AWB130 Dynamics 06 Transient

Customer Training Material

L t 6Lecture 6

Transient Analysisy

ANSYS MechanicalANSYS MechanicalLinear and Nonlinear Dynamics

L06-1ANSYS, Inc. Proprietary© 2011 ANSYS, Inc. All rights reserved.

Release 13.0March 2011

Dynamics

ANSYS Mechanical Linear and Nonlinear Dynamics

Customer Training MaterialOverview• Transient structural analysis provides users with the ability to

determine the dynamic response of the system under any type of time-varying loads.– Unlike rigid dynamic analyses, bodies can be either rigid or flexible. For

flexible bodies, nonlinear materials can be included, and stresses and strains can be output.Transient structural analysis is also known as time history analysis or– Transient structural analysis is also known as time-history analysis or transient structural analysis.

– To perform Flexible Dynamic Analyses, an ANSYS Structural,ANSYS Mechanical, orANSYS Multiphysicslicense is required



Assembly shown here is from an Autodesk Inventor sample model


Customer Training MaterialTopics CoveredBackground Information:A. Introduction to Transient Structural AnalysesB. Preliminary Linear Dynamic StudiesC B k d I f ti N li A lC. Background Information on Nonlinear Analyses

Procedural Information:D Demo – Impact ProblemD. Demo – Impact ProblemE. Part Specification and MeshingF. Nonlinear MaterialsG. Contact; Joints; and Springs; ; p gH. Initial ConditionsI. Loads; Supports; and Joint ConditionsJ. DampingK. Transient Structural Analysis SettingsL. Reviewing Results




Customer Training MaterialA. Introduction• Transient structural analyses are needed to evaluate the response of

deformable bodies when inertial effects become significant.– If inertial and damping effects can be ignored, consider performing a

linear or nonlinear static analysis instead– If the loading is purely sinusoidal and the response is linear, a harmonic

response analysis is more efficientIf th b di b d t b i id d th ki ti f th t– If the bodies can be assumed to be rigid and the kinematics of the system is of interest, rigid dynamic analysis is more cost-effective

– In all other cases, transient structural analyses should be used, as it is the most general type of dynamic analysisthe most general type of dynamic analysis




Customer Training Material… Introduction• In a transient structural analysis, Workbench Mechanical solves the

general equation of motion:

[ ]{ } [ ]{ } ( )[ ]{ } ( ){ }FKCM &&&

Some points of interest:

[ ]{ } [ ]{ } ( )[ ]{ } ( ){ }tFxxKxCxM =++ &&&

– Applied loads and joint conditions may be a function of time and space.– As seen above, inertial and damping effects are now included. Hence,

the user should include density and damping in the model.– Nonlinear effects, such as geometric, material, and/or contact

nonlinearities, are included by updating the stiffness matrix.




Customer Training Material… Introduction• Transient structural analysis encompasses static structural analysis

and rigid dynamic analysis, and it allows for all types of Connections, Loads, and Supports.

• However, one of the important considerations of performing transient structural analysis is the time step size:– The time step should be small enough to correctly describe the time-

varying loads– The time step size controls the accuracy of capturing the dynamic

response. Hence, running a preliminary modal analysis is suggested in Section BSection B.

– The time step size also controls the accuracy and convergence behavior of nonlinear systems. Background information on the Newton-Raphson method is presented in Section C.p




Customer Training MaterialB. Preliminary Modal Analysis• While transient structural analyses use automatic time-stepping,

proper selection of the initial, minimum, and maximum time steps is important to represent the dynamic response accurately:– Unlike rigid dynamic analyses which use explicit time integration,

transient structural analyses use implicit time integration. Hence, the time steps are usually larger for transient structural analysesThe dynamic response can be thought of as various mode shapes of the– The dynamic response can be thought of as various mode shapes of the structure being excited by a loading. The initial time step should be based on the modes (or frequency content) of the system.

