one dataset.

q For patch loads (2, 3, 4 or 8) points define the vertices for a single patch.

Load magnitude Specified at each given coordinate set of the general point or patchload, therefore the load may be varied over features.


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Load ProjectionLoad Projection Vector (untransformed)defines the direction in which the load isprojected onto the model. The vector isexpressed by inputting an X Y and Zcomponent.

For patch loads this direction is alwaysperpendicular to the patch.

Discrete loads are not restricted to elementslying in the XY plane. For Point and PatchLoad types, options are available for theapplication of the load in the global X, Y or Zaxes directions, or normal to the surface ontowhich the load is projected.

This example shows a typical 3D patch load where the patch is defined in space andprojected onto the model.

Load Direction(untransformed)defines the direction ofthe loads in the patchbefore anytransformation iscarried out at theassignment stage.Options are: Global X,Y and Z and SurfaceNormal.

In this example, loadsare projected onto amodel normal to thepatch definition. Thepatch normal directionis denoted by a double-headed arrow on a visualised patch. The direction of the loadapplied to the model is defined using the Untransformed Load Direction optionsform on the define load dialog.

Untransformed LoadGlobal X

Untransformed LoadGlobal Z or Surface Normal

X

Y

Z

Assigning Discrete Loads

161

Assigning Discrete LoadsDiscrete loads are independent of features therefore their application can be moreflexible. The load assignment parameters are explained below:

Patch Transformation Changes thepatch orientation. For example, a patchload may be skewed by applying arotation transformation dataset whenassigning the load.

In the example shown right the Pointload defined about local xy axes isassigned to Point 1 subject to a patchdirection transformation using a 30degree xy rotation about the globalorigin. Note that the local origin of thepatch load is rotated and repositioned aswell as the patch itself.

To rotate a patch about its centre, define the patch with its local origin at its centre.

Load Transformation Changes the load orientation from the (untransformed)direction given in the load definition. The transformation applies to the direction ofthe individual load components rather that to the patch as a whole. For example, itcan be used to model breaking loads on a 3D model that have horizontal and verticalcomponents by specifying a transformation that will rotate the loads out of thevertical direction and into an inclined plane in the direction of vehicle travel.

Search Area A search area restricts loading to a specified portion of the model. If asearch area is not specified, the load is projected onto the active model. For 2Dmodels it is usually acceptable to default to the whole model, but for 3D modelswhere multiple intersections of the load projection onto the model may occur it issafer to restrict the loading to the required face using a search area. In either case thetime taken to assemble the loads is significantly improved by using a search area torestrict the number of elements tested for intersection with the load.

Options for Processing Loads Outside Search Area The load outside the searcharea can be moved into the search area along the paths defined by the local x and yaxes of the loading patch. The patch load is transferred into the path along theprojected directions and added to the first loading positions found inside the patch inthe projected direction. Options are:

q Exclude All Load (default)q Include Local X Projected Load

P1

x

y

Y

X


162

q Include Local Y Projected Loadq Include Local X and Y Projected Loadsq Include Non-Projected Loadq Include Full Local X Loadq Include Full Local Y Loadq Include Full Load

The load cannot be moved if the entire patch load lies outside the search area. Loadsinside the search area are not moved. See Processing Loads Outside the Search Areabelow for explanations of each option.

Number of Divisions inLocal X and Y Directionspecifies the numbers ofdivisions in the local x andy directions of the patchbeing assigned. Thedivisions are used to splitthe applied patch intoindividual componentloads before they are inturn used to calculateequivalent nodal loads onthe model. By default, 10divisions are used in thelocal x direction and theaspect ratio of the patch isused to calculate the divisions in the y direction. At least one division should be usedper element division. The more individual loads a patch is split into, the moreaccurate the solution obtained. Equivalent weighting values are used to calculate theportion of each discrete load that is applied to each corner of the element that it lieswithin. The load is then applied as Concentrated Loads. These weighting values arebased on element shape functions and may vary with element type.

Note. Discrete patch loads are not work equivalent as the discrete points are simplylumped at the nearest node.

Load Case specifies which loadcase the loading is to be applied. Load cases canthemselves be manipulated. See Load Case Management for more details.

Load Factor specifies a factor by which the loading is multiplied before theequivalent nodal loads are calculated.

DiscretePatchLoads

ExtrapolatedConcentratedNodal Loads

LoadExtrapolationPath


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Case Study. Hydrostatic Loading

In this example, a Patch Load will be used to apply a hydrostatic load to the side-wall of an underground box culvert.

1. Assuming the box culvert wall is defined using a Surface in the global XZplane with corners at coordinates (0,0,0), (5,0,0), (5,0,3) and (0,0,3). Define aSurface using the New Surface button at the specified corner positions.

2. Rotate the view until the Surface can be visualised using the DynamicRotate button.

3. Using Attributes > Mesh > Surface, define a mesh using Thick Shell,Quadrilateral, Linear elements. Specify the spacing as 15 divisions in the local xand 9 divisions in the local y directions. Since only one Surface is present in themodel, the divisions for the mesh can be entered directly onto the Surface meshdialog.

4. With the cursor in normal mode assign the mesh to the Surface by draggingthe attribute from the Treeview onto the selected Surface.

5. To define a patch load that is coincident with the side-wall Surface, first selectthe four Points defining the Surface in the order they were defined. Choose themenu command Attributes > Loading > Discrete, click on the Patch tab, thenspecify a 4 node patch. Notice that LUSAS has filled the Point coordinates intothe patch coordinates.

The load direction coincides with the global Y axis direction so select Y from theUntransformed Load Direction. Specify patch corner load intensity values of-3, -3, -1, -1 respectively.

6. The defined patch uses a local coordinate system that is coincident to the globalCartesian axis system, so it can be assigned to the Point at the origin (Point 1).Assign the load to Point 1 (0,0,0). The Assign Leave all dialog entries as default.Press OK to assign the load.

7. Visualise the loading by selecting the loading attribute in the Treeview,clicking the right mouse button, then choosing Visualise from the shortcut menu.Note that the patch is drawn as discrete point loads. This is because the patchload is automatically split into point loads by LUSAS. .

8. The number of discrete loads in each direction is dependent on the numbers ofdivisions entered in the Assign Loading dialog. In this case, the default numberof divisions (4) is insufficient as there are insufficient loads to apply at least oneload per element along the culvert. To improve the load application accuracy,deassign the load from the Point, and reassign using 15 divisions in the local Xdirection. Leave the Y divisions field blank. Draw the load again. Note that


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LUSAS has automatically used the aspect ratio of the patch load to calculate asuitable number of divisions in local Y.

Hydrostatic Patch LoadDefault number of divisionsshowing insufficient discrete pointloads.

Hydrostatic Patch LoadIncreased number of divisions on assignment.The double arrow vector indicating patchorientation.

Processing Loads Outside the Search AreaPatch loads outside the search area are lumped onto the nearest edge of the searcharea


165

Patch Load DivisionsNumber of divisions in local x (div x)and y (div y) are specified at loadassignment. The load intensity is thensplit into individual load componentswith an associated area of application.

Patch Load Local CoordinatesThe local coordinate set is dependenton the order in which the coordinates ofthe patch vertices are defined.

SearchArea

Boundary

Area ofindividual Load

Application

Patch Loaddivs x = 6divs y = 5

1 2 3

5

4

67

8

X

Y

X

Y

1 2

567

8

1 2 3

4

34

Local X Projected LoadLoads in the local y projected region(dark area) are lumped at nearestloading positions within the search area(light area).

Local Y Projected LoadLoads in the local y projected region(dark area) are lumped at nearestloading positions within the search area(light area).

Search Area

Patch load

Search Area

Patch load


166

Local X and Y Projected LoadsLoads in the local x and y projectedregions (dark area) are lumped atnearest loading positions within thesearch area (light area).

Non-Projected LoadLoads not in the local x and yprojected regions (dark area) arelumped at nearest loading positionswithin the search area (light area).

Search Area

Patch load

Search Area

Patch load

Full Local X LoadLoads in the full local x region of thepatch (dark area) are lumped at nearestloading positions within the search area(light area).

Full Local Y LoadLoads in the full local y region of thepatch (dark area) are lumped at nearestloading positions within the search area(light area).

Search Area

Patch load

Search Area

Patch load

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Full LoadAll patch loads lying outside the searcharea (dark area) are lumped at nearestloading positions within the search area(light area).

Search Area

Patch load

Local Coordinate SystemsLocal Coordinate datasets define coordinate systems that differ from the defaultglobal Cartesian system. Local coordinate datasets are attributes and are definedfrom the Attributes menu. Local coordinate datasets have several uses in LUSAS:

q Feature Definition They may be defined and activated in order to entercoordinates in place of the global coordinate system. When a local coordinatesystem is active, alldialog entriesrelating to global X,Y and Z coordinateinput use thetransformed axis setas a basis for input.

q Transforming Nodal Freedoms When assigned to features theeffect is to transform the degrees of freedom on the mesh on those features.This has the effect of transforming the directions of applied global load andsupport conditions. In this example, global freedoms are transformed to radialdirections by assigning a cylindrical coordinate set to the Lines around thehole. This method oftransforming nodalfreedoms is only validfor small deflections,since the freedom

XZ

Y

P1 (0,0,0)

Global

P2 (10,3,0)

Global

x

z

y

Local Coordinate 1

Origin at P2,

Local X at P3

P3 (19,10.5,0)

Global

P4 (5,0,0)

Local 1


168

directions are not updated during analysis.

q Material assignments A local coordinate set may be used to alignorthotropic and anisotropic materials.

q Variations Thermal variations may be defined using functions in terms ofthe coordinate variations. The function may use alternative coordinates if alocal coordinate set is specified in the variation.

q Composites A local coordinate set may be used to align materialdirections in composite layups.

q Element Orientation May be used at the mesh assignment stage toorient beam and joint elements.

q Results Transformation When activated during post-processingresults can be output relative to the local coordinate set. For example, this isuseful when looking at local results for triangular elements, where axes arenot consistent.

