A simple local error estimator and an adaptive time-stepping procedure for direct integration method in dynamic analysis. (English) Zbl 0777.73079
A simple a posteriori local error estimator for time discretization in structural dynamic analysis is presented. It is derived from the difference of the solutions between an ordinary integration method (the Newmark scheme) and another higher-order one which assumes that the derivatives of accelerations vary linearly within each time step. Furthermore, it is shown that this error estimator may also be obtained by Taylor expansion or by a post-processing technique. Accordingly, an adaptive time-stepping procedure, which automatically adjusts the time- step size so that the local error at each time step is within a prescribed accuracy, is described.
MSC:
| 74S20 | Finite difference methods applied to problems in solid mechanics |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L12 | Finite difference and finite volume methods for ordinary differential equations |
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