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Finite Element Analysis (FEA) provides a reliable numerical technique for analyzing engineering designs. The process

starts with the creation of a geometric model. Then, the program subdivides the model into small pieces of simple

shapes (elements) connected at common points (nodes). Finite element analysis programs look at the model as a

network of discrete interconnected elements.

The Finite Element Method (FEM) predicts the behavior of the model by combining the information obtained from all

elements making up the model.

Meshing is a very crucial step in design analysis. The automatic mesher in the software generates a mesh based on a

global element size, tolerance, and local mesh control specifications. Mesh control lets you specify different sizes of

elements for components, faces, edges, and vertices.

The software estimates a global element size for the model taking into consideration its volume, surface area, and

other geometric details. The size of the generated mesh (number of nodes and elements) depends on the geometry

and dimensions of the model, element size, mesh tolerance, mesh control, and contact specifications. In the earlystages of design analysis where approximate results may suffice, you can specify a larger element size for a faster

solution. For a more accurate solution, a smaller element size may be required.

Meshing generates 3D tetrahedral solid elements, 2D triangular shell elements, and 1D beam elements. A mesh

consists of one type of elements unless the mixed mesh type is specified. Solid elements are naturally suitable for

bulky models. Shell elements are naturally suitable for modeling thin parts (sheet metals), and beams and trusses are

suitable for modeling structural members.

This section discusses the following topics:

Solid,Shell, andBeamMeshing

Meshing Parameters

Meshing Options

Controlling the Mesh

Contact Options for Structural and Thermal Studies

Mesh Quality Checks

Probing the Mesh Plot

Meshing Failure Diagnostics

Meshing Tips

Background on Meshing

Page 1 of 1Background on Meshing

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In meshing a part or an assembly with solid elements, the software generates one of the following types of elementsbased on the active mesh options for the study:

Draft quality mesh . The automatic mesher generates linear tetrahedral solid elements.

High quality mesh. The automatic mesher generates parabolic tetrahedral solid elements.

Linear elements are also called first-order, or lower-order elements. Parabolic elements are also called second-order,or higher-order elements.

A linear tetrahedral element is defined by four corner nodes connected by six straight edges. A parabolic tetrahedralelement is defined by four corner nodes, six mid-side nodes, and six edges. The following figures show schematicdrawings of linear and parabolic tetrahedral solid elements.

In general, for the same mesh density (number of elements), parabolic elements yield better results than linearelements because: 1) they represent curved boundaries more accurately, and 2) they produce better mathematicalapproximations. However, parabolic elements require greater computational resources than linear elements.

For structural problems, each node in a solid element has three degrees of freedom that represent the translations inthree orthogonal directions. The software uses the X, Y, and Z directions of the global Cartesian coordinate system informulating the problem.

For thermal problems, each node has one degree of freedom which is the temperature.

Solid Mesh

Linear solid element Parabolic solid element

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When using shell elements, the software generates one of the following types of elements depending on the activemeshing options for the study.:

Draft quality mesh. The automatic mesher generates linear triangular shell elements.

High quality mesh. The automatic mesher generates parabolic triangular shell elements.

A linear triangular shell element is defined by three corner nodes connected by three straight edges. A parabolictriangular element is defined by three corner nodes, three mid-side nodes, and three parabolic edges. For studiesusing sheet metals, the thickness of the shells is automatically extracted from the geometry of the model.

To set the desired option for a study, right-click the Meshicon, select Create Mesh, and expandAdvanced .

Shell elements are 2D elements capable of resisting membrane and bending loads.

For structural studies, each node in shell elements has six degrees of freedom; three translations and three rotations.The translational degrees of freedom are motions in the global X, Y, and Z directions. The rotational degrees offreedom are rotations about the global X, Y, and Z axes.

For thermal problems, each node has one degree of freedom which is the temperature.

Shell Mesh

Linear triangular element Parabolic triangularelement

Sheet metal model Shell mesh created at mid-surface

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NOTE: For drop test studies only, sheet metal parts mesh with solid elements.

The software generates a shell mesh automatically for the following geometries:

Sheet metals with uniform thicknesses. Sheet metals mesh with shell elements, except for drop test

studies. The software assigns the thickness of shell based on sheet metal thickness. You can edit thedefault shell definition before running the study, except thickness.

