The boundary node method for three-dimensional linear elasticity

The Boundary Node Method (BNM) is developed in this paper for solving three-dimensional problems in linear elasticity. The BNM represents a coupling between Boundary Integral Equations (BIE) and Moving Least-Squares (MLS) interpolants. The main idea is to retain the dimensionality advantage of the former and the meshless attribute of the later. This results in decoupling of the `meshʹ and the interpolation procedure. For problems in linear elasticity, free rigid-body modes in traction prescribed problems are typically eliminated by suitably restraining the body. However, an alternative approach developed recently for the Boundary Element Method (BEM) is extended in this work to the BNM. This approach is based on ideas from linear algebra to complete the rank of the singular sti ness matrix. Also, the BNM has been extended in the present work to solve problems with material discontinuities and a new procedure has been developed for obtaining displacements and stresses accurately at internal points close to the boundary of a body.