Variationally–based hybrid boundary element methods

The hybrid stress boundary element method (HSBEM) was introduced in 1987 on the basis of the Hellinger-Reissner potential, as a generalization of Pian’s hybrid finite element method. This new two-field formulation makes use of fundamental solutions to interpolate the stress field in the domain of an elastic body, which ends up discretized as a superelement with arbitrary shape and arbitrary number of degrees of freedom located along the boundary. More recently, a variational counterpart – the hybrid displacement boundary element method (HDBEM) – was proposed, on the basis of three field functions, with equivalent advantages. The present paper discusses these methods as well as the traditional, collocation boundary element method (CBEM). The mechanical properties of the resulting matrix equations are investigated and a series of concepts in both HDBEM and CBEM that have not been properly considered by previous authors, particularly in which concerns body forces, are redefined. This is not a review paper, but rather a theoretical, comparative analysis of three methods, with many physical considerations, some innovations and a few academic illustrations.