Surface bodies. Surface bodies mesh with shell elements. The software assigns a thin shell formulation to

each surface body. You can edit the default shell definition before running the study.

NOTES:

The program automatically creates a mixed mesh when solid and surface or sheet metal geometries are

included in the same model.

A reasonably fine draft quality mesh gives results that are generally similar to results obtained from a high

quality mesh with the same number of elements. The difference between the two results increases if themodel includes curved geometry.

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Beam elements can resist bending, shear, and torsional loads. The typical frame shown below is modeled with beamselements to transfer the load to the supports. Modeling such frames with truss elements fails since there is nomechanism to transfer the applied horizontal load to the supports.

Beam elements require defining the exact cross section so that the program can calculate the moments of inertia,neutral axes and the distances from the extreme fibers to the neutral axes. The stresses vary on the cross-section andalong the beam.

Consider a small segment along a beam element subjected to simplified 2D forces ( axial force P, shearing force V,and bending moment M):

In a general case 3 forces and 3 moments act on the segment.

Uniform axial stress = P/A (similar to truss elements)

Uniform shearing stress = V/A

The bending moment M causes a bending stress that varies linearly with the vertical distance y from the neutral axis.

Bending stress (y) = My/I

where I is the moment of inertia about the neutral axis.

The bending stress is the largest at the extreme fibers. In this example, the largest compression occurs at the top fiber

Beams

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and the largest tension occurs at the extreme bottom fibers.

Joints

A joint is identified at free ends of structural members and at the intersection of two or more structural members. TheEdit JointPropertyManager provides a tool to help you define joints properly. The program creates a node at thecenter of the cross section of each joint member. Due to trimming and the use of different cross sections for differentmembers, the nodes of members associated with a joint may not coincide. The program creates special elements nearthe joint to simulate a rigid connection based on geometric and material properties.

Material Properties

The modulus of elasticity and Poisson's Ratio are always required.

Density is required only if gravitational loads are considered.

Restraints

You can apply restraints to joints only. There are 6 degrees of freedom at each joint. You can apply zero or non-zero

prescribed translations and rotations.

Bonding

In a study with beams, solids and shell surfaces, you can bondbeams and beam joints to solid and shell faces.

Bonding between touching structural members with a surface or sheet metal face is automatically created.

Loads

You can apply:

Concentrated forces and moments at joints and reference points.

Distributed loads along the whole length of a beam.

Gravitational loads. The program calculates gravitational forces based on the specified accelerations anddensities.

Meshing

Beam and truss members are displayed as solid cylinders regardless of their actual cross-section shape. A structuralmember is automatically identified as a beam and meshed by a number of uniform elements so you can view the

variation of deformation and stresses along the length of the member.

Results

Results for each element are presented in its local directions. There is no averaging of stresses for truss and beamelements. You can view uniform axial stresses, torsional, bending stresses in two orthogonal directions (dir 1 and dir2), and the worst stresses on extreme fibers generated by combining axial and bending stresses.

A beam section is subjected to an axial force P and two moments M1 and M2 as shown below:

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The software provides the following options for viewing stresses:

Ax ial : Uniform axial stress = P/A

Bending in local direction 1: Bending stresses due to M2. This is referred to as Bending Ms/Ssin theplot name, title, and legend.

Bending in local direction 2: Bending stress due to M1. This is referred to as Bending Mt/Stin the plotname, title, and legend.

Click hereto learn about beam directions.

Worst case: The software automatically calculates the highest stresses at a critical point on the cross-section by combining axial and bending stresses due to M1 and M2. This is the recommended stress to

view.

In general, the software calculates 4 stress values at the extreme fibers of each end. When viewing worstcase stresses, the software shows one value for each beam segment. This value is the largest in magnitudeout of the 8 values calculated for the beam segment. These values are accurate for beam with cross-sectionsthat are symmetric in two directions. These values are conservative for other cases.

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You set meshing options for studies using solid, shell, and mixed mesh. Beam studies do not use thisPropertyManager.

