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Module 3
TRANSIENT DYNAMIC ANALYSIS
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TRANSIENT DYNAMIC ANALYSIS
A. 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 & PURPOSE
What 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 quantitiessuch as stresses and strains.
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TRANSIENT ANALYSIS
… DEFINITION & PURPOSE
Transient 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 & CONCEPTS
Topics covered:
• Equation of motion
• Solution methods
• Integration time step
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TRANSIENT ANALYSIS - TERMINOLOGY & CONCEPTS
EQUATION OF MOTION
t F u K uC u M
• 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.
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TRANSIENT ANALYSIS - TERMINOLOGY AND CONCEPTS
… INTEGRATION TIME STEP
Response frequency• Different types of loads excite different
natural frequencies of the structure.
• Response frequency is the weightedaverage of all frequencies excited by a
given load.• The ITS should be small enough to
capture the response frequency .
• Twenty time points per cycle should besufficient, i.e,
Dt = 1/20f
where f is the response frequency.
Response period
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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 BC’s and initial conditions
• Apply time-history loads and solve
• Review results
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TRANSIENT ANALYSIS PROCEDURE
BUILD THE MODEL
Model
• All nonlinearities are allowed.
• Remember density!
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Build the model
Choose analysis type and options:
• Enter Solution and choose
transient analysis.• Choose Full transient
• Solution options - discussed
next.
• Damping - discussed next.
TRANSIENT ANALYSIS PROCEDURE
CHOOSE ANALYSIS TYPE & OPTIONS
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TRANSIENT ANALYSIS PROCEDURE
… CHOOSE ANALYSIS TYPE & OPTIONS
Solution options
• Choose large displacement transient or small
displacement transient .
• When in doubt, choose large displacement
transient
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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TRANSIENT ANALYSIS PROCEDURE
… CHOOSE ANALYSIS TYPE & OPTIONS
Automatic time stepping
• An algorithm that automatically calculates appropriate ITS sizesduring the transient.
•
Recommendation is to activate it and also specify minimum andmaximum values of ITS.
• If nonlinearities are present, use the “Program Chosen” option.
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TRANSIENT ANALYSIS PROCEDURE
… CHOOSE ANALYSIS TYPE & OPTIONS
Output controls
• Used to determine what is written to the results file.
• Use the OUTRES command or choose Solution > Sol’n 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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TRANSIENT ANALYSIS PROCEDURE
… CHOOSE ANALYSIS TYPE & OPTIONSTurn transient effects on/off
• useful for setting up initial conditions
Ramp or Step apply load
• Specify damping)
• Use default values for time integration
parameters
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TRANSIENT ANALYSIS PROCEDURE
… CHOOSE ANALYSIS TYPE & OPTIONS
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:
b = 2/w
where is the damping ratio and w 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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TRANSIENT ANALYSIS PROCEDURE
… CHOOSE ANALYSIS TYPE & OPTIONS
• Choose solver
• By default ANSYS chooses Sparse solver
• For large problems (>100000 dofs) use PCG solver
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TRANSIENT ANALYSIS PROCEDURE
… SPECIFY BC’S & INITIAL CONDITIONS
•
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
t 0.0005 0.001Load step 1
Application of Temporal Acceleration
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TRANSIENT ANALYSIS PROCEDURE
… SPECIFY BC’S & INITIAL CONDITIONS
• Load step 2:
• Transient effects ON.
• Delete the imposed displacement.
• Specify ending time and continue with the transient.
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TRANSIENT ANALYSIS PROCEDURE
… SPECIFY BC’S & INITIAL CONDITIONS
Example - A stationary plate subjected to an impulse load
• In this case u0 = v0 = a0 = 0.
• These are the default initial conditions in ANSYS, so there is no
need to specify them!
• Simply apply the boundary conditions and the impulse load,
then solve.
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TRANSIENT ANALYSIS PROCEDURE
APPLY TIME-HISTORY LOADS & SOLVE
Build the model
Choose analysis type and options
Specify BC’s and initial conditions
Apply time-history loads and solve
• 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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TRANSIENT ANALYSIS PROCEDURE
… APPLY TIME-HISTORY LOADS & SOLVE
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 boundary conditionscan be expressed directly with tabular input
For more informationrefer to “Applying LoadsUsing Function Boundary
Conditions” in the BasicAnalysis Guide.
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Method 1
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A l i f d 2
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Acceleration response of node 2
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Method 2
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Acceleration response of node 2
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Method 3
TRANSIENT ANALYSIS PROCEDURE
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TRANSIENT ANALYSIS PROCEDURE
… APPLY TIME-HISTORY LOADS & SOLVE
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, each with 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
TRANSIENT ANALYSIS PROCEDURE
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TRANSIENT ANALYSIS PROCEDURE
… APPLY TIME-HISTORY LOADS & SOLVE
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.
TRANSIENT ANALYSIS PROCEDURE
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TRANSIENT ANALYSIS PROCEDURE
… APPLY TIME-HISTORY LOADS & SOLVE
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.)
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TRANSIENT ANALYSIS PROCEDURE
… APPLY TIME-HISTORY LOADS & SOLVE
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
and either solve the load step or write it to a load step file
(LSWRITE).
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TRANSIENT ANALYSIS PROCEDURE
… APPLY TIME-HISTORY LOADS & SOLVE• 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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TRANSIENT ANALYSIS PROCEDURE
… APPLY TIME-HISTORY LOADS & SOLVE
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.
TRANSIENT ANALYSIS PROCEDURE
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TRANSIENT ANALYSIS PROCEDURE
… APPLY TIME-HISTORY LOADS & SOLVE
Solution
• Use SOLVE command (or LSSOLVE if
load step files were written).
• At each time step, ANSYS calculates
load values based on the load-vs-timecurve.
TRANSIENT ANALYSIS PROCEDURE
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TRANSIENT ANALYSIS PROCEDURE
REVIEW RESULTS
Build the model
Choose analysis type and options
Specify BC’s and initial conditions
Apply time-history loads and solve
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.
TRANSIENT ANALYSIS PROCEDURE
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TRANSIENT ANALYSIS PROCEDURE
… REVIEW RESULTS - POST26
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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TRANSIENT ANALYSIS PROCEDURE
Build the model
Choose analysis type and options
Specify BC’s and initial conditions
Apply time-history loads and solve
Review Results