Computational Structural Dynamics

This chapter presents an overview and a state-of-the art compilation of time integration methods for solving problems of dynamics, with a particular focus on developments that have occurred during the past 25 years. Various classifications of time integration algorithms are provided that assist the reader in understanding the many different types of numerical methods available for solving time-dependent problems. Time integration algorithms for linear structural dynamics are reviewed thoroughly, from classical Newmark-type schemes, to recent developments in time finite element-based approaches. The distinction between linear and nonlinear dynamics is articulated and numerical methods developed for direct application towards solving nonlinear dynamics probems are presented. The chapter concludes with guidelines towards selecting an appropriate time integration method, along with guidelines towards choosing appropriate time step sizes. Keywords: time integration algorithms; structural dynamics; nonlinear dynamics; ordinary differential equations