Local Coordinate System TypesThree main types of local coordinate systems can be defined. All three types aredefined in LUSAS by indicating three positions in space defining a local Cartesianxy plane (origin, x axis, xy plane). The type of coordinate set selected will dictatehow features are defined based on the specified plane.

q Cartesian Based on standard X, Y and Z coordinates arbitrarily oriented inspace.

q Cylindrical Based on the axes of acylinder - radius, angle subtendedand distance along the cylinderaxis.

Coordinates of a Point are specifiedas (r, t, z), where

r is the radius perpendicular to thelocal z axis;

t is the angle in degrees measured from the positive x direction of the localxz plane, clockwise about the local z axis when looking in the positive zdirection;

z is the distance along the z axis.

Y

Zz

r

P1

t

2

1

3

X

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169

q Spherical Based on the axes ofa sphere defined by a radius,subtended tangential angle andsubtended angle around ameridian. Note that there is noequivalent spherical set in theLUSAS Solver so nodalfreedoms cannot be transformedusing this method.

Coordinates of a Point arespecified as (r, t, c), where:

r is the radius of the sphere on which the Point lies from the local origin;t is the angle in degrees measured from the positive x direction of the local

xz plane, clockwise about the local z axis when looking in the positive zdirection;

c is the angle in degrees measured from the positive z axis to the radius line

Defining Local Coordinate SystemsLocal coordinate datasets are defined from the Attributes Menu. Local coordinatesets are defined by specifying an origin and either a rotation about a global plane,rotation matrix or a scale factor (Cartesian only). They may also be defined by firstselecting 3 Points (to specify 3 required positions), then selecting Attributes > LocalCoordinate.

Note. Defining a new coordinate set does not automatically make it the active set,see Using Local Coordinate Sets below.

q Rotation about a global plane specifying angular rotations about theglobal planes, XY, YZ or XZ. When defining coordinate systems using thismethod, the local x axis is oriented parallel to the global X axis and rotatedinto position using the specified angle in the specified plane.

q Scale Factors specifying scale factors in all three global directions abouta specified origin. This method is only used to define local Cartesiancoordinate sets. Scale factor local coordinate sets can be used to scale a modelor portions of a model. See the case study below for more details.

q Rotation matrix specifying a direction cosine matrix.

q Rotation matrix from selected Points using a Cartesian set generated fromselected Points. Three Points define a cartesian set anywhere in space, twoPoints define a Cartesian set with the XY plane parallel to the global XYplane. 1st Point defines the origin, 2nd Point defines the positive direction of

c

Y

X

Zr

P1

t

1

2

3


170

the local x axis, 3rd Point defines the local xy plane. Note that the Cartesianset generated from Points can be changed to a cylindrical or spherical set.

Using Local Coordinate SetsThere are three ways of using a local coordinate set:

q By setting it as the active coordinate set. In order to use local coordinatesystems for entering coordinate values, the active coordinate set must bechanged from global Cartesian by selecting a local coordinate dataset fromthe geometry tab of the model Properties box.

q From the geometry by coordinates dialogs. When defining Points, Lines,Surfaces or Volumes by coordinates a different coordinate set to the active onemay be used. An option also exists to set the active set from the bycoordinates dialogs.

q By assigning a local coordinate set to geometry. To transform degrees offreedom, (as described above), the local coordinate set must be assigned tounderlying geometry by dragging a saved dataset from the Treeview ontothe geometric features.

Warning. There is no equivalent spherical set in the LUSAS Solver, thereforefreedoms cannot be transformed using this type of local coordinate system.

Visualising Coordinate setsThe active coordinate set is visualised on the graphics area by default, this can beswitched off from the Window properties. To display the Window properties double-click in the current window away from any features (i.e. in the space around themodel). Click on the View Axes tab to alter change the view axes settings.

Local coordinate sets assigned to features may be visualised in the same way as allattributes.

Case Study. Scaling a Model

Local coordinate systems defined by scale factors can be used to shrink or enlarge amodel. This case study will scale a model defined in mm units to metre units. Followthe procedure outlined below:

1. Load the model to be scaled. Next, create a command file using Files > Save as.Choose Command file from the Save as type, specify a suitable file name, forexample fullscale.cmd.

2. Start a new model using File > New.

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171

3. Define a local Cartesian coordinate set using Attributes > Local Coordinate.Select the Scale option. Enter scale factors in X, Y and Z of 1e-3 to scale frommm to metres. A scaling origin can be entered if any position other than theglobal Cartesian origin is required. OK the dialog.

4. Set the scaling local coordinate set as the active coordinate set from the Geometrytab of the model properties. (From the Treeview select the top level branch in the

layers tab, click the RH mouse button and select Properties from the shortcutmenu. Click on the Geometry tab.) OK the dialog.

5. Finally, read in the command file using File > Command File > Open,specifying the file in which the model was saved in step 1 above, for examplefullscale.cmd. As the command file replays, the model features are redefined atscaled coordinates.

Caution. The method outlined in the case study above should not be used if alocal coordinate system is already active in the model. If this is the case, it is better todefine a scale transformation and then move all the Points in the model using themove command. Higher order features will be updated also.

CompositesComposite datasets are used to represent the material characteristics that are formedby applying layers of differing materials in varying orientations and thicknesses.

Using Composite DatasetsComposite lay-up properties are defined from the Attributes Menu. Previouslydefined material datasets are combined in a composite property dataset, specifyingthe layer name, the relative thickness and the relative angle for each layer.


172

The composite dataset must then be assigned to Surfaces or Volumes, specifying theoverall composite orientation. Options for orientation are: Local Coordinate Set,Local Element Axes, Axes From Support Surface. Note that an angle of 0° alignswith the appropriate x axis and an angle of 90° with the y axis.

Tips

q Material directions may be used when viewing the results to display stresseson or off axis.

q Only Isotropic and Orthotropic materials can be used in composite lay-ups.q Orthotropic plane stress and orthotropic solid materials can be used for shell

composite lay-ups, but solid composites must use the orthotropic oranisotropic solid material model. Isotropic materials may additionally be usedin either.

q For shell elements an appropriate plane stress material model must be usedwhile for solid elements a 3D continuum model should be used (see theLUSAS Element Library).

q The lay-up sequence is from bottom to top. In the case of a shell this will bein the direction of the Surface normal. In the case of a solid this will be in thedirection of the local z.

q In the case of composites assigned to Volumes, nodal positions may be movedby LUSAS to correspond with layer positioning/thicknesses.

q In the case of composites assigned to Volumes, the number of layers mustcorrespond with the number of elements through the Volume.

q Composite datasets can only be used with Surfaces and Volumes that usecomposite elements.

q Composite datasets may not include materials that contain variations.q The layer thicknesses are relative and determine the proportion of the total

thickness (specified in geometric properties) apportioned to each layer.

Composite properties for Surface models can also be defined using the CACE-Drapesystem.

Composite Material Visualisation1. When defining a composite layup click on the Visualise button to display a

layered representation of the composite with annotations of layer orientationangle and material dataset number automatically included. This representationmay also be annotated to the screen if desired, to do so click on the CreateAnnotation button.

2. Once assigned to Surface or Volume features which have a mesh assigned, thecomposite material definition can be displayed in a number of ways using theAttributes layer .

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• Material Axes Material directions can be plotted in the form of anaxes set at any layer within a composite. For solids the axes set is placedat the top/bottom or middle of the selected layer, for shells the axes set isplaced on the centroid of the shell element. If no layer is specified (i.e.layer 0) the zero degrees fibre direction of the composite is drawn at theelement centroid. If a layer is specified the axes will only be drawn forelements with orthotropic or anisotropic material property types. If anelement has a material property in which material directions are not valid,a warning message is output.

• Layer Element/layer material directions and element layers can bedrawn in both pre- and post-processing models.

3. Note. Good use can be made of the LUSAS cycling facility, where featurelocal axes can be cycled relative to a reference feature to ensure a consistent set ofcomposite material axes.

Composite Post-ProcessingIt is often useful to change Results orientation to material directions to view theresults from a composite analysis. For shells, plates, membrane and solid elementsstresses and stress resultants can be displayed and printed in the element local andelement material directions. See Local and Global Results for more details.

When setting a results layer, LUSAS accepts the layer name in addition to the layernumber.

q Layer stresses are output by requesting output at Gauss points. All layers willthen be output.

q To get stresses for a shell layer, the layer must be set and results set to‘stresses’. If the results are set to Top/Middle/Bottom, then the results for theT/M/B of the element will be obtained, and the layer is not relevant.

q A layer of a solid composite element will act like a shell. Thus both stressresultants and T/M/B stresses can be obtained.