– It is recommended to use automatic time-stepping (default):It is recommended to use automatic time stepping (default):• The maximum time step can be chosen based on accuracy concerns. This

value can be defined as the same or slightly larger than the initial time step• The minimum time step can be input to prevent Workbench Mechanical from

l i i d fi it l Thi i i ti t b i t 1/100 1/1000 fsolving indefinitely. This minimum time step can be input as 1/100 or 1/1000 of the initial time step




Customer Training Material… Preliminary Modal Analysis• A general suggestion for selection of the initial time step is to use the

following equation:

lt 1=Δ

where fresponse is the frequency of the highest mode of interestresponse

initial ft

20Δ

• In order to determine the highest mode of interest, a preliminary modal analysis should be performed prior to the transient structural analysisanalysis– In this way, the user can determine what the mode shapes of the

structure are (i.e., how the structure may respond dynamically)– The user can also then determine the value of fresponseThe user can also then determine the value of fresponse




Customer Training Material… Preliminary Modal AnalysisPoints of Consideration:• The automatic time-stepping algorithm will increase or decrease the

size of the time step during the course of the analysis based on the calculated response frequency.– Automatic time-stepping algorithm still relies on reasonable values of

initial, minimum, and maximum time steps– If the minimum time step is being used, that may indicate that the initial

time step size was too large. The user can plot the time step size by selecting “Solution Output: Time Increment” from the Details view of the Solution Information branchSolution Information branch

• When performing a modal analysis to determine an appropriate response frequency value, it is not sufficient to request a certain number of modes then to use the maximum frequency It is a goodnumber of modes, then to use the maximum frequency. It is a good idea to examine the various mode shapes to determine which frequency may be the highest mode of interest contributing to the response of the structure.



p


Customer Training MaterialC. Including Nonlinearities• There are several sources of nonlinear behavior, and a transient

structural analysis may often include nonlinearities:

– Geometric nonlinearities: If a structure experiences large deformations, its changing geometric configuration can cause nonlinear behaviorcause nonlinear behavior.

– Material nonlinearities: A nonlinear stress-strain relationship, such as metal plasticity shown onp p ythe right, is another source of nonlinearities.

– Contact: Include effects of contact is a typef “ h i t t ” li it hof “changing status” nonlinearity, where an

abrupt change in stiffness may occur whenbodies come in or out of contact with each other.




Customer Training Material… Including Nonlinearities• In a linear analysis, the applied force F and

displacement x of the system are related such that doubling the force would double the Fdisplacement, stresses, and strains– This assumes that the change in the original and

final deformed shapes is negligible since the same stiffness matrix [K] is used

K

stiffness matrix [K] is used

• In a nonlinear analysis, the relationship between th li d f F d di l t i t

x

the applied force F and displacement x is not known beforehand– As the geometry undergoes deformation, so too,

does the stiffness matrix [K] changeF

does the stiffness matrix [K] change– The Newton-Raphson method needs to be

implemented to solve nonlinear problems



x


Customer Training Material… Including Nonlinearities• Nonlinear analyses require several solution iterations:– The actual relationship between applied load and deformation (dotted

green line below) is not known a priori– The Newton-Raphson method, which can be thought of as a series of

linear approximations with corrections, is performed (solid blue lines)• The load Fa is applied to the structure. Based on the new deformed shape,

internal force F1 is calculated If F ≠F1 then the system is not in equilibrium Ainternal force F1 is calculated. If Fa ≠F1 then the system is not in equilibrium. A new stiffness matrix [K] (slope of blue line) is calculated based on the current conditions.

• This process is repeated until Fa =Fi for iteration i, at which point the solution is said to be convergedsaid to be converged

• Oftentimes, the applied load Fa must besplit into smaller increments in order forconvergence to occur Hence for a ramped

Fa

3 4convergence to occur. Hence, for a rampedload, a smaller time step may be neededto ensure convergence

1

2

3

F1



xx1


Customer Training Material… Including Nonlinearities• As shown from the previous slides, the time step size will also have

an influence on nonlinear analyses:– The time step size should be small enough to allow the Newton-Raphson

method to obtain force equilibrium (convergence)– The user may also need to specify the initial, minimum, and maximum

timesteps based on nonlinear considerations

• Usually, the dynamic considerations for picking a time step size as discussed in Section B is sufficient.

Si W kb h M h i l l t f ti t l i– Since Workbench Mechanical only uses one set of time steps, resolving the dynamic response often provides a small enough time step to resolve nonlinear effects as well.

– Determination of the time step size based on nonlinear considerations is– Determination of the time step size based on nonlinear considerations is often not as straightforward as choosing the dynamic time step size. Hence, the user may rely on automatic time-stepping algorithm to ensure convergence and accuracy.




