Structure preserving integrators for non‐linear structural dynamics

Abstract

AbstractA well known and major drawback of standard time integration schemes in the field of non‐linear elastodynamics is their unstable behavior in the case of stiff material behaviour. Even second order accurate implicit time integration schemes are unable to resolve the problem under consideration effectively. To remedy this drawback, structure preserving integrators have been developed. Therefore, the goal of this paper is to compare recently developed integrators. In particular, an energy and momentum conserving scheme, based on a publication by Betsch & Steinmann [1], as well as a symplectic variational integrator, proposed by Lew et al. [4] and Wendlandt & Marsden [3], based on a mid‐point evaluation of the discrete Lagrangian, are presented. Two representative numerical examples will outline the characteristics of the different approaches. In particular, a stiff non‐linear spring pendulum and a finite element model of non‐linear structural dynamics are considered. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)