SlidelinesSlidelines are attributes which are used to model contact and impact problems, or totie dissimilar meshes together. They can be an alternative to joint elements orconstraint equations, and have advantages when there is no exact prior knowledge ofthe contact process. Their applications range from projectile impact, vehicle crashworthiness, the containment of failed components such as turbine blades, tointerference fits, rock joints and bolt/plate connections. Note. The slideline facilityis inherently nonlinear, except for tied slidelines used in an implicit dynamic orstatic analysis where the solution may be linear.


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Slidelines allow the definition of properties such as the stiffness scale factor, frictioncoefficient and pre-contact. They are assigned to corresponding pairs or groups offeatures, known as master and slave. This diagram shows a contact application usinga slideline with friction between two bodies and a tied slideline to join dissimilarmeshes without the need for stepped mesh refinement.

Tiedslideline

Tiedslideline

Frictionslideline

Slideline properties are defined from the Attributes > Slideline menu entry.

Slideline TypesThere are several different types of slide:

q Null used to perform a straightforward linear analysis ignoring the slidedefinition. Useful for performing a preliminary check on the model.

q No Friction used for contact analyses but ignores friction between the twosurfaces.

q Friction used for constant or intermittent contact or impact.

q Tied used to tie together two dissimilar meshes.

The tied slideline option eliminates the requirement of a transition zone inmesh discretisation comprising differing degrees of refinement and isextremely useful in creating a highly localised mesh in the region of highstress gradients.

q Sliding used for problems where surfaces are kept in contact, allowingsliding without friction.

The general slideline options may be utilised for modelling finite relativedeformations of colliding solids in two or three dimensions which involvesliding (with or without friction) and constant or intermittent contactconditions. The sliding only option is similar to the general sliding optionsbut does not permit intermittent contact conditions. The figure below showsthe use of both the general and the tied slideline options.

Slidelines

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Slideline Propertiesq Master/Slave interface stiffness scale factor Controls the amount of

interpenetration between the two slidelines. Increasing the stiffness scales willdecrease the amount of penetration between the slides, but may cause ill-conditioning. Recommended values:

Implicit/static solution 1.0 Explicit solution 0.1 Tied slidelines 100 to 1000 The scale factor should be increased slightly for slidelines involving rigid

wall contact.

Note. Scaling of the slideline stiffnesses is automatically invoked at thebeginning of each analysis if the ratio of the average stiffness values for eachconstituent slideline differ by a factor greater than 100. In this manneraccount is made for bodies having significantly different material properties.Option 185 will suppress this facility.

q Coulomb friction coefficient Only applicable for friction slidelines.

q Zonal contact detection parameter Controls the extent of the contactdetection test. The zonal detection distance for a slideline is taken as theproduct of the detection parameter and the longest segment found on bothslidelines. If the zonal contact detection parameter is less than 0.5, undetectedmaterial interpenetration may occur. To apply the refined contact detectiontest for every contact node, the parameter should be set to a large number. Forfurther information refer to the LUSAS Theory Manual.Explicit solution schemes (default = 5/9)Implicit/static solution schemes (default = 10/9)

q Slideline extension parameter Slideline extensions are continuations of aslideline segment beyond that of the original definition. The extensioneliminates interpenetration for slidelines which are significantly irregular.

q Close contact detection parameter The close contact detection parameter isused to check if a node is threatening to contact a slideline. The surfacetolerance used is the product of the detection parameter and the length of thesurface segment where the node is threatening to penetrate. If the distancebetween the surfaces is less than the surface tolerance a spring is included atthat point just prior to contact. By default, the stiffness of the spring is takenas 1/1000 of the surface stiffness. The inclusion of springs in this mannerhelps to stabilise the solution algorithm when surface nodes come in and outof contact during the iteration process. The close contact detection facility isnot available for explicit dynamics.


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Temperature DependencySelecting the Temperature dependent check box enables a reference temperature tobe attached to each slideline property allowing multiple properties to be used in aslide table to provide temperature dependence.

If temperature dependent properties are specified linear interpolation is applied tothe interface stiffness scale factors and the friction coefficient. The zonal contactdetection parameter and the slideline extension distance are unchanged wheninterpolation of temperature dependent properties is carried out.

Pre-contact ParameterPre-contact is used to overcome problems encountered when applying an initial loadto a discrete body which would be subjected to unrestrained rigid body motion. Thisprocedure is only applicable to static analyses and it is required when an initial gapexists between the slidelines and a loading is to be applied (other than PrescribedDisplacement).

The surfaces of a slideline are initiallybrought into contact under the actionof the applied loading and interfaceforces between the surfaces. Thisallows the surfaces of a slideline to bedefined with a gap between them andan automatic procedure is invoked tobring the bodies into contact to avoidunrestrained rigid body motion. The interface forces which bring the bodies togetheract at right angles to each surface. One of the surfaces must be free to move as arigid body and the direction of movement is dictated by the interface forces, appliedloading and support conditions. In the example above pre-contact is defined forslideline 1 but not for slideline 2.

Warning. Incorrect use of this procedure could lead to initial straining in thebodies or to an undesirable starting configuration. By selecting specific slidelines forthe pre-contact process (i.e. slidelines where initial contact is expected) minimuminitial straining will occur and more control over the direction of rigid bodymovement can be exercised.

Loadcase TitleSpecification of the loadcase allows the slide properties and type to be changedbetween load increments. The slideline properties need only be defined for loadcaseswhere there is a change in the definition. For example, if the slideline stiffnesschanges on loadcase 4 then slidelines need only be defined for loadcases 1 and 4,loadcases 2 and 3 taking the properties of loadcase 1.

2

1P

P

Slidelines

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Assigning SlidelinesSlides are defined by assigning the slideline dataset to the required Lines or Surfacesand specifying whether they are to be treated as Master or Slave slides. In general,the smaller of the two contact areas should be the slave.

Slideline Modelling Considerationsq Only the expected region of contact should be defined as a slideline surface

for tied slideline analyses.q Coarse mesh discretisation in the region of contact should be avoidedq Slides must be continuous and should not subtend an angle greater than

90 degrees. Sharp corners are best described by two separate slides.q Rigid target surfaces may be modelled by fully restraining the slideline

surfaceq The surface scale factors and friction coefficient are not utilised in explicit

tied slideline analysesq The nodal constraint slideline (explicit tied slideline) treatment is more robust

if the mesh with the greatest contact node density is designated the slavesurface.

q The use of a larger value of Young's modulus to simulate a rigid surface in adynamic contact analysis is not advisable since this will increase the wavespeed in that part of the model and give rise to a reduced time step. Thispractice significantly increases the computing time required.

q Do not converge on residual norm with PDSP loading. This norm usesexternal forces to normalise which do not exist with PDSP loading

q The use of tied slidelines to eliminate transition meshes is recommended forareas removed from the point of interest in the structure.

q Slidelines may be used with automatic solution procedures (constant loadlevel and arc-length methods). The line search and the step reductionalgorithms are also applicable to analyses that contain slidelines.

Using Slidelines with LUSAS ElementsThe slideline facility may only be used with the following elements:

Element Type Element Name

Plane Stress TPM3, QPM4, QPM4M, TPM3E, QPM4E

Plane Strain TPN3, QPN4, QPN4M, TPN3E, QPN4E

Axisymmetric TAX3, QAX4, QAX4M, TAX3E, QAX4E

Shell TTS3, QTS4

Solid TH4, PN6, HX8, HX8M, TH4E, PN6E, HX8E


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q When defining slidelines for use in implicit dynamics or static analyses linearcontinuum elements are recommended.

q Slidelines may be utilised with higher order elements (quadratic variation ofdisplacements). However, this is generally not recommended because it isnecessary to constrain the displacements of the slideline nodes so that theybehave in a linear manner (LUSAS Modeller will do this automatically).

Slideline OptionsOptions relating to slidelines are set from the Attributes tab of the ModelProperties, File menu.

Case Study. Metal Forming Analysis

Initial configuration. Deformed configuration.

Processing Slideline ResultsThe results from analyses involving slidelines may be processed in the same manneras other problems. However, extra information is available concerning theperformance of the slide and the results on the interface.

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Viewing Slideline Results

LUSAS automatically creates a group of every slideline used in the analysis. Toview results on the slideline alone make the whole model invisible (top level group)then make the slideline group visible. Use the right-click shortcut menu to makegroups visible or invisible .

Graph datasets can be generated containing the variation of slide variables throughan analysis (time or load increments) using the Graph Wizard.

Note. When looking at a deformed mesh plot of contact analysis results, theexaggeration factor should be set to unity to avoid a misleading visualisation.

Constraint EquationsA constraint can be defined to constrain the movement of a geometric or nodalfreedom. Constraint equations allow linear relationships between nodal freedoms tobe set up.

This facility allows the user to constrain plane surfaces to remain plane while theymay translate and/or rotate in space. Similarly straight lines can be constrained toremain straight, and different parts of a model can be connected so as to behave as ifconnected by rigid links. These geometric constraints are only valid for smalldisplacements. Constraint equations can also be used to model cyclic symmetry, forexample a single blade from a complete rotor may be modelled and then constrainedto behave as if it were part of the complete model. As constraint equations in LUSASrefer to transformed nodal freedoms, any local coordinate datasets assigned to thefeatures are taken into account during tabulation when the constraint equations areassembled.