Customer Training Material… Including Nonlinearities• The automatic time-stepping algorithm takes into account the

following nonlinear effects:– If force equilibrium (or some other convergence criterion) is not satisfied,

bisection occursbisection occurs– If an element has excessive distortion, bisection occurs– If the maximum plastic strain increment exceeds 15%, bisection occurs– Optional: if contact status changes abruptly, bisection occursp g p y,

• Bisection is part of the automatic time-stepping algorithm, when the solver goes back to the previously converged solution at time ti and uses a smaller time increment Δti.– Bisections provide an automated means to solve nonlinear problems

more accurately or to overcome convergence difficulties.Note however that bisections result in wasted solver time since the– Note, however, that bisections result in wasted solver time since the solution returns to the previously converged solution and tries again with a smaller time step. Hence, choosing the right initial and maximum time step can minimize the number of bisections that occur




Customer Training Material… Including Nonlinearities• By default, large deformation effects and automatic time-stepping will

be active:– The user does not need to do anything special to account for

nonlinearities.• However, as noted before, if nonlinear effects dominate, the time step size may

be dictated by nonlinear considerations rather than dynamic concerns.• “Large Deflection” can be toggled in the Details view of the “Analysis Settings”Large Deflection can be toggled in the Details view of the Analysis Settings

branch– If the user wants to turn on time step size checks based on contact

status, this can be done in with “Time Step Controls” in the Details view of a given contact region.

• Using this option may decrease the time step to ensure correct momentum transfer between parts in impact-type of situations

• Note however that the time step may become excessively small so this is notNote, however, that the time step may become excessively small, so this is not recommended in general, especially for preliminary analyses



Customer Training Material

T i tTransient

Procedure

ANSYS MechanicalANSYS MechanicalLinear and Nonlinear Dynamics



Dynamics


Customer Training MaterialE. Part Specification• In a transient structural analysis, parts may be rigid or flexible:– Under the “Geometry” branch, the “Stiffness Behavior” can be toggled

from “Flexible” to “Rigid” on a per-part basis– Rigid and flexible parts can co-exist in the same model

• Consideration for flexible parts are the same as in static analyses:– Specify appropriate material properties, such as density, Young’s

Modulus, and Poisson’s ratio– Nonlinear materials, such as plasticity or hyperelasticity, can also be

includedf• For rigid parts, the following apply:

– Line bodies cannot be set to rigid– Multibody parts must have all bodies set to rigid– Density is the only material property needed to

calculate mass properties. All other materialspecifications will be ignored.An “Inertial Coordinate System” will automatically



– An Inertial Coordinate System will automaticallybe defined at the centroid of the part


Customer Training Material… Part Specification• For flexible bodies, the mesh density is based on the following:– The mesh should be fine enough to capture the mode shapes of the

structure (dynamic response)– If stresses and strains are of interest, the mesh should be fine enough to

capture these gradients accurately• For rigid bodies, no mesh is produced– Rigid bodies are rigid, so no

stresses, strains, or relative deformation is calculated. Hence no mesh is requiredHence, no mesh is required

– Internally, rigid bodies are represented as point masses located at the center of its “Inertial Coordinate System”

On the figure on the right, one can see flexible bodies (meshed) and




see flexible bodies (meshed) and rigid bodies (not meshed) in the same model.


Customer Training MaterialF. Nonlinear Materials• For flexible bodies, nonlinear materials may be defined:– Metal plasticity:

• Define Young’s modulus and Poisson’s ratio• Select either isotropic or kinematic hardening law and either bilinear or

multilinear representation of stress-strain curve– For multilinear stress-strain curve, remember that values should be logarithmic plastic

strain vs. true stress

– Hyperelasticity:• Select a hyperelastic model based on strain invariants (neo-Hookean,

Polynomial, Mooney-Rivlin, or Yeoh) or principal stretch (Ogden):If material constants are not known enter test data then select hyperelastic model on– If material constants are not known, enter test data, then select hyperelastic model on which to perform curve-fit

– If material constants are known, select hyperelastic model and enter constants

• To account for inertial effects, density should also be defined for both flexible and rigid bodies.

• Material damping, discussed in Section I, may also be input for flexible bodies.




Customer Training MaterialG. Contact; Joints; Springs• Contact, joints, or springs can be defined under the “Connections”

branch in transient structural analyses– Contact is defined between solid and surface bodies (rigid parts must be

single body). Contact is used when parts can come in and out of contact or if frictional effects are important.

• Nonlinear contact (rough, frictionless, frictional) may be defined for faces of solid or surface bodies (flexible or rigid) at v12.solid or surface bodies (flexible or rigid) at v12.

– Joints are defined for 3D rigid or flexible bodies only. Joints can be defined between two bodies or from one body to ground. Joints are meant to model mechanisms where the part(s) are connected but relative motion is possible.

• Joints are defined faces, lines, or keypoints of 3D solid, surface, or line bodies, both flexible and rigid.

