A Preliminary Study on Finite Element-Hosted Couplings with the Boundary Element Method

Abstract

Abstract : This study investigated the theoretical and numerical basis of finite element-hosted couplings with the boundary element method (BEM). The emphasis of the study is on (1) conceptually unifying the different coupling approaches and (2) providing an algorithm to facilities future implementation. Overviews of both the indirect and direct boundary element formulations are included. The theoretical development of BEM stiffness matrices is limited to a physically intuitive derivation based on the indirect BEM. Discontinuity between finite element and boundary element regions is an inherent trait of the boundary element method; this behavior is not eliminated by simply matching the order of shape functions between the two methods. A discussion of the numerical implementation of BEM-formulated stiffness matrices addresses both the direct and indirect BEMs. The direct BEM is better suited in coupled solution approaches due to its simpler traction-displacement relationship. Algorithms are included which outline the calculations unique to obtaining a stiffness matrix from the BEM.