Dynamics 70 M4 Transient

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Transient Dynamic Analysis

Module 4


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Module 4

Transient Dynamic AnalysisA. Define transient dynamic analysis and its purpose.

B. Learn basic terminology and concepts underlying transient analysis.

C. Learn how to do a transient analysis in ANSYS.D. Work on a transient analysis exercise.


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Transient Analysis

A. Definition & PurposeWhat is transient dynamic analysis?

A technique to determine the response of a structure to arbitrary

time-varying loads such as an explosion.

Input

Loads as a function of time.

Output

Time-varying displacements and other derived quantities such asstresses and strains.


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Transient Analysis

Definition & PurposeTransient dynamic analysis is used in the design of:

Structures subjected to shock loads, such as automobile doors

and bumpers, building frames, and suspension systems.

Structures subjected to time-varying loads, such as bridges, earth

moving equipment, and other machine components.

Household and office equipment subjected to bumps and

bruises, such as cellular phones, laptop computers, and vacuum

cleaners.


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Transient Analysis

B. Terminology & ConceptsTopics covered:

Equation of motion

Solution methods Integration time step


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Transient Analysis - Terminology & Concepts

Equation of Motion Equation of motion for a transient dynamic analysis is the same

as the general equation of motion.

This is the most general form of dynamic analysis. Loading may

be any arbitrary function of time.

Depending on the method of solution, ANSYS allows all types of

nonlinearities to be included in a transient dynamic analysis -

large deformation, contact, plasticity, etc.

[ ]{ } [ ]{ } [ ]{ } ( ){ }tFuKuCuM =++


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Transient Analysis - Terminology and Concepts

Solution Methods

Solving the equation of motion

Direct Integration Mode Superposition

Implicit Explicit

Full Reduced Full Reduced


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Solution MethodsTwo methods of solving the equation of motion:

Mode superposition (discussed in Module 6)

Direct integration Equation of motion is directly integrated step by step over time. At

each time point ( time = 0, t , 2t, 3t,.) a set of simultaneous,

static equilibrium equations (F=ma) is solved.

An assumption (integration scheme) is made regarding how

displacement, velocity and acceleration will vary over t

Various integration schemes are available in literature such as

Central difference, Average acceleration, Houbolt, Wilson,

Newmark etc.


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ANSYS uses Newmark integration scheme.

Varying values of and causes integration scheme to change (implicit /

explicit / average acceleration ).

Newmark is an implicit scheme. ANSYS/LS-DYNA uses explicit scheme. See module 1 for a discussion of

implicit and explicit.

[ ] [ ] [ ] ( ){ }

tttutututtu

ttt

ut

utt

ut

utt

u

tF

tt

uK

tt

uC

tt

uM

+++=+

+

+++=+

=

+

+

+

+

+

])1[(

2])2/1[(


Solution Methods


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Solution Methods Solution can use either reducedor fullstructure matrices.

Reduced matrices

Used to speed up the solution.

No nonlinearities (except gap) allowed.

[K], [C], and [M] are written in terms of master DOF, which form a

subset of the full DOF set.

Reduced [K] is exact, but reduced [C] and [M] are approximate. There

are other disadvantages also, not discussed in this seminar.

Full matrices

No reduction. Uses full [K], [C], and [M].

All nonlinearities allowed.

All discussions in this seminar assume this approach.


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Integration Time Step An important concept in time integration techniques is the

integration time step (also ITS ort).

ITS = time increment t from one time point to the next.

Determines solution accuracy, so its value should be chosen

carefully.

ANSYS allows only a constant value of ITS for reduced and mode

superposition transient analyses.

In a FULL transient analysis, ANSYS can automatically vary the timestep size within limits set by user (discussed later).


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The integration time step ( ITS) size should be small enough to

capture the following:

the response frequency

the contact frequency (if applicable)

wave propagation effects (if applicable)

Nonlinear response (plasticity, creep, contact status)


Integration Time Step


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Response frequency

Different types of loads excite differentnatural frequencies of the structure.

