Scaled-coordinate BEM for 3D elasticity problems with efficient domain integral treatment

Abstract

The boundary element method (BEM) has long been recognized as an efficient numerical technique for the analysis of three-dimensional (3D) elasticity problems due to its intrinsic advantage of dimensionality reduction. However, for inhomogeneous materials or elasticity formulations involving body forces, domain integrals arise, compromising the boundary-only nature of the method. This work proposes a novel scaled-coordinate transformation BEM (SCT-BEM) for 3D elasticity, which inherits the SCT framework recently developed for potential and heat transfer problems. The proposed SCT-BEM transforms the elasticity domain integrals into low-dimensional boundary integrals without invoking particular solutions or volume discretization. Further, a unified treatment is provided for weakly- and strongly-integrals using an SCT-based coordinate translation. Numerical examples demonstrate that the proposed framework significantly improves the applicability of BEM to complex elasticity problems while preserving its fundamental advantages.