Inelastic transient dynamic analysis of three‐dimensional problems by BEM

Abstract

A direct Boundary Element formulation and its numerical implementation for inelastic transient dynamic analysis of three‐dimensional solids is presented. The formulation is based on an initial stress approach and is the first ever of its kind in the field of the Boundary Element Method. This formulation employs the Navier–Cauchy equation of motion, Graffi's dynamic reciprocal theorem, Stokes' fundamental solution and the Divergence theorem, together with Kinematical and Constitutive equations to obtain the pertinent integral equations of the problem in the time domain within the context of small displacement theory of elastoplasticity. The boundary integral equations are cast in an incremental form, in which elastoplastic relations of the incremental type are used for the material description. These equations are then solved using a time‐stepping algorithm in conjunction with an iterative solution scheme to satisfy the constitutive relations. Higher order shape functions are used to approximate the field quantities in space as well as in time. Finally, the applicability of this methodology is demonstrated by presenting a few example problems. Copyright © 1990 John Wiley & Sons, Ltd