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Formulation of Weakly Singular Displacement/Traction Integral Equations; and Their Solution by the MLPG Method

机译：弱奇异位移/牵引积分方程的形式; mLpG方法及其解决方案

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In this paper, a very simple method is used to derive the weakly singular traction boundary integral equation based on the integral relationships for displacement gradients. The concept of the MLPG method is employed to solve the integral equations, especially those arising in solid mechanics. A moving Least Squares (MLS) interpolation is selected to approximate the trial functions in this paper. Five boundary integral Solution methods are introduced: direct solution method; displacement boundary-value problem; traction boundary-value problem; mixed boundary-value problem; and boundary variational principle. Based on the local weak form of the BIE, four different nodal-based local test functions are selected, leading to four different MLPG methods for each BIE solution method. These methods combine the advantages of the MLPG method and the boundary element method.

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作者
Atluri, S. N. ; Shen, S.;
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年度 2002
页码 1-42
总页数 42
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Boundary element method; Singular integral equations; Variational principles; Boundary value problems; Displacement; Interpolation; Microwave landing systems; Solid mechanics;

机译：边界元法;奇异积分方程;变分原理;边值问题;位移;插值;微波着陆系统;固体力学;

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专利

1. Weakly-singular traction and displacement boundary integral equations and their meshless local petrov-galerkin approaches [J] . Han Zhidong, Yao Zhenhan, Atluri S. N. Tsinghua Science and Technology . 2005,第1期

机译：弱奇异牵引力和位移边界积分方程及其无网格局部Petrov-Galerkin方法
2. Weakly-Singular Traction and Displacement Boundary Integral Equations and Their Meshless Local Petrov-Galerkin Approaches [J] . HAN Zhidong, YAO Zhenhan, S.N.Atluri 清华大学学报（英文版） . 2005,第001期

机译：弱奇异位移边界积分方程及其无网格局部Petrov-Galerkin方法
3. A polynomial collocation method for the numerical solution of weakly singular and singular integral equations on non-smooth boundaries [J] . G. Monegato, L. Scuderi International Journal for Numerical Methods in Engineering . 2003,第13期

机译：非光滑边界上的弱奇异和奇异积分方程数值解的多项式配置方法
4. Complete treatment of double surface weakly singular integrals arising in Galerkin mixed potential integral equation formulations via the direct evaluation method [C] . Athanasios G. Polimeridis, Juan R. Mosig IEEE Antennas and Propagation Society International Symposium . 2010

机译：通过直接评估方法完全治疗Galerkin混合电位整体式配方中的双表面弱奇异积分
5. CONVERGENCE AND SUPERCONVERGENCE OF NUMERICAL SOLUTIONS OF WEAKLY SINGULAR INTEGRAL AND DIFFERENTIAL EQUATIONS (GALERKIN, COLLOCATION, EIGENVALUES, EIGENVECTORS, SPLINES) [D] . LEBBAR, RACHID. 1986

机译：弱奇异积分和微分方程数值解的收敛性和超级度验收（Galerkin，Collocation，特征值，特征向量，花键）
6. Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations [O] . Michael Feischl, Gregor Gantner, Dirk Praetorius -1

机译：弱奇异积分方程的自适应IGA边界元方法的可靠高效后验误差估计
7. Spectral methods for weakly singular Volterra integral equations with smooth solutions [O] . Chen Yanping, Tang Tao 2009

机译：具有光滑解的弱奇异Volterra积分方程的谱方法
8. On the Formulation of Weakly Singular Displacement/Traction Integral Equations; and Their Solution by the MLPG Method [R] . Atluri, Satya N., Shen, Shengping 2002

机译：关于弱奇异位移/牵引积分方程的形式; mLpG方法及其解决方案

Formulation of Weakly Singular Displacement/Traction Integral Equations; and Their Solution by the MLPG Method

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