A revisited time domain formulation of boundary integral equations for two-dimensional elastodynamics

TL;DR

This paper develops a new time domain boundary integral equation formulation for 2D elastodynamics, deriving kernels from 3D identities and applying an implicit scheme to solve transient wave problems.

Contribution

It introduces a novel 2D BIE formulation based on 3D integral identities with an implicit time marching scheme for elastodynamics.

Findings

Derived explicit time-dependent kernels for 2D elastodynamics.

Implemented an implicit time marching scheme for transient problems.

Validated the formulation with an analytical solution for a cylindrical cavity.

Abstract

A boundary integral equation (BIE) formulation for 2-D transient elastic wave propagation problems is presented. On the basis of the three-dimensional integral identity, the time-dependent kernels for the two-dimensional boundary integral equation are obtained. A linear time variation of displacements and tractions is assumed over each time step and an implicit time marching scheme is deduced. The formulation is used to obtain an analytical solution for the cylindrical cavity under transient pressure at the boundary surface.