The mesh that the software generates depends on the following factors:

Active meshing options for the study (specified in the MeshPropertyManager)

Mesh control specifications

Contact conditions defined in the Connectionsfolder

NOTES

When you create a new study (StudyPropertyManager), it inherits the default meshing options set in the

Meshpage of the Default Options tab. You can modify the meshing options for each study in the MeshPropertyManager. If you create a duplicate of a study, the new study inherits the meshing options of thesource study.

Meshing options are essential factors in determining the quality of the results. Results based on differentoption settings should converge to each other, i f an adequately small element size is used.

To modify the meshoptions for a study, right-click the Meshicon in the Simulation study tree, select CreateMesh, and expandMesh Parameters andAdvanced .

Mesh Quality

Sets the mesh quality:

Draft.Each solid element will have 4 corner nodes only. Each shell element will have 3 corner nodes.

High. Each solid element will have 10 nodes: 4 corner nodes and one node at the middle of each edge (atotal of six mid-side nodes). Each shell element will have 6 nodes: 3 corner nodes and 3 mid-side nodes.

It is highly recommended to use the Highquality option for final results and for models with curvedgeometry. Draft quality meshing can be used for quick evaluation.

Jacobian points. Sets the number of integration points to be used in checking the distortion level oftetrahedral elements. You can select 4, 16, 29points orAt Nodes. See the Mesh Quality Checkssectionfor more details.

The software performs Jacobian check by default for high quality mesh. It is recommended to use theAtNodesoption when using the p-method to solve static problems.

Mesher type

Sets the preferred meshing technique to be used.

Standard mesh. Activates the Voronoi-Delaunay meshing scheme for subsequent meshing operations.This mesher is faster than the curvature- based mesher and should be used in most cases.

Default Options - Mesh

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Curvature based mesh. Activates the Curvature-based meshing scheme for subsequent meshingoperations. The mesher creates more elements in higher-curvature areas automatically (without need formesh control). For assemblies, the mesher requires setting the globalbond option to incompatible. Ifcomponentcontact features are created, they should also specify incompatible bonding.

Curvature-based mesh is always compatible for touching or partially touching edges of sheet metal bodiesand surface bodies.

Min number of elements in a circle. Sets the minimum number of elements the mesher creates atcurvatures.

See how the element size is determined

Show advanced options fo r contact set definitions (No penetration and shrink fi t only). Whenselected, the contact options are displayed in the Contact SetPropertyManager underAdvanced . If thisoption is not selected, the software applies by default a node to surface contact type to all contact setdefinitions.

Mesher Options (for Standard Mesher)

Sets mesh options for the standard mesher.

Automatic transit ion. When checked, the program automatically applies mesh controls to small features,holes, fillets, and other fine details of your model. UncheckAutomatic transit ionbefore meshing largemodels with many small features and details to avoid generating a very large number of elementsunnecessarily. Example1| Example2

Automatic tr ials for solid. Instructs the program to automatically retry to mesh the model using a differentglobal element size. You control the maximum number of trials allowed and the factors by which the globalelement and tolerance are scaled for each trial.

Number of trials. Sets the maximum number of mesh trials.

Global element size factor for each trial. Factor by which the new global element size ismultiplied to calculate the new global element size.

Tolerance factor for each loop. Factor by which the new tolerance is multiplied to calculate thenew tolerance.

Remesh failed parts wi th incompatible mesh. If selected, the software tries to use incompatible meshingfor bonded bodies that fail compatible meshing. Used for solid mesh only.

Automatic shell surface re-alignment for non-composite shel ls . When selected, the softwareautomatically realigns the shell surfaces (non-composites) so that all bottom/top faces have uniformorientation. If this option is not selected, you may need to flip the misaligned shell surfaces manually.Select the desired faces, right-click the Meshicon in the Simulation study tree and select Flip ShellElements.

Mesher Options (for Curvature Based Mesher)

Sets mesh options for the alternate mesher.

Min number of elements in a circle. Sets the minimum number of elements on a full circle. The maximumangle for any element is 360 divided by the specified number. The limits are 4 and 36.

To set default meshing opt ions for new studies:



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1. Click Simulation, Options, Default Options, Mesh.

