The technique of domain superposition to solve piecewise homogeneous elastic problems

The Boundary Element Method, a numerical technique that is not based on domain discretization, faces difficulties to model piecewise homogeneous problems that do not appear in many other applications. Thus, in this paper it is presented an alternative methodology for solution of this kind of problem, previously tested successfully for the Laplace Equation, applied here to static cases of linear elasticity. It is substantially different from the classic sub-region technique, since it is based on the sum of elastic energy retained in each distinct sector. Several examples that include cases with irregular domains are simulated showing the robustness and adequacy of the proposed technique. In the absence of analytical solutions, Finite Element Method solutions are used as reference for error evaluation.