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The boundary node method for three-dimensional linear elasticity. (English) Zbl 0951.74075
Summary: We develop the boundary mode method (BNM) for solving three-dimensional problems in linear elasticity. The BNM represents a coupling between boundary integral equations and moving least squares 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 ‘mesh’ and the interpolation procedure. For linear elasticity, problems with prescribed free rigid-body modes in traction are typically eliminated by suitably restraining the body. However, an alternative approach developed recently for the boundary element method is extended in this work to the BNM. This approach is based on ideas from linear algebra to complete the rank of the singular stiffness matrix. Also, the BNM has been extended in the present work to solve problems with material discontinuities, and a procedure has been developed for obtaining displacements and stresses accurately at internal points close to the boundary of a body.

MSC:
74S15 Boundary element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74B05 Classical linear elasticity
74B10 Linear elasticity with initial stresses
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