Response frequency is the weightedaverage of all frequencies excited by agiven load.

The ITS should be small enough tocapture the response frequency .

Twenty time points per cycle shouldbe sufficient, i.e,

t = 1/20f

where f is the response frequency.Response period


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Response frequency (continued)

During solution, the full transient method (discussed in this seminar)

prints the response frequency and the number of points per cycle at

every time point.

The goal is to maintain about 20 points per cycle.

By default, ANSYS automatically increases or decreases ITS to

maintain about 20 points per cycle at the response frequency.




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Contact frequency

When two objects come in

contact, the gap or contact

surface is usually represented bya stiffness (gap stiffness).

The ITS should be small enough to

capture the frequency of the gap

spring.

Thirty points per cycle are

recommended. This is sufficient

to capture the momentum transfer

between the two objects. A larger

ITS might result in energy loss,

and the impact may not beperfectly elastic.

The response frequency printed

during solution includes contact

frequency.

masseffectivem

stiffnessgapk

frequencycontactf

m

k

2

1f

f30

1ITS

c

c

c

=

=

=

=

=


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Integration Time StepWave propagation

Caused by impact. More

prominent in slender structures

(such as a thin rod dropped onone end).

Requires a very small ITS and a

fine mesh along the direction of

the wave.

Explicit method (available inANSYS-LS/DYNA) may be better

suited for this.

densitymass

modulussYoung'

speedwaveelastic

directionwavealonglength

20/sizeelement3

=

=

==

=

=

E

Ec

L

Lxc

xITS


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Nonlinear response

A full transient analysis can include any type of nonlinearity.

Nonlinearities can be classified into 3 types: Material nonlinearity (plasticity , creep, hyperelasticity )

Geometric nonlinearity (large strain , large rotation, buckling)

Element nonlinearity (contact , cable)

Nonlinearities require an iterative solution at each time point.

These iterations are called equilibrium iterations.




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Nonlinear response (continued)

Smaller ITS sizes generally help equilibrium iterations to converge

quickly.

Nonlinearities such as plasticity, creep and friction are non-

conservative in nature and require the load history to be followed

accurately. A small ITS size helps in following the load history

accurately.

A small ITS size is also required to capture changes in contactstatus.




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So how do you choose an ITS?

Recommended way is to activate automatic time stepping

(AUTOTS), then provide tinitial , tmin , and tmax. ANSYS uses an

automatic time stepping algorithm (AUTOTS) to determine theoptimum t value for a given problem.

Example: If AUTOTS is on with tinitial= 1 sec, tmin= 0.01 sec, and

tmax= 10 sec; then ANSYS starts with an ITS= 1 sec and allow it to

vary between 0.01 and 10 depending on the structures response.




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AUTOTS is on by default for full transient analyses and is not

available for reduced and mode superposition methods.

AUTOTS will reduce the ITS (up to tmin) if:

less than 20 points are being used at the response frequency

solution is diverging

solution takes a large number of equilibrium equations (slow

convergence)

plastic strain is accumulated in one time step exceeds 15%

Creep ratio exceeds 0.1

if contact status is about to change ( controlled by KEYOPT(7) of most

contact elements)




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Transient Analysis

C. Procedure We will discuss the Full method only in this section.

Five main steps:

Build the model

Choose analysis type and options

Specify BCs and initial conditions

Apply time-history loads and solve

Review results


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Transient Analysis Procedure

Build the ModelModel

All nonlinearities are allowed.

Remember density!

See also Modeling Considerations in Module 1.


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Choose Analysis Type & Options Build the model

Choose analysis type and options:

Enter Solution and choose transient

analysis. Choose Full transient

Solution options - discussed next.

Damping - discussed next.


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Solution options

Choose large displacement transient

or small displacement transient .

When in doubt, choose largedisplacement transient


Choose Analysis Type & Options

Specify output controls

(discussed next)

Specify time at end of load step.

Automatic time stepping

(discussed next)

Specify initial, min and max

values of t for this load step.


