Weakly-Singular Traction and Displacement Boundary Integral Equations and Their Meshless Local Petrov-Galerkin Approaches |
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Authors: | Zhidong Han ýì Zhenhan Yao Ú SN Atluri |
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Institution: | aCenter for Aerospace Research and Education, University of California, Irvine, 5251 California Avenue, Suite 140, Irvine, CA 92612, USA;bDepartment of Engineering Mechanics, Tsinghua University, Beijing 100084, China |
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Abstract: | The general meshless local Petrov-Galerkin (MLPG) weak forms of the displacement and trac- tion boundary integral equations (BIEs) are presented for solids undergoing small deformations. Using the directly derived non-hyper-singular integral equations for displacement gradients, simple and straight- forward derivations of weakly singular traction BIEs for solids undergoing small deformations are also pre- sented. As a framework for meshless approaches, the MLPG weak forms provide the most general basis for the numerical solution of the non-hyper-singular displacement and traction BIEs. By employing the various types of test functions, several types of MLPG/BIEs are formulated. Numerical examples show that the pre- sent methods are very promising, especially for solving the elastic problems in which the singularities in dis- placements, strains, and stresses are of primary concern. |
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Keywords: | meshless local Petrov-Galerkin (MLPG) approach boundary integral equation (BIE) non- hyper-singular dBIE/tBIE moving least squares (MLS) MLPG/BIE |
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