A review of automatic time-stepping strategies on numerical time integration for structural dynamics analysis

This paper discusses some of the algorithms available for the automatic adaptive selection of time step size, applied to the step-by-step direct time integration methods of structural dynamics problems. Three adaptive strategies based on different concepts are explored and compared: the algorithm of Bergan and Mollestad (1985), which is based on the ‘current characteristic frequency’; the strategy of Hulbert and Jang (1995), which uses a ‘local error estimator’; and the method of Lages et al. (2013), which is based on the ‘geometric indicator of displacements history curvature’. The reviewed strategies are applied to the Newmark integration scheme to solve various numerical examples of linear dynamic systems, which are presented to compare the performance between the three algorithms that are tested. To conclude, a brief analysis about the considerations of the computational cost is made.

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