Several different types of Constraint Equations can be defined from the Attributesmenu, grouped under the following types (described below):

q Displacement Controlq Geometricq Cyclicq Tied Mesh


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Displacement Controlq Specified Variable a nodal freedom takes

a specified value across all the nodes in theassigned features.In this example, a specified variableconstraint of Displacement in X directionwith value 1.0 is assigned to Point 1. Theunderlying node is then allowed to displaceonly by the specified distance in thespecified X direction.

P1

u=1.0

q Constant Variable used where a nodalfreedom value is constant but unknownacross all the nodes in the assignedfeatures.In this example, a constant variableconstraint of displacement in the Xdirection is assigned to Line 1. Theunderlying nodes move a constant amountin that direction.

L1

u=C

q Vector Path The nodes in the assignedfeatures may be constrained to movealong a specified vector defined by 2Points or by 2 sets of X, Y and Zcoordinates.In this example, vertical and horizontalvectors are used to restrict movement inthose directions. Note that the vectors areused purely to define a direction. Nodescan travel along a vector in eitherdirection.

Constraint Equations

181

Geometricq Rigid Displacements The nodes in the

assigned features may be constrained to berigid, the group of nodes may translateand/or rotate but their positions relative toone another remain constant. Onlytranslational displacements can beconstrained using this type of constraint.This type of constraint is only valid forsmall displacements.

Assigning a constraint of this type to Lineson either side of a gap, as in the exampleshown, maintains the underlyingundeflected node positions relative to eachother as if a rigid block were in placebetween the structures.

Gap=δδ

Gap=δδ

q Rigid Links A rigid link will create arigid fixity between two features. It issimilar to the Rigid Displacementsconstraint type, except that rotationalfreedoms are also constrained to be rigid.In the example shown here, the end of abeam is rigidly linked to the shell edgesaround a cylinder. The plane containingbeam and cylinder end will remain planethroughout the analysis.

q Planar Surface A surface may beconstrained to remain plane, the surfacemay translate and/or rotate but remainsplane. Nodal positions may vary relative toother nodes on the surface. This type ofconstraint is only valid for smalldisplacements. In this example, a planarSurface constraint is assigned to the topSurface to force the underlying nodes toremain planar during loading. Constrainednodes may move relative to each other aslong as they remain in plane.


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q Straight Line A straight line may beconstrained to remain straight, the linemay translate and/or rotate but will remainstraight. Nodal positions may vary relativeto other nodes along the line. Thisconstraint type is only valid for smalldisplacements. In the example shown, astraight Line constraint is assigned to Line3 to force underlying nodes to remain in astraight line relative to each other duringloading. Constrained nodes may movetogether or apart as long as they remain ina straight line.

L3

Cyclicq Cyclic Rotation Cyclic rotational

symmetry may be used to model a sectionfrom a continuous ring. The mesh on thetwo planes of symmetry may be different.In the example shown, the radial Lines aredefined as a Master and Slave pairmaintaining cyclic symmetry around thestructure. Meshes on the Master and SlaveLines need not match.

Master

Slave

q Cyclic Translation Cyclic translationalsymmetry may be used to model a sectionfrom a continuous strip. The mesh on thetwo planes of symmetry may be different.In the example shown here, Master andSlave Surfaces define start and finishpositions of repeating sections. Meshes onMaster and Slave need not match.

Master Slave

Tied Mesh

q Tied Mesh Specified Tied meshes may beused to force two sets of assigned featuresto move together in a similar manner totied slidelines. The meshes are tied alongMaster and Slave Lines to restrict relativemovement. The mesh on the two sets offeatures need not match. A search directionvector is defined to limit the mesh to which

Master

Slave

Vector

Thermal Surfaces and Heat Transfer

183

it is tied. A vector defines the direction inwhich the constraint is applied.

q Tied Mesh Normal Meshes tied alongMaster and Slave Lines to restrict relativemovement. The underlying nodes maintaintheir original relative positions underloading. Meshes on Master/Slave need notmatch. This form of tied mesh constraintuses a search direction normal to theMaster/Slave surfaces to detect the mesh towhich it is tied.

Master

Slave

Case Study. Using Constraint Equations

Differing meshes may be constrained to displace together in a similar way to a tiedslideline.

1. Define two Surfaces separated by a small gap using Geometry > Surface >Coordinates.

2. Mesh the Surfaces with Linear Plane Strain elements using different meshspacing on each Surface using Attributes > Mesh > Surface.

3. Define and assign a valid Material to the Surfaces and define and assignSupports and Load datasets so that the Surfaces are being forced towards eachother.

4. Define a normal tied mesh Constraint using Attributes > Constraint Equation> Tied Mesh. Assign it to the Lines on either side of the gap. One Line must beselected as a Master and the opposing Surface as a slave. If meshes on tied Lineshave different spacing, choose the Line containing the finer mesh as the master.

5. Run the model through LUSAS and use the plot file to view the deformed mesh.The constraint equations will have prevented one surface from passing throughthe other.

Thermal Surfaces and Heat TransferThe thermal surface facility in LUSAS allows thermal gaps, contact and diffuseradiation to be modelled. Thermal surfaces are used to model the thermal interactionof two distinct bodies, or two different parts of the same body through a fluidmedium.

q Thermal Gaps are used to model gaps between structures that arerelatively close together.

q Contact is used in a thermo-mechanical coupled analysis where contacttakes place and the contact pressure effects are then included in the analysis.


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q Diffuse Radiation is the process of heat transfer from a radiationsurface to the environment or to another thermal surface defining the sameradiation surface. Radiation is modelled by specifying radiative properties forthermal surfaces.

Thermal Surfaces are the thermal equivalent of structural slidelines. They aredefined from the Attributes menu, and are assigned and manipulated in the sameway as all attributes, see Manipulating Attributes.

Heat TransferThermal Surfaces work in conjunction with Thermal Gaps, Radiation Surfacesand Surface Properties, defined from the Utilities > Heat Transfer menu. They areutilities meaning they can be used in the definition of thermal surfaces but notassigned to features.

q Surface Properties Gap conductance, Contact conductance, Environmentand Radiation.

q Thermal Gaps Thermal gaps are used to model heat transfer across a gapand heat transfer by contact when a gap is deemed to have closed. If theseeffects are required, a thermal gap dataset must be specified during definitionof a thermal surface.

q Radiation Surfaces Diffuse radiation exchange may be modelled with aradiation surface that is defined by any number of thermal surfaces. Planes ofsymmetry that cut through the radiation enclosures may be defined so that itis not necessary to model the whole structure. Radiation surfaces allow for thecalculation of diffuse view factors. These view factors may be output to a printfile.

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185

Radiation Surface

Contact

Gap

Heat transfer across a gap.

Heat transfer between twocontacting Surfaces(includes slideline contactpressure effects, so can onlybe used in a coupled analysis).

Environment

Radiation

Heat transfer to the environment(convection and conduction).

Heat transfer by radiationexchange.

Utilities > Heat Transfer> Radiation Surface...

Controls heat transferfrom body to body overlarge distances (whereradiation is dominant).

Thermal Surface

Attributes > ThermalSurface...

Used to associated heattransfer properties withparts of the model.

Thermal Gap

Utilities > Heat Transfer> Thermal Gap...

Controls heat transferfrom body to body inclose proximity (whereconduction andconvection are dominant).

Surface Properties

Utilities > Heat Transfer >Surface Properties ...

Assign tofeatures

The thermal surface definition process is shown in the above table. Environment andRadiation thermal properties are referred to directly in the thermal surface definition.Gap and contact thermal properties are used to define a thermal gap dataset which isthen referred to in the thermal surface definition. A radiation surface pair, can bereferenced from the thermal surface definition to control heat transfer from one bodyto another over large distances where radiation is dominant.

Choosing Thermal PropertiesThe following flowchart guides the decision making process for choosing thermalproperties. The process is simplified if the analysis only considers a single body,when only environmental thermal properties are required. For analyses wherediscrete (multiple) bodies are considered, factors such as body proximity and whetherthe bodies are touching, or are likely to touch during the analysis, become importantand the choice of thermal properties changes. Follow a route through the flowchartbelow and define your thermal surfaces using the properties given in the shaded box.


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Are the bodies closetogether (conduction and

convection effectsdominant)?

Is the structure made upof discrete bodies?

Are the bodies touching(include pressure

effects)?

Start Here

No

Yes

Thermal Surface +Thermal Properties

(Environment)or Environmental Loading

No

Thermal Surface +Thermal Properties

(Radiation)+Radiation Surfaces

Yes

Yes

No

Thermal Surface +Thermal Properties (Gap + Contact) +

Thermal Gap +Coupled Analysis

Thermal Surface +Thermal Properties (Gap) +

Thermal Gap

Environmental Nodes (LUSAS datafile)Environmental nodes may be used to represent the medium which separates thethermal surfaces between which heat is flowing. As the length of a link directlyconnecting two surfaces increases, the validity of the assumed flow becomes moretenuous. Alternatively, instead of forming a link, heat could flow directly to thesurroundings, but in this case, the heat is lost from the solution. This, in some cases,is a poor approximation to reality, particularly when the thermal surfaces form anenclosure. In this instance an environmental node can be used to model theintervening medium, with all nodal areas which are not directly linked to other areaslinked to the environmental node. The environmental node then re-distributes heatfrom the hotter surfaces of the enclosure to the cooler ones without defining the exactprocess of the transfer.

