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Introduction
• Transient dynamic analysis (sometimes called time-history analysis) is a technique used to
determine the dynamic response of a structure under the action of any general time-dependent
loads.
• We use this type of analysis to determine the time-varying displacements, strains, stresses, and
forces in a structure as it responds to any combination of static, transient, and harmonic loads.
• The time scale of the loading is such that the inertia or damping effects are considered to be
important.
• If the inertia and damping effects are not important, you might be able to use a static analysis
instead
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• The basic equation of motion solved by a transient dynamic analysis is where:
[M]{Ẍ} + [C]{Ẋ} + [K]{X} = F(t)
[M] = mass matrix; [C] = damping matrix; [K] = stiffness matrix; {Ẍ} = nodal acceleration vector; {Ẋ}=
nodal velocity vector; {X} = nodal displacement vector; {F(t)} = load vector
• At any given time t, these equations can be thought of as a set of "static“ equilibrium equations
that also take into account inertia forces ([M]) and damping forces ([C]).
• The ANSYS program uses the New-mark time integration method to solve these equations at
discrete time-points.
• The time increment between successive time-points is called the integration time step.
Governing Equation
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• A load step is a set of loads applied over a given time
span.
• Sub-steps are time points within a load step at which
intermediate solutions are calculated.
• The difference in time between two successive sub-
steps can be called a time step or time increment.
• Equilibrium iterations are iterative solutions calculated
at a given time point purely for convergence purposes
General Terminology of Loading
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Load steps & Sub-steps
• A load step is simply a configuration of loads for which a solution is obtained.
• In a linear static or steady-state analysis, you can use different load steps to apply different sets of loads -
wind load in the first load step, gravity load in the second load step, both loads and a different support
condition in the third load step, and so on.
• In a transient analysis, multiple load steps apply different segments of the load history curve.
- Sub-steps are points within a load step at which solutions are calculated
• In a nonlinear static or steady-state analysis, use sub-steps to apply the loads gradually so that an accurate
solution can be obtained.
• In a linear or nonlinear transient analysis, use sub-steps to satisfy transient time integration rules (which
usually dictate a minimum integration time step for an accurate solution).
• In a harmonic analysis, use sub-steps to obtain solutions at several frequencies within the harmonic
frequency range.
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Procedure
The procedure for a full transient dynamic analysis (available in the ANSYS/Multi-physics, ANSYS/Mechanical,
and ANSYS/Structural products) consists of 5 main steps:
1. Build the model
2. Choose analysis type and options
3. Specify BC’s and initial conditions
4. Apply time-history loads and solve
5. Review Results
If pre-modal analysis is preferred
Geometry
Material
properties
Contacts
Meshing
Transient settings,
loads & supports
Solve the
model
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General Transient Analysis
• Inputs:
1. Analysis settings :
2. Time steps : no. of steps, initial
time, end-time, solver type,
damping controls
3. Load varying with the time : any
type of force like pressure,
acceleration, gravity, remote force
,rotational velocity, rotational
acceleration
4. Boundary conditions : supports are
requirement and constraints are as
per problem
• Outputs :
1. Stress tool-different types of
stress
2. Deformation: Total and directional
3. Strains
4. Strain energy
5. Other quantities like fatigue.
Linearised stress
8. Solution Methods
Solving the equation of motion
Direct Integration Mode Superposition
Implicit Explicit
Full Reduced Full Reduced
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Geometry
• Any type of geometry may be present in a
harmonic analysis
• Solid bodies, surface bodies, line bodies,
and any combination thereof may be used
• Recall that, for line bodies, stresses and
strains are not available as output
• A Point Mass may be present, although
only acceleration loads affect a Point Mass
Rotor-Shaft-Fan assembly of an EV-MOTOR
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Material Properties
• In a transient analysis, Young’s
Modulus, Poisson’s Ratio, and
Mass Density are required input
• All other material properties can be
specified but are not used in a
harmonic analysis
• Damping is not specified as a
material property but as a global
property
Double click on
engineering materials to
define material & their
properties
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Contact Regions
• Contact regions are available in modal analysis.
However, since this is a purely linear analysis,
contact behavior will differ for the nonlinear contact
type
• The contact behavior is similar to free vibration
analyses, where nonlinear contact behavior will
reduce to its linear counterparts since harmonic
simulations are linear.
• It is generally recommended, however, not to
use a nonlinear contact type in a harmonic
analysis Friction
Bonded
No Separation
Rough
Frictionless
Types of Connections available and they are used as per the
requirements
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Analysis Settings
• A general suggestion for selection of the initial time
step is to use the following equation: where fresponse
is the frequency of the highest mode of interest
• 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. One can impose initial conditions with
multiple load steps
• 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”
• The initial, minimum, and maximum time steps should
be defined
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Time-step consideration in Transient Analysis
- 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.
- The “Step End Time” is the actual simulation ending
time for the “Current Step Number”
- The initial, minimum, and maximum time steps
should be defined to ensure
• Accuracy
• Convergence
• Minimize solve time
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Stepped Versus Ramped Loads
• When you specify more than one sub-step
in a load step, the question of whether the
loads should be stepped or ramped arises.
• If a load is stepped, then its full value is
applied at the first sub-step and stays
constant for the rest of the load step.
• If a load is ramped, then its value increases
gradually at each sub-step, with the full
value occurring at the end of the load step.
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Loads with Time steps
Graph between load Vs time step
Time steps
Stepped Type of Loading w.r.to Time
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Rammed Type of Loading(Shock) w.r.to Time
Time steps Load applied w.r.to time
Graph between load Vs time step
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Apply Time-History Loads & Solve
Structural loads and joint conditions can be input as time-dependent
load histories
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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• Solution : we choose the required quantities like stresses, deformations , frequency
response plots (Amplitude Vs Frequency) , Phase Response plots .
• Press SOLVE for the solution
• Results : We observe the critical locations in which direction(X,Y,Z) the response is
acquired matching with natural frequency of the component . In the frequency response
plots , we find the response peaks matching with the natural frequency.
Results