2. Specify the desired settings.

3. Click OK.

To modify meshing options for a study:

1. In the Simulation study tree, right-click the Meshicons and select CreateMesh.

2. Specify the desired settings under Mesh ParametersandAdvanced

3. Under Options select Save setting without meshing, or Run (solve) the analysis.

4. Click



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Mesh control refers to specifying different element sizes at different regions in the model. A smaller element size in aregion improves the accuracy of results in that region. You can specify mesh control at vertices, points, edges, faces,and components. Mesh control is not available for beams.

To access the Mesh ControlPropertyManager, right-click the Meshicon and selectApply Mesh Contro l.

Mesh Control Parameters

The mesh control parametersare:

Element size (e) for the specified entities

Element growth ratio (r)

Assuming that the element size used for meshing an entity is (e), the average element size in layers radiating from the

entity will be: e, e*r, e*r2, e*r

3, ...., e*r

n. If the calculated average element size of a layer exceeds (E), where (E) is the

Global Size , the program uses (E) instead. The mesh radiates from vertices to edges, from edges to faces, fromfaces to components, and from a component to connected components.

To apply mesh control to mixed types of entities:

1. In the Simulation study tree, right-click the Meshicon and selectApply Mesh Cont ro l.

The Mesh ControlPropertyManager appears.

2. In the graphics area, select the entities for which you want to apply mesh controls.

3. Under Control Parameters, do the following:

a. Select a unit and type a value in the Element Sizebox .

b. Type a value in the Ratiobox .

4. Click .

To apply mesh control t o multiple components:

1. In the Simulation study tree, right-click the Meshicon and selectApply Mesh Cont ro l.

The Mesh ControlPropertyManager appears.

2. Click the FeatureManager design tree tab .

3. In the FeatureManager flyout, select the components to which you want to apply mesh control.

The selected components appear in the Selected Entitieslist box.

4. Under Selected Entities, select Use per part size.

Mesh Control Parameters

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The software assigns an optimum element size for mesh control to individual components based on theirvolume. Move the Mesh Densityslider towards Coarseto increase the element size by a factor of 2, ortowards Fineto decrease the element size by a factor of 0.5.

5. Click .

Related Topics

Component Mesh Control

Examples of Mesh Control

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Meshing Options are essential factors in determining the quality of the mesh and hence the results. Results based ondifferent preference settings should converge to each other if an adequately small element size is used. Meshingoptions are not used for beams.

You can set the Meshqualityto Draftor High. A draft quality mesh does not have mid-side nodes. Draft quality canbe used for quick evaluation and in solid models where bending effects are small. High quality mesh is recommendedin most cases, especially for models with curved geometry.

The Standardmesher uses the Voronoi-Delaunaymeshing scheme for subsequent meshing operations. This mesheris faster than the Curvature basedmesher and should be used in most cases. Try the Curvature based mesheronlywhen the standard mesher keeps failing. The Curvature based meshersupports mesh control on components, facesand edges.

The Jacobian points whenMesh quality is set toHigh sets the number of points to be used in checking thedistortion level of high order tetrahedral elements.

For high order shells, the Jacobian checkuses 6 points located at the nodes.

Automatic transit ionautomatically applies mesh controls to small features, details, holes, and fillets. UncheckAutomatic transit ionbefore meshing large models with many small features and details to avoid generating a verylarge number of elements unnecessarily.

Automatic tr ials for solids instructs the mesher to automatically retry to mesh the model using a smaller globalelement size. You control the maximum number of trials allowed and the ratio by which the global element size andtolerance are reduced each time.

Remesh failed parts with incompatible mesh. Using this option can help mesh bonded solids that fail compatiblemeshing. IfAutomatic loopingis on and bonding solids using compatible mesh is requested, the software tries

incompatible meshing automatically for solids that fail to mesh with the compatible option.

Setting the color for plotting the bottom faces of shell elements helps you align shell elements properly.

Setting the meshing Options

Meshing Options

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The quality of mesh plays a key role in the accuracy of the results. The software uses two important checks tomeasure the quality of elements in a mesh.

Aspect Ratio Check. For a solid mesh, numerical accuracy is best achieved by a mesh with uniformperfect tetrahedral elements whose edges are equal in length. For a general geometry, it is not possible tocreate a mesh of perfect tetrahedral elements. Due to small edges, curved geometry, thin features, andsharp corners, some of the generated elements can have some of their edges much longer than others.When the edges of an element become much different in length, the accuracy of the results deteriorates.