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Automatic time stepping

An algorithm that automatically calculates appropriate ITS sizes

during the transient.

Recommendation is to activate it and also specify minimum and

maximum values of ITS.

If nonlinearities are present, use the Program Chosen option.

Note: The global solution controls switch [SOLCONTROL] is ON

by default. We recommend leaving it as is. More importantly, do

not turn this switch on and off between load steps.




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Output controls

Used to determine what is written to the results file.

Use the OUTRES command or choose Solution > Soln Control.. >

Basic in the menu

Typical choice is to write all items at every substep to the

results file.

Allows smooth plots of results vs. time.

Might cause results file to be large.




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Turn transient effects on/off

useful for setting up initial

conditions (discussed later)

Ramp or Step apply load

Specify damping (discussed

next)

Use default values for time

integration parameters




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Damping

Both alpha damping and beta damping are available.

In many cases, alpha damping (viscous damping) is ignored and

only beta damping (damping due to hysteresis) is specified:

= 2/

where is the damping ratio and is the dominant response

frequency (rad/sec).

Material damping (e.g. rubber) and element damping (e.g. shock

absorber) are also available.


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Choose Analysis Type & Options Choose solver

By default ANSYS chooses Sparse solver

For large problems (>100000 dofs) use PCG solver


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Specify BCs & Initial Conditions

Build the model


Specify BCs and initial conditions BCs in this case are loads or

conditions that remain constant

throughout the transient, e.g:

Fixed points (constraints)

Symmetry conditions

Gravity

Initial conditions are discussed next.


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Initial conditions

Transient analyses require initial

displacement (u0) and initial

velocity(v0) to be specified.

By default, u0= v0 = a0 = 0.

Examples where non-zero initial

conditions may be required:

Aircraft landing gear (v00).

A golf club striking a ball (v00).

Drop test of an object (u0= v0 =0 ,

a00).


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Two ways to apply initial conditions:

Start with a static load step

Useful when initial conditions need to be applied on only a portion of

the model, such as plucking the end of a cantilever beam with an

imposed displacement (u0 is known , v0 =0)

Required for applying a non-zero initial acceleration.

Use the IC command

Solution > Define Loads > Apply > Initial Conditn > Define

Useful when a non-zero initial displacement or velocity needs to be

applied on the entire body.


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Example - Dropping an object from rest

In this case a0=g (gravitational acceleration) and u0 = v0=0.

Use the static load step method.

Load step 1:

Transient effects OFF. Use TIMINT,OFF command or

Solution > Soln Control

Select the Transient Tab and unselect Transient effects

Small time interval, e.g, 0.001.

2 substeps, stepped loads. (If ramped or with one substep, v0 will benon-zero.)

Hold the object at rest, i.e, fix all DOFs on the object.

Apply acceleration of g.

SOLVE.


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Load step 2:

Transient effects ON.

Release the object, i.e, delete DOF

constraints on the object.

Specify ending time and continue with

the transient. Acel

t0.0005 0.001

Load step 1

Application of Temporal Acceleration


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Example - Plucking the free end of a cantilever beam

In this case u00 at one end of the beam, and v0=0.

Use the static load step method.

Load step 1:

Transient effects OFF. Use TIMINT,OFF command or

Solution > Soln Control

Select the Transient Tab and unselect Transient effects

Small time interval, e.g, 0.001. 2 substeps, stepped loads. (If ramped or with one substep, v0 will be

non-zero.)

Apply the desired non-zero displacement at the free end of the beam.

SOLVE.


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Load step 2:

Transient effects ON.

Delete the imposed displacement.

Specify ending time and continue with the transient.


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Example - Initial velocity on a golf club head

Assuming that only the club head is modeled and that the entire head

moves, we have v00. We will also assume that u0 = a0 = 0.

The IC command method is convenient for this case.

1 Select all nodes on the club.

2 Use the IC command to apply initial velocity, or

Choose Solution > Define Loads > Apply > Initial Conditn > Define

Pick all nodes. Select direction and enter velocity value.

