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A meshless singular boundary method for three‐dimensional elasticity problems
Author(s) -
Gu Yan,
Chen Wen,
Gao Hongwei,
Zhang Chuanzeng
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5154
Subject(s) - singular boundary method , regularized meshless method , curse of dimensionality , elasticity (physics) , boundary element method , method of fundamental solutions , linear elasticity , meshfree methods , boundary (topology) , collocation (remote sensing) , computer science , boundary knot method , boundary value problem , mathematics , benchmark (surveying) , mathematical optimization , finite element method , mathematical analysis , structural engineering , engineering , artificial intelligence , physics , geodesy , machine learning , thermodynamics , geography
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. Copyright © 2015 John Wiley & Sons, Ltd.