Finite element analysis of elastic-plastic wave propagation effects

Abstract

The feasibility of dynamic analysis by means of the finite element method, in conjunction with direct time step integration procedures, has been demonstrated and documented in the literature. However, there appears to be some uncertainty concerning the validity of such analyses in cases involving wave propagation effects. It is the purpose of this paper to demonstrate that under appropriate conditions, nonlinear finite element analysis techniques, utilizing a variable time step integration procedure, may be applied to obtain a reliable description of the response of a body undergoing wave propagation effects. The method employs Taylor series expansions to obtain predictor-corrector expressions, truncated to difference form, of the solution to a system of first order nonlinear equations. The corresponding second order system of equations of motion are employed to construct the corrector expression. The incorporation of this procedure within the tangent modulus method of nonlinear analysis is described and numerical results are presented for a number of axisymmetric structures subjected to elastic-plastic wave propagation effects, including those cases involving reflections from boundaries.