The Indirect-BEM for 3D Elastostatic and Elastodynamic Problems: Constraints, Convergence and Computational Cost

Abstract

This work reports an investigation of some issues found in an implementation of the Indirect version of the Boundary Element Method (IBEM) for three-dimensional elastostatic and elastodynamic problems. Two different Green’s functions, or auxiliary states, are used in the implementations. Numerical results show that the IBEM presents a much slower convergence rate with respect to the number of boundary elements than the Direct-BEM counterpart. The numerically synthesized non-singular dynamic auxiliary states is computationally much more demanding and expensive, but are much more versatile in terms of incorporating non-isotropic behavior and general linear viscoelastic models. These trade offs, which oppose computational efficiency and modeling abilities are addressed. Finally, it is investigated whether the discontinuity observed in the traction components in diagonal terms of the influence matrix S constrains the applicability of IBEM to open domains.