Nonlinear Structural Dynamic Analysis by A Discontinuous Galerkin Finite Element Method

Abstract

This paper discusses computational aspects of the discontinuous Galerkin (DG) finite element method as applied to nonlinear structural dynamic problems, by which displacements and velocities are approximated as piecewise bilinear functions in space-time and may be discontinuous at the discrete time levels. Both implicit and explicit iterative algorithms for solving the resulting system of coupled equations are derived. An h-adaptive procedure based on the Zienkiewicz-Zhu error estimate using the SPR technique is described. Numerical examples are provided to show the suitability of the DG method for nonlinear structural dynamics.