Springs are defined for 3D rigid or flexible bodies Springs provide– Springs are defined for 3D rigid or flexible bodies. Springs provide longitudinal stiffness and damping for the scoped region(s), meant to represent stiffness/damping effects of parts not explicitly modeled.

• Springs can be defined on vertices, edges, or faces of 3D bodies



• Defined springs cannot have zero length


Customer Training Material… Contact• Contact regions can be defined between flexible bodies:– Contact is useful when the contacting area is not known beforehand or if

the contacting area changes during the course of the analysis – Any type of contact behavior (linear, nonlinear) can be specified,

including frictional effects

In the animation, some surfaces of two parts are initially not in contact, but y ,as the analysis progresses, the surfaces come into contact, as shown on the right, allowing for forces to be



allowing for forces to be transmitted between the two bodies.


Customer Training Material… Contact• In contact, parts are prevented from penetrating into each other. The

different type of contact describe behavior in the separation and sliding directions:

Normal Direction Tangential DirectionContact Type Separate Slideyp pBonded no noNo Separation no yesRough yes noFrictionless yes yesFrictional yes yes (when Ft≥μN)




Customer Training Material… Contact• Different contact formulations allow for establishing the mathematical

relationship between contacting solid bodies:– For bonded and no separation contact, the contacting areas are known

beforehand based on the geometry and pinball region• The recommended contact formulation to use is either “Pure Penalty” (default)

or “MPC”For rough frictionless and frictional contact– For rough, frictionless, and frictional contact, the actual contacting areas are not known a priori, so an iterative approach is required

• The recommended contact formulation to useis “Augmented Lagrange”




Customer Training Material… Joints

• Joints can be defined between bodies or from a body to ground:– Joints define the allowed motion (kinematic constraint) on surface(s)

Various types of joints can be defined for flexible or rigid bodies:– Various types of joints can be defined for flexible or rigid bodies:• Fixed, Revolute, Cylindrical, Translational, Slot, Universal, Spherical, Planar,

or General Joints– Definition and configuration of joints is covered in a separate training g j p g

course named “ANSYS Rigid and Flexible Dynamic Analysis”.– Unlike rigid dynamic analysis, the actual – not relative – degrees of

freedom are specified.

The animation on the right shows an assembly using cylindrical and



an assembly using cylindrical and revolute joints



Customer Training Material… Joints• In transient structural analyses, the user has an additional option of

specifying the behavior of the joint:– “Rigid” (default) behavior means that the scoped surface(s) will not

deform but be treated as rigid surface(s). This means that a scoped cylindrical surface will remain cylindrical throughout the analysis.

– “Deformable” behavior means that while the joint constraint is satisfied the scopedjoint constraint is satisfied, the scoped surface(s) are free to deform. This means thata scoped cylindrical surface may not remaincylindrical throughout the analysis.




Customer Training Material… Springs

• Springs can be defined between bodies or from body to ground:– Springs define the stiffness and/or damping of surface(s)

• Refer to Section I for additional details on damping• Refer to Section I for additional details on damping– Springs can be defined for rigid or flexible bodies– These are longitudinal springs, so the stiffness or damping is related to

the change in length of the springthe change in length of the spring• The spring must not have zero length• Springs can be defined on vertices, edges, or surfaces• Definition and configuration of springs is covered in a separate training

course named “ANSYS Rigid and Flexible Dynamic Analysis”.




Customer Training MaterialH. Initial Conditions• For a transient structural analysis, initial displacement and initial

velocity is required:– User can define initial conditions via “Initial Condition” branch or by

using multiple Steps

• Defining initial displacement & velocity with the “Initial Condition” object:– Default condition is that all bodies are at rest

• No additional action needs to be taken

– If some bodies have zero initial displacement butnon-zero constant initial velocity, this can be input

• Only bodies can be specified• Enter constant initial velocity (Cannot specify more

than one constant velocity value with this method)



than one constant velocity value with this method)


Customer Training Material… Initial Conditions• Defining initial displacement & velocity by using multiple Steps:– This technique is required for all other situations– Leave “Initial Conditions” to “At Rest.” For “Analysis Settings,” use 2

Steps over a small time interval:• First Step should have very small “Step End Time” in Details view. Also,

change “Time Integration: Off” and “Auto Time Stepping: Off” only for the first Step. Modify “Define by: Substeps” with “Number of Substeps: 1”.Step. Modify Define by: Substeps with Number of Substeps: 1 .

