TSTEP

Bulk Data Entry Defines time step parameters for control and intervals at which a solution will be generated and output in transient analysis.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
TSTEP SID N1 DT1 N01 W3,1 W4,1
N2 DT2 N02 W3,2 W4,2
etc.
TMTD TC1 TC2 TC3 TC4 Alpha Beta
MREF TOL TN1 TN2

Example

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
TSTEP 2 10 .001 5
9 0.01 1

Definitions

Field Contents SI Unit Example
SID Set identification number.

No default (Integer > 0)

N# Number of time steps of value DT#.

No default (Integer ≥ 1)

DT# Time increment.

No default (Real > 0.0)

N0# Skip factor for output. Every N0i-th step will be saved for output.

Default = 1 (Integer > 0)

W3,# The frequency of interest in radians per unit time; used for the conversion of overall structural damping into equivalent viscous damping. 3

Default = blank (Real > 0.0, or blank)

W4,# The frequency of interest in radians per unit time; used for the conversion of element structural damping into equivalent viscous damping. 3

Default = blank (Real > 0.0, or blank)

TMTD Time integration method.
For Linear Direct Transient Analysis:
= blank (Default)
= 1
Newmark-Beta method.
For Nonlinear Direct Transient Analysis:
= 1 (Default)
Generalized alpha method.
= 2
Backward Euler method.

(Integer > 0) 6

TC1 Time integration parameters for transient subcases.

Default = -0.05 (-1/3 < Real < 0) 6

TC2 Time integration parameters for transient subcases.

Default= 0.25*(1-TC1-TC4)2 (Real ≥ 0.25 - 0.5*(TC4 + TC1)) 6

TC3 Time integration parameters for transient subcases. 6

Default = 0.5-TC1-TC4 (Real)

TC4 Time integration parameters for transient subcases. 6

Default = 0 (-1 < Real < 0.5)

Alpha Rayleigh damping coefficient for transient subcases. 7

Default = 0.0 (Real)

Beta Rayleigh damping coefficient for transient subcases. 7

Default = 0.0 (Real)

MREF Controls activation of automatic time-stepping for linear transient and nonlinear transient analysis.
Linear direct transient analysis (Newmark-Beta method):
= 0
Automatic time-stepping is deactivated.
= 1 (Default)
Automatic time-stepping is active via the reference displacement method.
Nonlinear direct transient analysis (Generalized alpha method):
= 0
Automatic time-stepping is deactivated.
= 1 (Default)
Automatic time-stepping is active via the reference displacement method.
Nonlinear direct transient analysis (Backward Euler method):
= 0 (Default)
Automatic time-stepping is deactivated.
= 1
Automatic time-stepping is active via the reference displacement method.

(Integer) See Comment 8

TOL Tolerance for automatic time stepping in transient subcases.

Default = 1.0 (Real > 0) 8

TN1 Control parameter for automatic time stepping in transient subcases. It specifies the maximum number of cut-backs in a single time step.

Default = 5 (Integer > 0) 8

TN2 Control parameter for automatic time stepping in transient subcases. It specifies the minimum number of time step enlargement requests required before the solver enlarges the next time step.

Default=1 (Integer > 0) 8

1. TSTEP entries must be selected with the Subcase Information command TSTEP=SID.
2. The entry permits changes in the size of the time step during the course of the solution. In the example shown, there are 10 time steps of value .001, followed by 9 time steps of value .01. Also, in the case of this example, you have requested that the output be recorded for t = 0.0, .005, .01, .02, .03, and so on.
3. W3 and W4 define frequencies used in linear transient analyses to convert structural damping to equivalent viscous damping. The W3 and W4 fields on TSTEP are not supported for Nonlinear Transient Analysis. For Nonlinear Transient, PARAM, W3 and PARAM, W4 can be used.
4. Different values for W3 and W4 may be set for each set of time increments. If any of the fields are left blank then the value is taken from the PARAM, W3 or PARAM, W4 definition.
5. Transient Response Analysis using Fourier Transformation cannot be used in a model, which also contains a Modal Frequency Response Analysis subcase. OptiStruct will error out in such cases.
6. Time integration method.
The TMTD field can be used to control the time integration scheme for both linear transient and nonlinear transient analysis.
• Linear Transient Analysis

If TMTD field is blank for linear transient analysis, the traditional time integration scheme is used. Automatic time-stepping (MREF=1) is not supported for traditional time integration.

If TMTD=1, the Newmark-Beta Integration scheme is used for linear transient analysis. Automatic time-stepping (MREF=1) is supported for Newmark-Beta time integration.

For more information, refer to Linear Transient Analysis in the User Guide.

• Nonlinear Transient Analysis

If the TSTEP entry is not referenced or present in the input deck, or if the TMTD field is blank, the Generalized Alpha method (more specifically, the HHT- $\alpha$ method) will be used by default.

When TMTD =1, coefficients of Generalized Alpha method are specified using TC1, TC2, TC3, and TC4, for four non-dimensional parameters ( $\alpha ,\beta ,\gamma ,$ and ${\alpha }_{m}$ ), respectively. In general, the Generalized Alpha method should be used for most nonlinear transient analyses. In this method, numerical damping can be adjusted through the parameters $\alpha ,\beta ,\gamma ,$ and ${\alpha }_{m}$ . In particular, non-zero $\alpha$ and ${\alpha }_{m}$ introduces damping for high-frequency response components. On the other hand, Backward Euler method can be used for quasi-static analysis, such as post-buckling problem, since this method is dissipative, and therefore stable.

When TMTD =2, the backward Euler method does not require the input of the TCi fields. The Alpha and Beta fields introduce subcase-dependent Rayleigh damping, so the viscous damping matrix $C$ in a particular subcase is $C=\alpha M+\beta K$ .

For more information, refer to Nonlinear Transient Analysis in the User Guide.

7. Subcase-dependent Rayleigh damping for nonlinear direct transient subcase is issued using Alpha, and Beta. Alternatively, they can be specified using PARAM, ALPHA1 and PARAM, ALPHA2, respectively.
8. Automatic time stepping.
Automatic time-stepping is applicable for both linear and nonlinear transient subcases and is controlled using the MREF field.
MREF=0
Indicates no automatic time stepping.
MREF=1
Automatic time stepping is activated, and the reference displacement is used to normalize the acceleration error measure.
TOL
Specifies the tolerance for time step adjustment error control.
TN1
Specifies the maximum number of cutbacks in a single time step.
TN2
Specifies the minimum number of time step enlargement requests required before the solver enlarges the next time step.

If DTMIN and DTMAX are specified on the NLADAPT entry for Nonlinear Transient Analysis, they have highest priority over the time-stepping process and they are always respected.

9. This card is represented as a loadcollector in HyperMesh.