Time History Analysis Parameters

Use this dialog to set up Time History Analysis parameters for a dynamic case.

Access

1. Ensure that a modal analysis has already been defined.2. Click Analysis   Analysis Types   New.3. Select Time History in the Analysis Type dialog, and then

click OK.

Dialog elements

Case

The name of the load case.

Method

The list of methods that you can use to perform the time history analysis.

Newmark method. Modal decomposition: Default value. Hilber-Hugues-Taylor. Newmark method (acceleration).Note: The modal decomposition method does not take into account loads in the form of a forced displacement, velocity, or acceleration of supports. If you want to include these loads in the time history analysis, you must select either the Hilber-Hughes-Taylor method or the Newmark (acceleration) method.Damping

Opens either of the following dialogs, depending on the selected method.

The Damping dialog allows you to determine detailed damping values of individual vibration modes for the modal decomposition method.

the Rayleigh Damping dialog allows you to determine Rayleigh factors for the Newmark and the Hilber-Hughes-Taylor (HHT) methods.Note: If you want to use the Hilber-Hughes-Taylor (HHT) method, you must specify the alpha coefficient.

Time

Time step - The step of time variable for which the results are stored.

Division - The number of time step divisions defining the storage frequency of analysis results.

End - The end value of time variable for which the analysis is carried out.

Note:If a method other than modal decomposition is selected, then the number of time step divisions (time step of saving results) is specified in the Division field to define the time step of integration. The time step of integration equals Time step / Division. When the division value equals 1, the time step of saving results is identical as the time step of integration.

If modal decomposition (linear time history analysis) is selected, the algorithm calculates the maximum value of the time step of integration for each mode, equaling the value of period divided by 20. This guarantees stability and the precision of results. Calculated step value is divided by the division value. The value received (step_1) is compared to the time step of saving results. A The smaller of these values ( step_1 and time step of saving results) is adopted as the time step of integration. Take note that if the first value is applied in calculations, it is slightly modified so the time step of saving results is a multiple of this value.

Geometric nonlinearity

P-Delta - Select this option to consider P-Delta effects during the analysis.

Large displacements - Select this option to take into account large displacements and/or rotations during the analysis.

Nonlinear analysis parameters - Opens a dialog which allows you to set up the options of the nonlinear analysis.

Time History analysis

Select a static load case or mass direction, and then click Add to define the function. You can also modify and delete active table rows by clicking the appropriate buttons.

Case - The list of the available simple static load cases or masses in the X, Y or Z directions.

Function - The list of the defined time functions and a preview of their associated diagram.

Factor - The factor used. Shift - The Phase shift. Function definition - Opens the Time Function Definition dialog

which allows you to set up a time function. Function table - A table containing the following columns.

Case - Indicates the number of the selected load case or mass direction.

Function - The name of the time function selected for the given load case.

Coefficient - The incremental coefficient for time function value for the given load case; the default value of the coefficient = 1.0.

Phase - Phase shift of the time function for the given load case; the default value = 0.0.

ExamplesTo perform a time analysis of the responses of a structure to an explosion, define a load case corresponding to air pressure on the structure and the explosion variability function.

To perform a time analysis of a structure behavior during an earthquake, define time functions for selected mass directions generated on the base of seismograms.

Parent topic: Theoretical basis for time history analysisRelated Reference

Static Analysis Parameters dialog Related Information

Non-linear time history analysis

Time history analysis - tables Diagram Definition/Modification Theoretical basis for time history analysis Capabilities and limitations of time history analysis

Non-linear time history analysisMay 04 2015  |  In-Product View

Applies to Robot Structural Analysis Professional 2016

Like (0)Login to like this ArticleShareNon-linear time history analysis obtains the response of the structure in which any non-linear elements have been defined. Time history analysis consists in reaching a solution of the following equation of the t time variable:

M * a(t) + C * v(t) + N (d(t)) = F(t)

with known initial values d(0)=d0 and v(0)=v0,

where:

M - mass matrix

K - stiffness matrix

C = α * M + β * K - damping matrix

N - internal force vector which is in a non-linear relation to the d shift vector

α - coefficient defined by a user

β - coefficient defined by a user

d - shift vector

v - velocity vector

a - acceleration vector

F - load vector.

A load vector is assumed as  , where n denotes a number of force components, Pi - i-th force component, φi(t) - i-th time-dependent function. The excitation may be expressed in the following

form:  , where Idir denotes a direction vector (dir = x, y, z) whereas   is an accelerogram.

Note: The following simplification is adopted for the Newmark method: C = α M. For most projects the M mass matrix may be assumed to be a diagonal matrix; it greatly speeds up calculations.To solve a non-linear task of time history analysis, the predictor-corrector approach is employed (see Hughes T.R.J., Belytschko T. Course notes for nonlinear finite element analysis. September, 4-8, 1995).

The input parameters defined for a non-linear time history analysis are almost identical to the parameters defined for a linear time history analysis. The non-linear parameters are identical as those for non-linear static analysis.