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187

Note. Environmental nodes cannot be defined in LUSAS Modeller, and must beedited directly into the LUSAS data file if required. See the Data Syntax Manual,Thermal Surfaces for further information.

Radiation OptionsRadiation options are set from the Model Properties dialog. Available options are:

q Temperatures Input and Output in Degrees Celsius [242](Model properties, Attributes tab). Changes the temperature units from thedefault of Kelvin to degrees Celsius.

q Suppress Recalculation of View Factors in CoupledAnalysis [256] (Model properties, Solution tab, Thermal options). Turnson/off the view factor recalculation. The option should be turned off when theradiation surface geometry is unchanged by the structural analysis. This stopsrecalculation of the view factors.

Processing Thermal Surface ResultsThe results from analyses involving thermal surfaces may be processed in the samemanner as other problems. However, extra information is available concerning theperformance of the thermal surface and the results on the interface.

Viewing Thermal surface ResultsLUSAS automatically creates a group of every thermal surface used in the analysis.To view results on the thermal surface alone make the whole model invisible (toplevel group) then make the thermal surface group visible. Use the right-click shortcutmenu to make groups visible or invisible .

Graph datasets can be generated containing the variation of slide variables throughan analysis (time or load increments) using the Graph Wizard.

Retained FreedomsRetained Freedoms are used to manually define the master freedoms for use in thefollowing analyses:

q Guyan reduction eigenvalue analysisq Superelement analysis

Retained Freedom datasets are defined from the Attributes menu. They contain thedefinition of the master and slave degrees of freedom and are then assigned to thefeatures with the master nodes.


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Full Subspace Iteration 20 Masters

15 Masters 10 Masters

5 Masters

Damping PropertiesThis facility is used to define the frequency dependent Rayleigh dampingparameters for elements which contribute to the damping of the structure. Viscous(modal) and structural (hysteretic) damping can be specified. If no damping datasetsare specified the properties are taken from the material properties (click on dynamicproperties).

Damping properties are usually required when distributed viscous and/or structuraldamping factors are required for Modal Damping control. A Modal dampinganalysis is performed as part of an eigenvalue analysis.

Defining Damping PropertiesLUSAS structural or viscous damping properties are defined from the Attributesmenu and assigned to features in the usual way. Mass and stiffness Rayleighdamping parameters are linked with the corresponding reference circular frequencyvalue at which they apply in a damping properties dataset. If more than one set ofdamping values is defined in a damping table, linear interpolation is used tocalculate damping values at intervening frequencies.

Birth and Death

189

Birth and DeathBirth and death enables the modelling of a staged construction process (e.g.tunnelling), whereby selected elements are activated and deactivated as thesimulation process requires. Birth and death datasets are defined from the Attributesmenu, and are assigned and manipulated in the same way as other attributes.

If an element is deactivated, all stresses/strains are set to zero and the magnitude ofthe stiffness matrix is reduced so that the element has negligible effect on thebehaviour of the residual structure. The main difference between deactivating anelement and assigning very weak material properties to an element is the way inwhich the internal forces that may exist in that element are processed. Of course, ifan element is deactivated from the outset there will be no difference but ifdeactivation occurs as the analysis progresses there will probably be internal stressesassociated with the element.

Percent to RedistributeThe deactivate command provides control over the way in which these internalforces are processed by specifying how much of the internal forces should beredistributed:

q Zero Redistribution 0% of the internal forces in a deactivated elementmay be redistributed in the system (if this is prescribed in a static analysis,and the load remains constant, the stress contours, displacements etc. in theother elements will remain unchanged).

q Full Redistribution 100% of the internal forces in a deactivatedelement may be redistributed in the system (this has the same effect as re-assigning very weak material properties to the element).

q Fractional Redistribution A percentage of the internal force to beredistributed is specified. Provides a solution which is part way between thetwo extremes.

Any remaining internal equilibrating force associated with a deactivated element ismaintained in the system until the element is subsequently activated. When anelement is activated it is assumed that the element has just been introduced to themodel (although all elements must be defined at the outset). The current (deformed)geometry for that element is taken as the initial geometry and the element is assumedto be in a stress/strain free state (unless initial stresses or strains are defined). Allinternal forces that exist in the element are redistributed and the computed strainsare incremented from the time at which the element becomes active.


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Tunnel Excavation Stage 1Top layer of soil deactivated and liningactivated. Lining and soil elementsduplicated in the model.

Tunnel Excavation Stage 2Second layer deactivated as soilexcavated. Surrounding lining elementsactivated.

Liningconstructed

Soilexcavated

Liningconstructed

Soilexcavated

Tunnel Excavation Stage 3Remaining second layer soil elementsdeactivated.

Tunnel Excavation Stage 4Supporting soil pillar removed and toplining activated.

Soilexcavated

Liningconstruction

Soilexcavated

Tunnel Excavation Stage 5Final central soil column removed.

Soilexcavated

Birth and Death

191

Equivalent Stresses in Surrounding Material

Equivalent Stresses in Tunnel Lining

Using Birth and Death DatasetsActivate and deactivate datasets are defined from the Attributes menu. The datasetsare assigned on a feature basis to control the history of the underlying elementsthroughout the analysis. The load case is specified during assignment to indicate atwhat point the elements are added or removed.

Notes on useq Elements cannot be activated and deactivated in the following circumstances:

• Field analyses

• Explicit dynamics analyses


192

• Fourier analyses

• When using updated Lagrangian or Eulerian geometric nonlinearity

• When they are adjacent to slidelinesq Deactivation and activation can take place over several increments if

convergence difficulties are encountered.q Deactivated elements remain in the solution but with a scaled down stiffness

so that they have little effect on the residual structure. The stiffness is scaleddown by a parameter which can be changed by the user. In a dynamic analysisthe mass and damping matrices are also scaled down by the same factor.

q When an element is deactivated, all loads associated with that element areremoved from the system and will not be re-applied if an element issubsequently re-activated. This includes concentrated nodal loads unless theload is applied at a boundary with an active element. The only exception tothis rule is a prescribed displacement which may be applied to a node ondeactivated elements. Accelerations and velocities may also be prescribed in adynamic analysis but this is not recommended.

q If required, initial stresses/strains and residual stresses may be defined for anelement at the re-activation stage.

q The activation of an element which is currently active results in aninitialisation of stresses/strains to zero, an update of the initial geometry tothe current geometry and the element is considered to have just becomeactive. The internal equilibrating forces which currently exist in the elementwill immediately be redistributed throughout the mesh. This provides asimplified approach in some cases.

q The direction of local element axes can change during an analysis whenelements are deactivated and reactivated. In particular, 3-noded beamelements that use the central node to define the local axes should be avoidedas this can lead to confusion. For such elements the sign convention forbending moments for a particular element may change after re-activation (e.g.it is recommended that BSL4 should be preferred to BSL3 so that the 4thnode is used to define the local axes and not the initial element curvature).

q Care should be taken when deactivating elements in a geometricallynonlinear analysis, especially if large displacements are present. It may benecessary to apply prescribed displacements to deactivated elements in orderto attain a required configuration for reactivation.

q It should be noted that the internal forces in the elements will not balance theapplied loading until all residual forces in activated/deactivated elements havebeen redistributed.

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193

Nodal EquivalencingThe equivalence facility is used to merge coincident nodes on otherwise unconnectedfeatures. If an equivalence dataset is assigned to any features LUSAS willautomatically equivalence the required nodes after meshing has been carried out.

There are several ways equivalencing can be set up to work:

q By assigning equivalence tolerances to certain features - only these featureswill be equivalenced, all other are ignored.

q By switching on the Automatic tolerancing, and accepting the defaulttolerance - all features are equivalenced according to the default tolerance.

q By switching on the Automatic tolerancing, and assigning other equivalencetolerances to certain features - all features are equivalenced according toeither the an assigned tolerance or the default tolerance.

In this example, Surfaces 1 and 2 donot share a common boundary Line,therefore the nodes created on theircommon boundaries will not be joinedand must be equivalenced. Node 2becomes node 1 if both δu and δv areless than the equivalence tolerance.

S1 S2

1

2

L1

L2

δu

δv

For a grillage, created with Linesspanning boundary to boundary, asshown in the above example, internalnodes on the Lines will not be commonto both longitudinal and transversemembers even when mesh divisionscause nodes to have identicalcoordinates. All Lines must thereforebe equivalenced.

δz

Using Nodal EquivalencingEquivalence datasets are defined from the Attributes menu, See About Attributes.They are defined as a tolerance, which is used to determine whether nodes areconsidered to be coincident.


194

The equivalence dataset is assigned to the features that are to be checked forcoincident nodes. When an equivalence dataset is assigned to a lower order feature itwill search through all higher order features for nodes to be checked. For example,in order to equivalence two Volumes at their boundaries, it is more efficient to assignthe equivalence to the Surfaces on the boundaries, as a smaller number of nodes needto be checked.

