A multi-time step integration algorithm for structural dynamics based on the modified trapezoidal rule Original Research Article

An explicit multi-time step (subcycling) integration method is proposed for solving semi-discretized structural dynamics problems. Based on nodal partition theory, this method is derived from the modified trapezoidal rule method (MTM). To achieve numerical stability virtually fixed physical quantities, displacement and velocity, are assumed for the non-updated nodal groups. The energy method is used to analyze the stability of the new algorithm and the critical time step for each nodal group is determined in terms of the maximum frequency of the elements in the associated subdomain. Some example problems are evaluated to numerically examine the accuracy and stability of the algorithm.