Knowledge of Transient Dynamics

CAE Structural
1

Transient Dynamics

Definition

Transient dynamics analysis, also known as time history analysis, is used to determine the dynamic response of structures under arbitrary, time-varying loads. This analysis can determine time-varying displacement, strain, stress, and force of the structure under combinations of steady-state loads, transient loads, and harmonic loads. The correlation of load and time makes inertial force and damping significant. If inertial force and damping are insignificant, static analysis can replace transient analysis.

Transient Dynamics Analysis Methods

There are three methods for transient dynamics analysis: Full Method, Reduced Method, and Mode Superposition Method.

  1. Full Method
    The full method calculates transient response using the complete system matrix without reduction. It allows for various nonlinear characteristics (plasticity, large deformation, large strain, etc.) but is the most resource-intensive.

    • Advantages:
      • Easy to use without selecting master DOFs or modes.
      • Allows various types of nonlinear characteristics.
      • Uses the complete matrix without approximating the mass matrix.
      • Provides all displacements and stresses in one analysis.
      • Allows all types of loads: node force, applied (non-zero) displacement (not recommended), and element loads (pressure and temperature), and can specify boundary conditions through TABLE array parameters.
      • Allows loads on solid models.
    • Disadvantages:
      • More resource-intensive than other methods.

  2. Mode Superposition Method
    This method calculates the structure’s response by multiplying and summing the modes (eigenvalues) from modal analysis. It’s the only transient dynamics analysis method available in ANSYS/Professional.

    • Advantages:
      • Faster and less resource-intensive for many problems than the full or reduced methods.
      • If modal analysis does not use the PowerDynamics method, element loads applied during modal analysis can be introduced into transient analysis through the LVSCALE command.
      • Allows consideration of modal damping (damping ratio as a function of mode shape).
    • Disadvantages:
      • Time step must remain constant throughout the analysis; automatic time stepping is not allowed.
      • Only simple point-to-point contact (gap conditions) is allowed for nonlinearity.
      • Forced (non-zero) displacement cannot be applied.

  3. Reduced Method
    This method reduces the problem size by using master DOFs and a reduced matrix. After calculating displacements at master DOFs, ANSYS can extend the solution to the original complete set of DOFs.

    • Advantages:
      • Faster and less resource-intensive than the full method.
    • Disadvantages:
      • Initial solution calculates displacement only at master DOFs, with a second step for complete spatial displacement, stress, and force.
      • Cannot apply element loads (pressure, temperature), but can apply acceleration.
      • All loads must be applied at user-defined master DOFs (limited load application on solid models).
      • Time step must remain constant throughout the analysis; automatic time stepping is not allowed.
      • Only simple point-to-point contact (gap conditions) is allowed for nonlinearity.

Time Step Selection Criteria

The key technology in transient analysis is selecting the integration time step. The precision of transient integration depends on the time step dt size. A smaller time step increases precision but may waste computational resources; a larger time step can cause high-order modal response errors and affect overall response. Selecting an appropriate time step is crucial. If the highest contributing modal frequency f of the overall structure can be determined, the time step can be 1/20f. A sufficiently small time step is needed to capture load changes during abrupt load variations. For contact problems, the time step should capture energy transfer between contact bodies. For beginners, automatic time stepping is recommended.

Example Analysis

Using beam188 element for transient dynamics analysis, fix the lower end of the beam and apply a load along the X direction at the top end, analyzing the response over 0.5 seconds. The APDL code is as follows:

/CLEAR
/PREP7
! Create element beam188
ET,1,BEAM188

! Set beam section
SECTYPE, 1, BEAM, CTUBE, BEAM1, 0
SECOFFSET, CENT
SECDATA,0.01,0.015,0,0,0,0,0,0,0,0,0,0

! Material 1: Steel
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,EX,1,,2.1E11
MPDATA,PRXY,1,,0.269
MPDATA,DENS,1,,7850

! Create points
FLST,3,3,8
FITEM,3,0,0,0
FITEM,3,0,1,0
FITEM,3,0,2,0
K, ,P51X

! Create two lines
LSTR, 1, 2
LSTR, 2, 3

! Set line mesh attributes
LATT,1, ,1, , , ,1

! Mesh lines
FLST,5,2,4,ORDE,2
FITEM,5,1 ! Select line
FITEM,5,-2
CM,_Y,LINE
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y
LESIZE,_Y1, , ,10, , , , ,1 ! Set 10 divisions

*FLST,2,2,4,ORDE,2
FITEM,2,1
FITEM,2,-2
LMESH,P51X
/UI,MESH,OFF

! Create load table with 5 rows and 1 column, and fill load table
*DIM,P(T),TABLE,5,1,1,time, ,
*SET,P(1,0,1) , 0
*SET,P(2,0,1) , 0.01
*SET,P(2,1,1) , 1000
*SET,P(3,0,1) , 0.02
*SET,P(3,1,1) , 1200
*SET,P(4,0,1) , 0.03
*SET,P(4,1,1) , 1400
*SET,P(5,0,1) , 0.04
*SET,P(5,1,1) , 1600

! Set loads
FLST,2,1,1,ORDE,1
FITEM,2,12
/GOF,P51X,FX, %P%
/REPLOT,RESIZE

! Add constraints
FLST,2,1,1,ORDE,1
FITEM,2,1
/GOD,P51X, , , , , ,ALL, , , , ,

! Set analysis type, transient analysis 4, full method
FINISH
/SOL
ANTYPE,4
TRNOPT,FULL
LUMPM,0

! Set integration time step
NSUBST,50,0.05,0.01 ! 50 steps, max interval 0.05, min interval 0.01
OUTRES,ERASE
OUTRES,ALL,ALL
AUTOTS,1 ! Automatic time step
TIME,0.5 ! Time

! Solve
FINISH
/SOL
/STATUS,SOLU
SOLVE