Automatic EquivalencingAutomatic equivalencing can be activated from the Meshing tab of the modelProperty box. This will equivalence all features in the model on meshing if they arewithin the default equivalence tolerance, or within an assigned tolerance. Note.Remeshing occurs each time a new command is issued, but a forced remesh ispossible from the command line. Automatic equivalencing can be time consumingfor models with a large number of nodes.

Visualising Nodal EquivalencesDisplays the features which have a specified equivalencedataset assigned to them in a chosen colour and line style.

In this example different equivalence tolerances areassigned to different parts of a model to merge morecoarsely or finely as required. Using visualisation, thelines to which the equivalence dataset is assigned can behighlighted. Equivalenced nodes can also be displayed asthey are removed (see below). In this diagram they areshown using the square symbol.

Summary

q Nodal equivalencing is useful when creating grillage structures whereunconnected longitudinal and orthogonal lines result in duplicate nodes.

q More than one equivalence dataset may be defined in order to rationalisemore than one section of the model independently.

q More than one equivalence dataset can be assigned to a feature to equivalenceit within a different subset of the model.

q A check for unconnected elements and nodes can be performed using anoutline mesh plot, (Mesh layer properties), or by checking for duplicate nodenumbers, (Label layer properties), .

q Nodal equivalencing may be used to position a point load or support at a node(which is not a defining feature Point). A Point must be created, the load orsupport assigned, and the Point and meshed feature equivalenced.

EQV1

EQV2

Search Areas

195

q Equivalencing may be used to merge nodes on the constituent Lines ofcombined Lines i.e. the entire combined Line may be equivalenced, includingthe Lines forming it.

Case Study. Removing Duplicate Nodes on Grillage Members

When a grillage is defined by a network of lines, two nodes will lie at each point atwhich the lines cross. In order to model the grillage correctly these pairs of nodesmust be merged into one node so that the grillage elements are connected.

1. Define a grillage using a series of criss-crossing Lines and mesh the Lines usingthe Engineering Grillage element. Take care to specify your mesh divisions sothat internal nodal positions on longitudinal and transverse members arecoincident.

2. Define an equivalence dataset with a suitable tolerance using Attributes >Equivalence. Nodes whose X, Y and Z coordinate lies within this tolerance ofeach other will be joined as one.

3. Assign the equivalence dataset to all the Lines in the model.4. Re-set the mesh using the syntax for the Force Remesh of Model command.5. Draw the mesh and node labels. If duplicates still exist, adjust the equivalence

tolerance and re-mesh the model.

Search AreasSearch areas may be used to restrict the area of application of discrete loads (pointand patch). This is useful for several reasons:

q Improved Control of Load Application the search area willeffectively limit the area over which the load is applied so that the effect ofloads on certain features may be removed from the analysis. For 3D models,where general loading is applied, it is possible that a chosen projecteddirection will cross a model in several locations. A search area is thereforeused to limit the application of load to one of these multiple intersections.

Restricting the area of application of discrete loads allows the same loaddatasets to be used to apply loads to different parts of the model.

q Speed Improvement the speed of calculation of equivalent nodal loadswill be increased by cutting down the number of features considered in thecalculation.


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In the example shown, a multiple spangrillage structure is defined with Span 1as the search area. A discrete Patch load,indicated by the grey shaded region in theupper diagram, is applied across thewhole structure, Span 1 and 2. The areaof the structure coinciding with both theSearch Area and the patch load will takethe load as shown in the lower diagram.

Tip. Search areas should be used if themodel is three dimensional and discreteloads are applied, for example box-section or cellular construction decks.

Defining and Assigning Search AreasSearch areas are defined from the Attributes Menu then assigned to the requiredfeatures, (Lines or Surfaces only). Control of application of load lying outside thesearch area is available when the load is assigned, see Assigning Discrete Loads. If asearch area dataset is not specified when the load is assigned, all of the highest orderfeatures, excluding volumes, in the model will be used as a default search area. Validsearch area configurations are shown below.

Rules for Creating Search AreasThe following general guidelines should be noted when defining a search area on amesh.

Overhanging elementsdefined such that onlyone side of a cell ismissing are included inthe search area, asshown in the left sidediagram.

Elements cannot be included in the search area when they overhang from the samenode, as shown in the right side diagram. In this case, dummy Lines can be addedwith ‘none’ type element mesh assignments to close the bay to make the search areavalid.

Search Area

Span 1Loaded

Span 2Unloaded

HALoad

ValidSearchAreas

Invalid: 2 edgesoverhanging fromsame node

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Cells of more than 4 edges aresubdivided into triangles (leftdiagram), but overhangingelements are only included ifdivided by no more than one edge(invalid left, valid right). There isno limit to the number of edgesthat may hang over the mainbody if the overhanging members are only separated by one edge (right).

Varying Attributes over FeaturesThe variation dataset allows values in Material, Geometry, Loading and Supportdatasets to be varied over a feature in a number of ways by defining the manner inwhich the chosen entity will vary. If a variation is not used the individualcomponents within an attribute, such as Young's modulus within a material dataset,are considered to be constant over a feature, which results in the definition of a largenumber of features to accurately describe the required variation. The variationfacility allows these analysis requirements, and many more, to be easily defined.

Depending on the type of variation defined, both continuous and discontinuousvariations can be modelled. Three different types of variation dataset can be defined.These are:

q Field allowing variation in terms of the global Cartesian coordinate systemvariables. This form of variation would be used for hydrostatic and windloading and is applicable to all feature types except Points. Variations onvolumes are limited to field variations.

q Interpolation variations may be applied to Lines and Surfaces. Thevariation is defined by interpolating between values at specified featuredistances. The order of the interpolation may be specified as constant, linear,quadratic and cubic in either actual (local) or parametric distance.

q Function variations are expressed as symbolic functions in terms of theparametric coordinates of a feature. They can be applied to Lines andSurfaces. For Lines, the parametric distance is the distance along the Line(u), and for a Surface the distances are the local x and y coordinates expressedas u and v.

Using Variation datasetsVariations are defined from the Utilities menu. Variation datasets are stored in theUtilities Treeview .

Invalid:overhangingedges separatedby 2 edges

ValidSearch

Area

ValidSearchAreas


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Once defined, a variation can be used in a Loading, Material, Geometry, Support orDamping dataset by clicking on the variation button in an edit box of anyparameter on the dialog. This way, different parameters can be varied in differentways by applying different variation datasets to them.

Notes on Varying AttributesIt is possible to apply variations to Loading, Geometry, Material, Support andDamping datasets. A variation dataset will apply to a particular parameter, forexample WZ in a uniformly distributed load or Young's modulus in an elasticisotropic material dataset.

q Loading It is possible to vary all load types except General Point andPatch loads and Element Point and Distributed loads, which incorporatevariable loading implicitly in their definition. Values of loads which areapplied to elements will be evaluated at the element centroid. Contouring iscarried out on an element by element basis and is available in pre-processingonly.

q Geometry Datasets containing a variation are tabulated as multipledatasets. An additional parameter is added to the assignment command torelate to the original defining dataset number for use in post-processing.Contouring is carried out on an element by element basis and is available inpre-processing only.

q Material Variations in materials are limited to elastic material values andcertain joint properties. Datasets containing a variation are tabulated asmultiple datasets containing the material value calculated at the elementcentroid. An additional parameter is tabulated to the assignment data chapterin the LUSAS data file to relate to the original defining dataset number foruse in post-processing. Contouring is carried out on an element by elementbasis and is available in pre-processing only.

q Supports Only spring stiffness values can be varied. In post-processingspring stiffness values are not scaled when drawn.

q Damping Variations of the Rayleigh parameters cannot be contoured asthey are calculated at element centroid positions.

Field VariationsField variations allow a variation according to a mathematical expression in terms ofcoordinate variables in either the global Cartesian or a specified local coordinatesystem. Coordinates may be Cartesian, cylindrical or spherical.

Field variations are applicable to Lines, Surfaces and Volumes and the value of thevariation at any position on the structure will be calculated by substituting the valuesof the coordinate variables at that position.


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A field variation is defined by specifying a field expression and an optional localcoordinate dataset number, which will be used to specify a coordinate system otherthan the global Cartesian set. Specifying a local coordinate number of zero willdefault to the global Cartesian set.

These examples (right)show field variationsexpressed in terms of theglobal X coordinatedisplayed along a Lineparallel to the global X axis.The typical field expressionsused are shown in the boxesnext to each diagram.

For example, a fieldexpression in Cartesiancoordinates would typicallybe:

-9.81*y

and in cylindrical coordinates:

10+r*tan(thetax)

Coordinate Systems in Field VariationsFunctions and variables used in field expressions are limited to those used in theparametric language plus the Cartesian, cylindrical and spherical coordinate variablenames. The coordinate variable names that should be used in a field expression aredependent on the type of coordinate systems in use. Definitions are given in thetables starting below. SeeLocal coordinate systems formore information.

In this example (right), a fieldexpression referring to theglobal axis coordinates (XY),is also used with a localcoordinate axis set (indicatedby xy) to create a variationrelative to a rotated system.Cylindrical and spherical axissets can also be used.

