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A meshless singular boundary method for three-dimensional elasticity problems. (English) Zbl 1352.74039
Summary: This study documents the first attempt to extend the singular boundary method, a novel meshless boundary collocation method, for the solution of 3D elasticity problems. The singular boundary method involves a coupling between the regularized BEM and the method of fundamental solutions. The main idea here is to fully inherit the dimensionality and stability advantages of the former and the meshless and integration-free attributes of the later. This makes it particularly attractive for problems in complex geometries and three dimensions. Four benchmark 3D problems in linear elasticity are well studied to demonstrate the feasibility and accuracy of the proposed method. The advantages, disadvantages, and potential applications of the proposed method, as compared with the FEM, BEM, and method of fundamental solutions, are also examined and discussed.

MSC:
74B05 Classical linear elasticity
74S15 Boundary element methods applied to problems in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
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