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Weakly-Singular Traction and Displacement Boundary Integral Equations and Their Meshless Local Petrov-Galerkin Approaches 被引量:2

Weakly-Singular Traction and Displacement Boundary Integral Equations and Their Meshless Local Petrov-Galerkin Approaches
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摘要 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. 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.
出处 《Tsinghua Science and Technology》 SCIE EI CAS 2005年第1期1-7,共7页 清华大学学报(自然科学版(英文版)
关键词 meshless local Petrov-Galerkin (MLPG) approach boundary integral equation (BIE) non- hyper-singular dBIE/tBIE moving least squares (MLS) MLPG/BIE 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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参考文献2

  • 1S. N. Atluri,T. Zhu.A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics[J].Computational Mechanics.1998(2)
  • 2H. Okada,H. Rajiyah,S. N. Atluri.Non-hyper-singular integral-representations for velocity (displacement) gradients in elastic/plastic solids (small or finite deformations)[J].Computational Mechanics.1989(3)

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