Download - AWB130 Dynamics 06 Transient
Customer Training Material
L t 6Lecture 6
Transient Analysisy
ANSYS MechanicalANSYS MechanicalLinear and Nonlinear Dynamics
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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
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Assembly shown here is from an Autodesk Inventor sample model
ANSYS Mechanical Linear and Nonlinear Dynamics
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
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ANSYS Mechanical Linear and Nonlinear Dynamics
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
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ANSYS Mechanical Linear and Nonlinear Dynamics
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.
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ANSYS Mechanical Linear and Nonlinear Dynamics
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
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ANSYS Mechanical Linear and Nonlinear Dynamics
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
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ANSYS Mechanical Linear and Nonlinear Dynamics
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
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ANSYS Mechanical Linear and Nonlinear Dynamics
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.
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p
ANSYS Mechanical Linear and Nonlinear Dynamics
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.
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ANSYS Mechanical Linear and Nonlinear Dynamics
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
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x
ANSYS Mechanical Linear and Nonlinear Dynamics
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
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ANSYS Mechanical Linear and Nonlinear Dynamics
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.
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ANSYS Mechanical Linear and Nonlinear Dynamics
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
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ANSYS Mechanical Linear and Nonlinear Dynamics
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
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Customer Training Material
T i tTransient
Procedure
ANSYS MechanicalANSYS MechanicalLinear and Nonlinear Dynamics
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ANSYS Mechanical Linear and Nonlinear 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
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– An Inertial Coordinate System will automaticallybe defined at the centroid of the part
ANSYS Mechanical Linear and Nonlinear Dynamics
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
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Assembly shown here is from an Autodesk Inventor sample model
see flexible bodies (meshed) and rigid bodies (not meshed) in the same model.
ANSYS Mechanical Linear and Nonlinear Dynamics
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.
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ANSYS Mechanical Linear and Nonlinear Dynamics
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
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• Defined springs cannot have zero length
ANSYS Mechanical Linear and Nonlinear Dynamics
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
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allowing for forces to be transmitted between the two bodies.
ANSYS Mechanical Linear and Nonlinear Dynamics
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)
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ANSYS Mechanical Linear and Nonlinear Dynamics
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”
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ANSYS Mechanical Linear and Nonlinear Dynamics
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
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an assembly using cylindrical and revolute joints
Assembly shown here is from an Autodesk Inventor sample model
ANSYS Mechanical Linear and Nonlinear Dynamics
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.
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ANSYS Mechanical Linear and Nonlinear Dynamics
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”.
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ANSYS Mechanical Linear and Nonlinear Dynamics
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)
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than one constant velocity value with this method)
ANSYS Mechanical Linear and Nonlinear Dynamics
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=
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time should be negligible.
ANSYS Mechanical Linear and Nonlinear Dynamics
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.
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ANSYS Mechanical Linear and Nonlinear Dynamics
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
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ANSYS Mechanical Linear and Nonlinear Dynamics
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
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ANSYS Mechanical Linear and Nonlinear Dynamics
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.
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ANSYS Mechanical Linear and Nonlinear Dynamics
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
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ANSYS Mechanical Linear and Nonlinear Dynamics
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)
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ANSYS Mechanical Linear and Nonlinear Dynamics
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
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ANSYS Mechanical Linear and Nonlinear Dynamics
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
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ANSYS Mechanical Linear and Nonlinear Dynamics
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
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Wheel