Transient elastodynamic boundary element analysis based on time-stepping scheme. Study on one-dimensional problems.

Abstract

A boundary element technique based on the time-stepping formulae is proposed for the transient elastodynamic problems. The acceleration term of the basic differential equation of elastodynamics is approximated by finite difference on time, Newmark's single-step formula and Wilson's formula. This approximation enables boundary element formulation by using the same fundamental solution as that of the steady-state elastodynamic equation. The present paper deals only with the one-dimensional problem under an impact force to confirm the effectiveness of the method. The numerical examples reveal that the Wilson θ method is the most suitable scheme among the three to incorporate with the Boundary Element Method, and that the proposed method is promising for two- or three-dimensional problems and other complicated coupled problems.