F=A+Bx

F=Sin(x)

F=x**n

F=Ax

Field Variationin Global AxisSystem

Field Variationin Local AxisSystem

x

X

Y

y

F=A+BX

F=A+Bx

X=0.25 X=0.75

x=0.75

x=0.25


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Cartesian (global/local) X Cylindrical (local) X Spherical (local)

x X coordinate x Distance alongcylinderlongitudinal axis

r Radial distance

y Y coordinate r Radial distance thetax Angle about x axis

x Z coordinate thetax Angle about axis ofcylinder

thetac Second angle

Z Cylindrical (local) Z Spherical (local)

r Radial distance r Radial distance

thetaz Angle about axis ofcylinder

thetaz Angle about z axis

z Distance alongcylinderlongitudinal axis

thetac Second angle

Cylindrical and spherical field variation expressions can use radians (default) ordegrees to specify angles. If trigonometric functions are used in a field expression,they will dictate what angular measure is used. For example, a function will usedegrees if degree-based trigonometric functions, such as sind, cosd, tand andatan2d are used. An expression may not mix radian and degree functions. Any anglecut-off values will use the same units as the expression.

Maximum and Minimum Cut-Off ValuesMaximum and minimumcut-off values may bespecified for the chosencoordinate system. Thisallows the range ofapplication of load to belimited, such as would benecessary to model astructure not whollysubmerged in water. Theseexamples (right) show fieldvariations in terms of theglobal X coordinatedisplayed along a Line parallel to the global X axis. The typical field expressionsused are shown in the boxes next to each diagram. All expressions are subject to acut-off in minimum and maximum X at parametric distances of 0.25 and 0.75respectively.

F=Sin(x)

F=A+Bx

F=x**n

F=Ax

[0.25] [0.75]


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This example shows a variation in terms of the global Z axis coordinate withminimum and maximum cut-offs at specified Z coordinate values.

X

Z

Field Variation in termsof global Z coordinate

Variation subject tocut-offs in global Z

Maximum Zcut-off

Minimum Zcut-off

Case Study. Applying Hydrostatic Loading

A hydrostatic loading may be modelled using a combination of a field variation anda Structural Face Loading. The loading can be considered to be dependent on thedepth varying as: water density*g*(h-y) where g is the acceleration due to gravity, his the height of the water above the structure origin and y is the height of thestructure. Use the following procedure:

1. Define a simple 100 unit square Surface using Geometry > Surface > ByCoordinates and entering the following coordinate (0,0,0), (100,0,0),(100,100,0) and (0,100,0).

2. Define a simple thin shell mesh using Attributes > Mesh > Surface. Assign themesh to the Surface.

3. Define a field variation using Utilities > Variation > Field and specify afunction of density*g*(h-y), where density is the water density (1000), g isacceleration due to gravity (9.81), h is the maximum height of the water abovethe structure origin (80) and y is the global Cartesian y coordinate. This functionwill apply a hydrostatic loading down the depth of the Surface (global y axis).Enter 1000*9.81*(80-y) on the dialog.

To model a water depth of 80 (and to avoid negative loading above the surface ofthe water), select a Cut-off in Maximum y at 80. Click on the Advanced buttonand set the maximum second coordinate to 80. Click the OK button.


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Give the dataset a suitable name. Type Hydrostatic variation into the dataset box.Click the OK button.

4. Using Attributes > Loading > Structural, define a Local Distributed loadentering the Z component as 1, notice that in doing so the variation button appears. Click on the button and select the Hydrostatic variation dataset. Thiswill factor a negative unit load using the variation defined in 1. Type Water loadinto the dataset box. Click the OK button. Assign the loading to the Surface.

5. The applied loading with the variation isvisualised as arrows on the model. Use the

dynamic rotate to get a 3D perspective ofthe surface.

If the load is not visualised, select the loaddataset in the Treeview , right-click andchoose Visualise from the shortcut menu. Note.Visualising attribute assignment requires thatthe model is meshed.

Line Interpolation VariationsLine variations by interpolating are defined by a series of pairs of distances, and thevalues to be interpolated between at those distances. The specified interpolationvalues may in turn reference field variation datasets. Discontinuous variations can bedefined in this way.

q By EqualDistancesdefines a set ofinterpolation valuesat a specifiednumber of equaldivisions along aLine. If n divisionsare specified, n+1interpolation valuesare required.

In the examplesshown right, anumber of equaldivisions arespecified along with

Quadratic2 Divisions4;3;4

Multiple Quadratic4 Divisions4;1;3;2;4

Cubic3 Divisions4;1;3;4

Linear4 Divisions4;1;3;2;4

4.0

1.03.0

2.0

4.0


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interpolation values for the end and internal interpolation positions. For n divisions, n+1 interpolation values must be specified. Discontinuities

cannot be defined using this method apart from those indicated at the junctionof separate quadratic variations.

q By UnequalDistancesdefines a set ofinterpolation valuesat a specified set ofdistances along aLine. Distances canbe entered as actualor parametricvalues.

The examplesshown right usedistances specifiedby actual orparametric values(indicated in squarebrackets) with acorrespondinginterpolation valueat each position.

Quadratic variations require a minimum of 3 interpolation values withmultiple quadratic variations being defined for 5, 7, 9 sets of interpolationvalues.

Repeating a coordinate and specifying an additional associated interpolationvalue will allow a discontinuity in the variation to be modelled. See thediscontinuous linear variation example above. The discontinuity tolerance isused to separate adjacent points within a variation at a discontinuity so as toavoid multiple values being present at an underlying node.

Quadratic[0;0.3;0.5]4;3;4

Cubic[0;0.3;0.5;1]4;1;3;4

Linear[0;0.3;0.5;1]4;1;3;4

4.0

1.0

3.02.0

4.0

200 [1.0]

140 [0.7]

100 [0.5]

60 [0.3]

Actual [parametric]distances

DiscontinuousLinear [0;0.3;0.5;0.5;0.5;0.7;1]4;1;3;2;4


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Line Function VariationsA Line function variation is defined by a series of pairs of distances, and thesymbolic functions at those distances and beyond. The function is a mathematicalfunction in terms of the parametric or actual coordinate along the Line. For a Linefunction variation, the value of the variation at any point on the Line is calculated byfinding the interval in which the point occurs and then substituting the parametric orlocal distance into the function.

q By Equal Distances [in u] defines a number of equal divisions and aset of functions (one for each division) in terms of u, the parametric distancealong the Line.

In this example,the Line is splitinto a specifiednumber ofdistances, eachwith an associated function.

q By Unequal Distances [in u] defines a series of parametric or actualdistances, and a set of functions. The distance specified is the starting pointfor the function associated with it. Each distance must have an associatedfunction specified. To enter a maximum cut-off point, associate a zerofunction with it.

In this example, adistance of 0 isassociated withfunction 0, 0.33 isassociated withu**2 and 0.92 isassociated with 2.

Surface Interpolation VariationsOn Surfaces, interpolation may be defined by either a grid of values or a set of linevariations which are to be applied to the boundary Lines and interpolated between.For interpolation by grid the order may be constant, linear, quadratic or cubic andthe grid values supplied are interpolated between.

q Surface By Grid defines a full grid of interpolation values by specifyingnumbers of equal divisions in Surface local X and Y directions andinterpolation values at each resulting grid position. Surface grid interpolationcan only be used on 3 and 4 sided Surfaces. For irregular Surfaces, thevariation can be supplied by a support Surface.

F=u**2 F=2F=0

u=0 u=0.33 u=0.92

F=-1.0+2*u F=0 F=-1.0+2*u F=0


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Care must be taken to supply the correct number of interpolation values forthe type of interpolation chosen (see table below). Values are specified alongthe local X axis first, then along each line of grid positions parallel to the xaxis in turn. Interpolation order can be different in each direction.

Order Number of Divisions (n) Interpolation Points

Constant Automatically set to 1 1

Linear No restriction n + 1

Quadratic Minimum of 2 (or 4 or 6 ...) n + 1

Cubic Minimum of 3 (or 4 or 5 ...)

n + 1

This example(right) showssimple Quadraticvs. Linear Surfacegrid variation. Thequadratic variationin the local Xdirection isspecified with 2divisions (3interpolation points). The constant variation in the local Y direction requiresno additional points. A total of 3 interpolation points are required.

This secondexample shows acubic vs. linearSurface gridvariation. Thelocal X directiontakes a cubicvariation definedwith 3 divisions (4interpolationpoints) and thelocal Y direction takes a linear variation using 2 divisions and 3 interpolationpoints. A total of 12 interpolation points are required.

q Surface By Boundary defines a set of interpolation values byspecifying variation datasets around the Surface boundary Lines. A variationmust be specified for each Line in the Surface definition. If no variation isrequired along a Line, a constant order variation must be specified. Care mustbe taken to ensure that interpolation values at corner points are common toboth variation datasets meeting there otherwise strange results may occur.

Local X Quadratic2 Divisions (3 Points)

1

2

3

Local Y Constant1 Division (1 Point)

12

34

56

7810

9

1112

Local Y (Linear)2 Divisions (3 Points)

Local X (Cubic)3 Divisions (4 Points)


206

Variations are defined in the same direction on opposite sides of the Surface(see the following example) and use the Line order in the Surface definitionon which to base the variation direction. Individual Line directions have noeffect on variation directions.