Time history analysis - tablesMay 04 2015  |  In-Product View

Applies to Robot Structural Analysis Professional 2016

Like (0)Login to like this ArticleShareSelect the Time history analysis tab in the Columns dialog for the presentation of nodal quantities.

Time history analysis, apart from the main load case, creates two auxiliary load cases containing the top (+) and bottom (-) envelope. Selecting the main load case displays the results for components of the complex case.

Select the components of velocity and acceleration of displacements for the case of time history analysis. (tables of structure nodes).

Note: Because a large number of results may be calculated for a large number of time steps, it is recommended to reduce the content of the opened tables of results by means of the Filter results tab in the Analysis Type dialog.If no single complex case of time history analysis is selected, the table will show results for auxiliary cases of the top (+) and bottom (-) envelope.

However, if a single complex case of time history analysis is selected, results are available for particular components. The first table column presents, from left to right, Node, Case, Component, and Time(s).

Note: The table of reactions presents results similarly to the table of displacements. For time history analysis, it is unnecessary to display equilibrium of forces and reactions in successive time steps.In tables of results for time history analysis for bars and surface elements, the relevant quantities are presented in the same way as in the table of nodes. The first table column contains the number of case components and the step of the time variable.

Parent topic: Results Parameters for Nodes

Theoretical basis for time history analysisMay 04 2015  |  In-Product View

Applies to Robot Structural Analysis Professional 2016

Like (0)Login to like this ArticleShareTime history analysis obtains the structure reaction at selected time points for a defined lasting interaction. This is contrary to other available analysis types that show the structure reaction in the form of amplitudes obtained for a single moment.

The time history analysis consists in finding a solution of the following equation of the time variable "t":

M * a(t) + C * v(t) + K * d(t) = F(t)

where the following initial values are known: d(0)=d0 and v(0)=v0,

where:

M - mass matrix.

K - stiffness matrix.

C = a * M + b * K - damping matrix.

α - user defined coefficient.

β - user defined coefficient.

d - shift vector.

v - velocity vector.

a - acceleration vector.

F - load vector.

All expressions containing the (t) parameter are time-dependent.

The Newmark method or the method of decomposition is used to solve the above-presented task. The Newmark method belongs to the group of algorithms that are unconditionally convergent for appropriately defined method parameters. It uses the following formulas for calculating displacements and velocity in the next step of integration.

Parameters β and γ control the convergence and precision of the results obtained by means of the method.

The unconditional convergence is assured for 0.5 ≤ γ 2≤ * b.

The values b = 0.25 and g = 0.5 are adopted. Modification of these values is possible, but only if the linear time history analysis with activated Newmark or Newmark (acceleration) method is used. These values (TransBeta and TransGamma) can be changed in the *.COV preference file saved in the CFGUSR folder. To perform calculations for different values of the parameters b and g, it is necessary to change the parameters TransBeta and TransGamma in the *.COV file, and to load that preference file.

It is advisable to use the Newmark method for short time histories when a concentrated load is applied to the structure. Such loads will induce a movement that will require a large number of eigenmodes to be described. Therefore, the Newmark method will be more efficacious than the modal decomposition method for this type of task. The Newmark method takes advantage of the initial equations without any simplifications. The precision of the obtained results depends on the precision of numerical integration of time equations, and it is defined by the value of the time step for the selected parameters α, β. The method does not require the eigenproblem to be solved to obtain the eigenvalues and eigenvectors. For long time histories, however, the method is very time-consuming. In the case of such tasks, calculations have to be performed for a large number of time steps with the required precision.

The Hilber-Hughes-Taylor (HHT) method implements numerical damping of higher frequencies without the loss of solution accuracy. A discrete form of the time history equation is as follows.

where:

-1/3 ≤ α ≤ 0

Assuming:

an unconditionally stable scheme of integration with second-order accuracy is obtained.

For the acceleration mode, trial values in n+1 step of integration are determined as follows.

The HHT method is a very efficient algorithm for numerical integration that allows removing the unfavorable impact of high frequencies on the quality of a solution.

The method of modal decomposition is a simple method of obtaining the required solution. It is based on the representation of structure movement as a superposition of the movement of uncoupled forms. Therefore, the method requires eigenvalues and eigenvectors to be determined. Lanczos method is recommended for this purpose, followed by Sturm verification. The method of modal decomposition takes advantage of reduced uncoupled equations.

The equation (without damping) may take the following form:

where

,

Ng - number of "load groups", φk(t) - time history for the k-th load group

 (2)

By inserting equation (2) into equation (1) and recognizing modal

damping and the conditions of orthogonality  , one obtains the following equation.

where  , ξ - modal damping parameters, ωi - frequency for the i-th form.

Each of the equations is solved numerically with the precision of the second order. The resultant displacement vector X(t) for the defined time points t* = t1, t2, ... is obtained after introducing qi(t*), i=1,2,…,m into equations (2).

