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

• We review the basic theory of numerical time integration of structural dynamic.
• We expose the concepts of three different automatic time-stepping algorithms.
• Numerical examples show the effects of the strategies in simple linear models.
• The strategies have different intuitive aspects and some improvements can be done.
• The results for the first and second strategies were closer than the third strategy.

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.