– Apply a “Displacement” support with appropriate values (discussed in next slide) in Step 1. Deactivate this “Displacement” support in Step 2.

– The idea behind such a technique is that the first Step, solved over a q psmall time interval Δt1, will provide an initial displacement & velocity based on an imposed xinitial “Displacement” support.

1xinitial

initial Δ

If the time interval Δt1 is small enough, the effect on the actual ending time should be negligible

1

1

txvinitialΔ

Δ=



time should be negligible.


Customer Training Material… Initial Conditions– Initial displacement = 0, initial velocity ≠ 0

• Ramp a very small displacement value over a small time interval to produce the desired initial velocity. Deactivate it for Step 2.

– Initial displacement ≠ 0, initial velocity ≠ 0• Ramp the desired initial displacement over a time interval to produce the

desired initial velocity. Deactivate it for Step 2.desired initial velocity. Deactivate it for Step 2.

– Initial displacement ≠ 0, initial velocity = 0• Step apply the desired initial displacement over a time interval to ensure that p pp y p

initial velocity is zero. Deactivate it for Step 2, if necessary.




Customer Training MaterialI. Loads; Supports; Conditions• For rigid bodies, just as in a rigid dynamic analysis, only inertial

loads, remote loads, and joint conditions are supported.– Rigid bodies do not deform, so structural & thermal loads do not apply

• For deformable bodies, any type of load can be used:– Inertial and structural loads– Structural supports– Joint (for defined joints) and thermal conditions




Customer Training Material… Time-Varying Loads• Structural loads and joint conditions can be input as time-dependent

load histories– When adding a Load or Joint Condition, the

magnitude can be defined as a constant, tabular value, or function.

– The values can be entered directly in the Workbench Mechanical GUI or entered inWorkbench Mechanical GUI or entered in the Engineering Data page




Customer Training MaterialJ. Damping• As noted in Section A, the equations solved for in transient structural

analyses also include a damping term

• Since the response frequency is not known in advance of running the simulation, are only two types of damping available:– Viscous dampingp g

• beta damping (optionally material-dependent) or by element damping– Numerical damping

• See Chapter 1 for more details.p

• The effect of damping is cumulative. Hence, if 2% material-dependent beta damping and 3% global beta damping is defined, thatdependent beta damping and 3% global beta damping is defined, that part will have 5% damping.




Customer Training MaterialK. Analysis Settings• Besides damping, there are various other

options the user can set under the “Analysis Settings” branch.

• It is important that the user specify the solution times in the “Step Controls” section– The “Number of Steps” controls how the load

history is divided. As noted in Section G, one can impose initial conditions with multiple load steps use “Time Integration” to toggle whethersteps – use “Time Integration” to toggle whether inertial effects are active for that step

– The “Step End Time” is the actual simulation ending time for the “Current Step Number”ending time for the Current Step Number

– The initial, minimum, and maximum timesteps should be defined as noted in Sections B & C




Customer Training Material… Analysis Settings• The “Solver Controls” section allows the user

to choose the equation solver, use of weak springs, and use of large deflection effects

– Transient structural analyses may typically involve large deformations, so “Large Deflection: On” should be used (default behavior)On” should be used (default behavior).

– “Output Controls” allows users to control how frequently data is saved to the ANSYS result filefrequently data is saved to the ANSYS result file. For multiple step analyses, one can save results only for the end of the step. Also, one can also save results at intervals that are as evenly-spaced as possible (depending on automatic time-stepping)




Customer Training MaterialL. Reviewing Results• After completion of the solution, reviewing transient structural

analysis results typically involves the following output:– Contour plots and animations– Probe plots and charts

• Generating contour plots and animations are similar to other g pstructural analyses– Note that the displaced position of rigid

bodies will be shown in the contour result, but the rigid bodies will not show any contour result for deformation, stress, or strain since they are rigid entitiesTypically animations are generated using– Typically, animations are generated using the actual result sets, not distributed sets




Customer Training Material… Reviewing Results• Probes are useful in generating time-history charts

to understand the transient response of the system.Some useful probe results are as follows:– Deformation, stresses, strains, velocities, accelerations– Force and moment reactions– Joint, spring, and bolt pretension results

• Chart objects, based on probes, can also be added to include in reports or as independent figures




Customer Training MaterialD. Workshop – Transient Analysis

• In this workshop, you will determine the dynamic response of a caster wheel exposed to a side impact such as hitting a curb.

WS6: Transient Analysis of a Caster Wheel

StrikerTool

Wh l



Wheel

AWB130 Dynamics 06 Transient

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