An Extended BEM Model for 2-D Elasticity Problems

Within the framework of Somigliana’s displacement and traction identities, we propose an extended equivalent elastic model that enables a BEM that is singularity-free in the primary solution stage for two-dimensional elastostatics. The central idea is to shift the integration boundary from the physical contour S1 to an auxiliary contour S2, introducing a geometric separation that removes boundary-source singularities from the discrete system. When the separation between S1 and S2 is sufficiently large, all integrals in the assembled algebraic equations become regular, and post-processing can be performed in a unified manner using the same nonsingular expressions for both boundary and interior evaluation. We introduce a practical separation measure, the dimensionless parameter δ, and verify that a moderate choice (e.g., δ≈0.5) is effective through a rigid-body displacement test. Benchmark examples demonstrate that, at lower computational cost, the proposed method improves accuracy and convergence compared with the conventional direct BEM (displacement boundary integral equation (BIE) with free-term coefficient c=1/2) and compares favorably with the finite element method (FEM). In particular, thin structures can be treated directly without invoking plate or shell theories.