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*TSTEPPING

Data format:

A single line with 9 values:

ITEMP ETOL DTSUP TSTAB COESUP COELO KONEWT DCONVS DTINF

Status :

Optional (dynamics)

Purpose :

To prescribe an adaptable time stepping

Details :

Parameter	Description
ITEMP	= 1 : automatic time stepping required = 0 : constant time stepping DT
ETOL	Tolerance for the relative third order error. See reference and note (def. = 0.1)
DTSUP	Maximum time step allowed. Must be lower than DTREC
TSTAB	Starting time for automatic stepping (Def. = 1s)
COESUP	See Reference and note (def. = 1.1)
COLELO	See Reference and note (def. = 0.1)
KONEWT	See Reference and note (def. = 5)
DCONVS	If convergence is not achieved with a given time step \(\Delta t = \frac{\Delta t}{DCONVS}\) (def. = 1.5)
DTINF	Minimum time step allowed. (def. 0.0001)

Reference : "A simple error estimator and adaptive time stepping procedure for dynamic analysis , O.C. Zienkiewicz and Y.M. Xie," Earthquake Engineering and Structural Dynamics, vol. 20, 871-887 (1991)

Note

Let \(\ddot{u}_x\) be the acceleration at \(t = t_n\), \(\ddot{u}_{n + 1}\) the acceleration at \(t = t_{n + 1}\)

A local error estimator is given by :

\[ e = \Delta t^2 \Bigl(\beta - \frac{1}{6} \Bigr) (\ddot{u}_{n + 1} - \ddot{u}_{n}) \]

If \(\eta = \frac{||e||}{||u_{max}||} \leq COESUP \times ETOL\) during \(KONEWT\) consecutive time steps, step size should be increased

If \(\eta = \frac{||e||}{||u_{max}||} \geq COESUP \times ETOL\) then step size should be decreased