The aspect ratio of a perfect tetrahedral element is used as the basis for calculating aspect ratios of otherelements. The aspect ratio of an element is defined as the ratio between the longest edge and the shortest normaldropped from a vertex to the opposite face normalized with respect to a perfect tetrahedral. By definition, theaspect ratio of a perfect tetrahedral element is 1.0. The aspect ratio check assumes straight edges connecting thefour corner nodes. The aspect ratio check is automatically used by the program to check the quality of the mesh.

Jacobian Points. Parabolic elements can map curved geometry much more accurately than linear

elements of the same size. The mid-side nodes of the boundary edges of an element are placed on theactual geometry of the model. In extremely sharp or curved boundaries, placing the mid-side nodes on theactual geometry can result in generating distorted elements with edges crossing over each other. TheJacobian of an extremely distorted element becomes negative. An element with a negative Jacobiancauses the analysis program to stop.

The Jacobian check is based on a number of points located within each element. The software gives you a choiceto base the Jacobian check on 4, 16, 29Gaussian points orAt Nodes.

It is recommended to set Jacobian checktoAt Nodeswhen using the p-method to solve staticproblems.

The Jacobian ratio of a parabolic tetrahedral element, with all mid-side nodes located exactly at the middle of thestraight edges, is 1.0. The Jacobian ratio increases as the curvatures of the edges increase. The Jacobian ratio ata point inside the element provides a measure of the degree of distortion of the element at that location. Thesoftware calculates the Jacobian ratio at the selected number of Gaussian points for each tetrahedral element.Based on stochastic studies it is generally seen that a Jacobian Ratio of forty or less is acceptable. The softwareadjusts the locations of the mid-side nodes of distorted elements automatically to make sure that all elements passthe Jacobian check.

For high order shells, the Jacobian checkuses 6 points located at the nodes.

To set the Jacobian check options fo r a study:

1. In the Simulation study tree, right-click the Meshicon and select Create.

2. ExpandAdvanced .

3. Specify the number of points for Jacobian points.

4. Under Options, select Save settings without meshingto save the options without meshing or clickto save the options and mesh the model.

Mesh Quality Checks

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When you mesh a study, the software meshes all unsuppressed solids, shells, and beams:

Use Solidmesh for bulky objects.

Use Shell elements for thin objects like sheet metals.

Use Beamor Trusselements for extruded or revolved objects with constant cross-sections.

For assemblies, check component interference. To detect interference in an assembly, click

Tools, Interference Detection. Interference is allowed only when using shrink fit. The Treatcoincidence as interferenceand Include multibody part interferencesoptions allow you todetect touching areas. Theses are the only areas affected by the global and component contactsettings.

You can also find touching faces by right-clicking the Connectionsfolder and selecting Find contactsets.

Compatible meshingis more accurate than incompatible meshing in the interface region. Requestingcompatible meshing can cause mesh failure in some cases. Requesting incompatible meshing can result insuccessful results. You can request compatible meshing and select Remesh failed parts withincompatible meshso that the software uses incompatible meshing only for bodies that fail to mesh.

If meshing fails, use the Failure Diagnosticstool to locate the cause of mesh failure. Try the proposed

options to solve the problem. You can also try different element size, define mesh control, or activateEnable automatic loop ing for solids .

The SolidWorks Simplifyutility lets you suppress features that meet a specified simplification factor. In the

Simulation study tree, right-click Meshand select Simplify Model for Meshing . This displays theSimplifyutility.

Simplification of geometry can alter stress results significantly.

It is good practice to check mesh options before meshing. For example, the Automatic transit ioncanresult in generating an unnecessarily large number of elements for models with many small features. Thehigh quality and Standard mesher are recommended for most cases. TheAutomatic loopingcan helpsolve meshing problems automatically, but you can adjust its settings for a particular model. TheAl ternate

mesher automatically uses smaller element sizes in regions with high curvature.