3 Activate all nodes.

4 Specify ending time, apply other loading conditions

(if any), and solve.


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Apply Time-History Loads & Solve

Build the model




Time-history loads are loads that vary

with time.

Three ways to apply them:

Function tool

Tabular input

Multiple load steps

Load

t

Load

t

Load

t


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Function Tool

Allows you to apply complicated boundary conditions. To access thefunction editor, choose Solution > Define Loads > Apply > Functions >Define/Edit

Recommendation: do not use the Function Tool if the boundaryconditions can be expressed directly with tabular input

For more informationrefer to Applying LoadsUsing Function BoundaryConditions in the Basic

Analysis Guide.


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Tabular input

Allows you to define a table of load vs. time (using array

parameters) and apply the table as a load.

Very convenient, especially if there are several different loads, eachwith its own time history.

For example, to apply the force-vs-time curve shown:

1. Choose Solution > Define Loads > Apply > Structural > Force/Moment >

On Nodes, then pick desired nodes.

0.5

Force

t

22.5

10

1.0 1.5


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2. Choose the force direction and

New table, then OK.

3. Enter table name and no. of rows

(no. of time points), then OK.

4. Fill in time and load values, then

File > Apply/Quit.

T i t A l i P d


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5. Specify ending time and integration time step.

Solution > Load Step Opts > Time/Frequenc > Time - Time Step

There is no need to specify the stepped or ramped condition. It is

implied by the load curve.

6. Activate automatic time stepping, specify output controls, and solve

(discussed later.)

T i t A l i P d


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Multiple load step method

Allows you to apply each segment of the load-vs-time curve in a

separate load step.

No need to use array parameters. Simply apply each segment andeither solve the load step or write it to a load step file (LSWRITE).



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For example, to apply the same force-vs-time curve

as before:

1. Plan the approach. We will need three load

steps in this case: one for the up-ramp load,

one for the down-ramp load, and one for the

step removal of the load.Force

t

22.5

10

0.5 1.0 1.52. Define load step 1:

Apply force = 22.5 units at the desired nodes.

Specify the ending time (0.5), integration time step, and ramped

loads.

Activate automatic time stepping, specify output controls*, and

either solve or write the load step to a load step file.

*Discussed later



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3. Define load step 2:

Change force values to 10.0.

Specify the ending time (1.0). No need to respecify the integration

time step or ramped condition. Solve or write the load step to a load step file.

4. Define load step 3:

Delete the forces or set their values to zero.

Specify the ending time (1.5) and stepped loads.

Solve or write the load step to a load step file.



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Solution

Use SOLVE command (or LSSOLVE if load

step files were written).

At each time step, ANSYS calculates loadvalues based on the load-vs-time curve.



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Review Results

Build the model




Review Results

Consists of three steps:

Plot results vs. time at specific points in the

structure. Identify critical time points.

Review results over entire structure at those

time points.

Use POST26, the time-

history postprocessor

Use POST1, the

general postprocessor



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Review Results - POST26

To plot results vs. time:

First define POST26 variables in the Variable Viewer.

Tables of nodal or element data.

Identified by a number 2.

Variable 1 contains time-points and is predefined.



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Define variables (cont'd)

Pick nodes that might deform the most, then choose the DOF

direction.

List of defined variables is updated.



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y


Once the variables are

defined, you can graph them

or list them. A Graphed Response in the Time Domain



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Identify critical time points

Use the List Extremes menu.

Note down the time points at which the minimum and maximum

values occur.



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Review results over entire structure at critical time points

Enter POST1, read results By Time/Freq..., and enter appropriate

time value.

Plot deformed shape and stress contours.



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Training ManualTransient Analysis Procedure

Build the model




Review Results

Lesson D:


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Training ManualWorkshop - Transient Analysis

In this workshop, you will examine the transient response of a

block bouncing on a beam.

See your Dynamics Workshop supplement for details

Transient Analysis Workshop - Bouncing Block, Page W-35

Documents

Dynamics 70 M4 Transient