A Novel Boundary Element Approach for Elastic Domains Using DST and Galerkin Tensor

Two techniques of the Boundary Elements Method (BEM) are coupled for solving piecewise homogeneous elastic problems with body forces. The Domain Superposition Technique (DST), which is an alternative to the classical sub-regions approach, is used to approach the sectorial homogeneities, modeling the domain as a sum of a homogeneous surrounding sector and other complementary ones with different constitutive properties. The Galerkin tensor, with the adoption of a primitive function of the fundamental solution, transforms domain integrals. A classical boundary element matrix system is formed in which, unlike the sub-region idea, no interfaces exist between regions, and compatibility and equilibrium conditions are not imposed. The necessary correlation between the surrounding domain and all sub-domains is performed through the classic boundary element procedure of scanning, in which source points are used as the basis for integration along the boundaries. This research contributes to BEM literature by addressing a specific and non-trivial gap: the simultaneous treatment of body forces and material heterogeneity in a simplified and computationally efficient manner, without resorting to classical sub-region formulations.