To improve results in important areas, use mesh control to set a smaller element size. When meshing an

assembly with a wide range of component sizes, default meshing results in a relatively coarse mesh forsmall components. Component mesh controloffers an easy way to give more importance to the selectedsmall components. Use this option to identify important small components.

For static studies, you can use the h-adaptivemethod to refine the mesh automatically.

Meshing Tips

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When you mesh a study, the software meshes all unsuppressed solids, shells, and beams:

Use Solidmesh for bulky objects.

Use Shell elements for thin objects like sheet metals.

Use Beamor Trusselements for extruded or revolved objects with constant cross-sections.

For assemblies, check component interference. To detect interference in an assembly, click

Tools, Interference Detection. Interference is allowed only when using shrink fit. The Treatcoincidence as interferenceand Include multibody part interferencesoptions allow you todetect touching areas. Theses are the only areas affected by the global and component contactsettings.

You can also find touching faces by right-clicking the Connectionsfolder and selecting Find contactsets.

Compatible meshingis more accurate than incompatible meshing in the interface region. Requestingcompatible meshing can cause mesh failure in some cases. Requesting incompatible meshing can result insuccessful results. You can request compatible meshing and select Remesh failed parts withincompatible meshso that the software uses incompatible meshing only for bodies that fail to mesh.

If meshing fails, use the Failure Diagnosticstool to locate the cause of mesh failure. Try the proposed

options to solve the problem. You can also try different element size, define mesh control, or activateEnable automatic looping for solids .

The SolidWorks Simplify utility lets you suppress features that meet a specified simplification factor. In the

Simulation study tree, right-click Meshand select Simplify Model for Meshing . This displays theSimplify utility.

Simplification of geometry can alter stress results significantly.

It is good practice to check mesh options before meshing. For example, the Au tomat ic transit ioncanresult in generating an unnecessarily large number of elements for models with many small features. Thehigh quality and Standard mesher are recommended for most cases. TheAutomat ic loopingcan helpsolve meshing problems automatically, but you can adjust its settings for a particular model. TheAl ternate

mesher automatically uses smaller element sizes in regions with high curvature.

To improve results in important areas, use mesh control to set a smaller element size. When meshing an

assembly with a wide range of component sizes, default meshing results in a relatively coarse mesh forsmall components. Component mesh controloffers an easy way to give more importance to the selectedsmall components. Use this option to identify important small components.

For static studies, you can use the h-adaptivemethod to refine the mesh automatically.

Meshing Tips

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In many cases, you may want to know the numerical value of the plotted field at a particular location. Use the probetool to display the numerical value of the plotted field at the closest node or element's center to the point of clicking.You can graph the results or save them to a file.

To probe a result plot at selected locations:

1. Activate the desired plot.

2. Click Probe (Simulation Result Tools toolbar) or Simulation, Result Tools, Probeor right-click the

plot in the Simulation study tree and select Probe .

3. In the PropertyManager, under Options, selectAt Locat ion.

4. Select locations on the model and view the results in the graphics area and under Resultsin thePropertyManager.

5. Click .

To probe a result plo t at sensor locations:




3. In the PropertyManager, under Options, select From Sensors. You must first define sensorsbefore thisoption becomes active.

4. Under Results, select a sensor name from Sensor List.

5. View the results in the graphics area and under Resultsin the PropertyManager.

6. Click .

When probing results from sensor locations defined at coordinates, the location of the nearest node isused instead of the exact location of the sensor.

To probe a result plot on selected entities:




3. In the PropertyManager, under Options, select On selected sntities.

4. Under Results, select entities for Faces, Edges, Vertices and click Update.

Probing Results

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5. View the results in the graphics area and under Resultsin the PropertyManager.

6. Click .

Related Topics

Probing Mesh Plots

Probing Section Plots

Graphing Probed Results

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You can probe section plots on the faces cut by a section plane. The software uses linear interpolation to calculate thevalue.

To probe a section plo t:

1. Create a section plotof the desired result on the undeformed shape of the model.

2. Click Probe (Simulation Result Tools toolbar) or Simulation, Result Tools, Probe.

3. In the PropertyManager, select a probing method under Options.

4. Select locations on the faces cut by the section plane and view the results in the graphics area and underResultsin the PropertyManager.

5. Click .

Probing Section Plots

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