This exampleshows aSurfaceboundaryinterpolationusing threeLineinterpolationdatasets. AdiscontinuousLineinterpolation(1) is specified for first and third Lines. Note that the Surface axes drawn heredictate the variation directions and that opposite sides of a Surface will varyin the same direction whatever the underlying Line directions indicate.

The second and fourth Lines in the Surface definition use constantinterpolation datasets. The variation sense is denoted by double and singlearrows shown on boundary Lines. The variation along the local X axis(signified by the double arrow) is specified first. The Surface variation in thiscase is 1;3;1;2.

Note. When variations are defined, distances may be defined by Points on a Line,as a number of divisions, or as a series of parametric or local distances. However, avariation is only stored in terms of parametric distances. Therefore, the values usedto define a variation can only be filled into the dialog when editing an existingdataset by using the unequal distance method.

Same Variation AsFirst Line (1) Line

InterpolationConstant (2)Value = 3

Line InterpolationDiscontinuous Linear(1) Values =4-5, 3-2, 4-3

LineInterpolation(3) ConstantValue = 4


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Surface Function VariationsA Surface function variation consists of asingle function in terms of the parametriccoordinates of the Surface u and v. Thevalue of the variation at any point on theSurface is given by finding the parametriccoordinates of the point within theSurface and substituting them into thespecified function. Surface functionvariations are only allowed for 3 and 4sided Surfaces.

The example shown here defines a variation using the function max(4,10*u) interms of the local Surface x direction parametric distance. The max function takestwo arguments and returns the maximum of both arguments. In this case, 4 is themaximum value until u exceeds 0.4.

Plotting Graphs of Variation DatasetsVariation datasets can be evaluated asdatasets and displayed using theLUSAS Graph Wizard from theUtilities menu. The variations can beevaluated along a specified Line bycreating a pair of datasets (distance andvariation) which can subsequently beplotted. A number of points at which tosample the variation can be specified.For variations that have more than oneinterval, the variation is evaluated atthe specified number of points on eachinterval. A factor may be applied to thevariation value before the dataset coordinates are calculated. This exampledemonstrates the graphical visualisation of a discontinuous Line interpolationvariation.

uv

VariationMax(4,10*u)

5.000

4.000

3.000

2.000

1.000

0.0000.0 0.2 0.4 0.6 0.8 1.0


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Influence LinesAn influence line is a physical break in the finite element mesh at a node. Additionalparameters define the behaviour of the structure around the influence node. Theinfluence type may be a force, reaction or displacement.

Defining Influence LinesInfluence lines may be defined from the Utilities menu. A single node must beselected for which the influence curve is required. Note. The Force type influence isonly available if a node and an element have been selected with the mouse, and anelement may also be added to selection memory to define element axes.

Influence Line Parametersq Freedom type defines the direction of the influence line: U, V, W, THX,

THY, THZ.

q Displacement direction defines the direction of the influence nodedeflection. A negative displacement direction will produce a negativedisplacement in the chosen axes direction.

Influence axes can be specified as:

q local (via a previously defined coordinate dataset)q globalq the axes of an element in memory selection

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209

The influence type may be specified as a force (moment), reaction or displacement:

q Force (Moment) breaks the mesh and defines constraint equations tofix the displacements and rotations of the nodes at the break, apart from thedisplacement in the force direction at which a unit relative displacement isimposed. A moment influence curve is produced by breaking the mesh at thespecified node and then defining constraint equations to fix the displacementsand rotations of the nodes at the break, apart from the rotation in the momentdirection at which a unit relative rotation is imposed. If the specified node isattached to more than two elements, then the elements defined by the node atwhich the break is required must also be selected before using the command.

q Reaction defines constraint equations to impose a unit displacement orrotation in the specified direction.

q Displacement for unit forces or moments applied at nodes.

Manipulating Influence LinesDefined Influence lines are stored in the Utilities Treeview and may bemanipulated from here using the right-click shortcut menu.

Writing a Datafile with Influence LinesOnce the correct influence datasets have been defined, they are tabulated to a LUSASdata file using the Files > LUSAS DataFile, then specifying the datafile type as aInfluence Line analysis. Data file names are generated from the specified file nameand the influence dataset number. For example, if the specified file name is root,then files root1.dat and root2.dat will be created for influence line datasets 1 and 2respectively.

Load CasesLoad cases are used differently during the modelling stage and the results processingstage.

q Modelling load cases (pre processing) contain the load assignments and theanalysis control. The order of the load cases in the Treeview defines the orderin which the load case are solved by the LUSAS Solver.

A model may be specified as a load curve problem from the Solution tab ofthe model properties.

q Results load cases (post processing) contain the results from an analysis.They exist in the Treeview but cannot be edited. Results load cases may bemanipulated using combinations and envelopes, fatigue loadcases and IMDloadcases. All of which are added as new load cases in the Treeview.


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Manipulating Load CasesLoad cases are contained in the Treeview ,.At least one load case always exists. New loadcases may be added to the Treeview using theUtilities menu. Double-clicking on a load casewill display the properties for editing, exceptresults load cases.

General editing commands are available byright-clicking a load case. The followingcommands are available for all (results loadcases have reduced commands):

q Delete Attribute assignments must be deassigned before a load case can bedeleted. A load case cannot be deleted if it is the first load case or the activeload case.

q Rename Sets the Load case title. Note. Load cases are tabulated in the orderlaid out in the Treeview.

q Remove Deassigns attributes from the load case, by choosing from a list ofattributes.

q Set active Sets the active load case for the current window. See below.

q Properties Displays the properties relating the a load case. Double-clickingthe load case also displays the properties. See below.

Setting the Active Load CaseAn important concept in LUSAS is the active load case in the current window. Theactive load case a window property, and is the load case that all results will comefrom when visualising results. This speeds up the process of comparing results byusing different windows for each load case to be compared.

The active load case is set from the Treeview using the shortcut menu. A black dotnext to a load case indicates the active load case.

Load CurvesLoad curves can be used to describe the variation of the applied loading in nonlinear,transient, dynamic and Fourier analyses. For example, in a transient thermalproblem the loading changes with time, and in a nonlinear problem the loading levelmay vary with load increment.

Load curves are used to simplify the input of load data in situations where thevariation of load is known with respect to a certain parameter. An example of this

Load Curves

211

could be the dynamic response of a pipe to an increase of pressure over a givenperiod. The data input would consist of the definition of the load and its variationwith time.

Using Load Curves1. Specify a Load Curve Problem

A model is specified as a load curve problem by clicking on Load Curves in theSolution tab of the Model properties, then click on the Set Control button to definethe analysis control.

Load curves scale all loads in the specified load case. Therefore, to scale loads usingdifferent load curves they must be assigned to different load cases. Further loadcurves may be added using the Utilities, Load case menu.

2. Define the Load Curve Properties

The load curve is made active by setting the load case properties, right-click on aload case and choose Properties from the shortcut menu.

A load curve is defined either using a sine, cosine or square wave input, or using adefined Variation.

q Sine, cosine, square wave input Values for peak (amplitude), frequency andphase angle must be defined along with activation and termination points.

q Variation dataset curve A line interpolation variation must be defined usingthe Utilities, Variation, Line menu command, and referenced on the loadcase properties. The dependent variable in the variation dataset will representtime or increment number depending on the type of analysis, and the value ofthe variation will be the factor by which to scale the values in the loadingdataset.

Notes

q When load curves are used, load cases cease to be analysed sequentially,instead they are used merely to allow load curves to reference different loaddatasets.

q Load curves are only applicable to nonlinear, transient, dynamic and Fourieranalyses.

q For Fourier analysis the load must only be applied over an angular range of 0to 360 degrees.

Evaluating a Load CurveLoad curves (and variation datasets) may be viewed using the Graph Wizard.


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Case Study. Pressurisation of Two Tanks with Multiple Load Curves

Two tanks are to be pressurised at different stages of a nonlinear dynamic analysis.This will be achieved using two different load cases and two load curves to vary theloads individually. The following procedure outlines the steps required:

1. Define 2 variation datasets which give the correct pressure variation with time.Use the Utilities, Variation, Line menu entry. Specify an Interpolationvariation, Actual distance type and enter coordinate pairs for load factor andtime values on each graph.

2. Click on File, Model Properties and go to the Solution tab. Set model to a LoadCurve Problem (checkbox), then click on the Set Control button. From theanalysis control dialog click on the nonlinear checkbox. Click on the transientcheckbox and choose dynamic from the drop-down list. OK the dialogs.

3. Using Utilities > Load Case add a second load case. Go to the load caseTreeview and double-click on the first load case. Click on the Activecheckbox, then specify the first variation dataset from the dataset list. Entersuitable activation, termination and increment values which will be used at thetabulation phase to define the curve. These curves can be evaluated usingUtilities, Graph Wizard.

4. Using Attributes, Loading, Structural, define 2 Face Load datasets containingthe pressure loads for each tank. Note that the pressure values entered in the loaddefinition will be multiplied by the load factors used on the load curve associatedwith it.

5. Finally, assign these loads to thefeatures in the model, specifyingdifferent load cases for each tank.For example assign load 1 to tank1 using load case 1, and load 2 totank 2 using load case 2. Theaccompanying diagram shows aschematic of the tanks underinternal pressure with theircorresponding force versus timegraphs.

P1 P2

F1 F2

t t

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