It is worth noting the differences between the available analysis types described in this topic. Moving load analysis differs from Time History Analysis in that it does not recognize dynamic effects. The difference between harmonic analysis and Time History Analysis consists in that it determines the structure reaction exclusively in the form of amplitudes, and not in that of a time function.

See also:

Non-linear time history analysis

Capabilities and limitations of time history analysisMay 04 2015  |  In-Product View

Applies to Robot Structural Analysis Professional 2016

Like (0)Login to like this ArticleShareThe potential and limitations of Time History Analysis includes the following.

The same structure and load types are available as in the case of linear statics.

The function of load variability may be defined for an arbitrary static load case with the exception of the moving load case. In order to model a dynamic impact of a moving load, successive vehicle positions should be defined in separate load cases and use the time functions with the phase shift corresponding to the vehicle movement.

Additional modeling options available in the linear static analysis can be used (such as releases, elastic connections, rigid links, and others).

Case components may be used in combinations after generating an additional load case containing the results of analysis for a given component.

It allows adopting initial displacements from a selected load case, assuming simultaneously zero values of initial velocities and accelerations.

It is solved only by the means of the modal decomposition method, which requires that modal analysis be carried out first.

Only one time function may be used to determine time variability of loads of a given load case. It is possible, however, to add time functions.

There are a considerable number of facilitating options in the time history analysis.

A graphical interface for introducing data, accompanied by the visualization of time function course.

The possibility of reading a time function from and saving it to an easily editable text file.

Scaling and phase shift of time functions. Calculation notes with all the pertaining data. The possibility of using the results for time history case components in

combinations Perfected graphical presentation of the resultant values in diagrams.

View diagram comparisons of several arbitrarily selected quantities in one viewer, with time function course displayed.

Diagrams of a new resultant value - foundations shearing forces.In order to obtain satisfactory results for time history analysis cases, it is required to carry out iterative analysis with multiple calculations for different case parameters. Modal analysis needs to be carried out again.

In the case of a large-scale structure, the modal analysis itself may be time-consuming, as will the time history analysis. Therefore, it is necessary to select cases for calculations or at least to mark the modal analysis as calculated. This may also be useful in the case of seismic analysis.

Parent topic: Theoretical basis for time history analysis

New Non-linear Hinge TypeMay 04 2015  |  In-Product View

Applies to Robot Structural Analysis Professional 2016

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After clicking   on the Non-linear Hinges dialog, the following dialog opens.

The top of the dialog has a Label field for assigning a label (name) to a defined non-linear hinge type. Normal stresses in complex stress state lets you check the state of normal stresses in a bar section and the interactions between individual forces and moments (degrees of freedom).

Clicking Definition of Hinge Model opens the dialog for defining a pushover curve and its parameters. The curves defined in the Definition of non-linear hinge model dialog are visible on the selection lists.

In the dialog, 3 non-linear hinge types are available: force-displacement, moment-rotation, and stress-strain. The stress-strain type is available

after the Normal stresses in complex stress state option is selected. By default, all hinge types are cleared. For example, if the FY option is selected, the non-linear hinge models for that hinge type are available. Depending on the type of structure only some hinge types are available, similar to bar releases. The description in the Type: stress-strain field changes depending on the type of structure and the available degrees of freedom.

2D frame - Sx(FX, MY) 2D truss - Sx(FX) Grillage and Plate - Sx(MY) 3D truss- Sx(FX) 3D frame- Sx(FX, MY, MZ) Shell - Sx(FX, MY, MZ) Solid - Sx(FX, MY, MZ) Plane stress structure, Plane deformation structure, Axisymmetric

structure - Sx(FX).Clicking Add adds a new non-linear hinge type to the list of available hinges in the Non-linear Hinges dialog. Clicking Close closes the dialog without changing or defining a non-linear hinge type.

Structure Type Available Degrees of Freedom

2D Frame FX, FZ, MY

Grillage FZ, MX, MY

Plate FZ, MX, MY

3D Frame all

Shell all

Solid all

Note: The sign convention for non-linear hinges (type: moment - rotation) is as follows:RY+ - tension of top fibers (local Z+ axis)

RY- - tension of bottom fibers (local Z- axis)

RZ+ - tension on the local Y- axis

RZ- - tension on the local Y+ axis

Normal forces:

UX+ - tension

UX- - compression

Shear forces (shear directions according to the Sign convention for bar elements:

UZ+ - FZ- shear direction

UZ- - FZ+ shear direction

UY+ - FY- shear direction

UY- - FY+ shear direction.

Parent topic: Non-linear Hinges

Non-linear HingesMay 04 2015  |  In-Product View

Applies to Robot Structural Analysis Professional 2016

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Non-linear Hinges Assigning a Hinge to Structure Bars New Non-linear Hinge Type Non-linear Hinge Model Characteristics of Non-linear Hinges Pushover Curves Points Parameters Screen Capture Diagram Parameters Bending Shear Longitudinal Force