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A STUDY ON THE WEIGHT FUNCTION OF THE moving least square approximation IN THE LOCAL BOUNDARY INTEGRAL EQUATION METHOD

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Acta Mechanica Solida Sinica 2003年第3期16卷 276-282页

作者： Long Shuyao Hu De’an (Department of Engineering Mechanics,Hunan University,Changsha 410082,China) Department of Engineering Mechanics Hunan University Changsha 410082 China

The meshless method is a new numerical technique presented in recent *** uses the moving least square(MLS)approximation as a shape *** smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight ***,the weight function greatly affects the accuracy of results *** kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many *** the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation *** effect of various weight functions on the accuracy, convergence and stability of results obtained is also *** show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.

关键词： weight function meshless methods local boundary integral equation method moving least square approximation

LOCAL PETROV-GALERKIN METHOD FOR A THIN PLATE

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Applied Mathematics and Mechanics(English Edition) 2004年第2期25卷 210-218页

作者：熊渊博龙述尧 Department of Engineering Mechanics Hunan University

The meshless local Petrov_Galerkin (MLPG) method for solving the bending problem of the thin plate were presented and discussed. The method used the moving least_squares approximation to interpolate the solution variables, and employed a local symmetric weak form. The present method was a truly meshless one as it did not need a finite element or boundary element mesh, either for purpose of interpolation of the solution, or for the integration of the energy. All integrals could be easily evaluated over regularly shaped domains (in general, spheres in three_dimensional problems) and their boundaries. The essential boundary conditions were enforced by the penalty method. Several numerical examples were presented to illustrate the implementation and performance of the present method. The numerical examples presented show that high accuracy can be achieved for arbitrary grid geometries for clamped and simply_supported edge conditions. No post processing procedure is required to computer the strain and stress, since the original solution from the present method, using the moving least squares approximation, is already smooth enough.

关键词： thin plate meshless local Petrov-Galerkin method moving least square approximation symmetric weak form of equivalent integration for differential equation

A MESHLESS LOCAL PETROV-GALERKIN METHOD FOR GEOMETRICALLY NONLINEAR PROBLEMS

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Acta Mechanica Solida Sinica 2005年第4期18卷 348-356页

作者： Xiong Yuanbo Long Shuyao Hu De＇an Li Guangyao Department of Engineering Mechanics Hunan University Changsha 410082 China Key Laboratory of Advanced Technology for Vehicle Body Design ~ Manufacture Ministry of Education of China Hunan University Changsha 410082 China

Nonlinear formulations of the meshless local Petrov-Galerkin （MLPG） method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficulties in the large deformation analysis. The essential boundary conditions in the present formulation axe imposed by a penalty method. An incremental and iterative solution procedure is used to solve geometrically nonlinear problems. Several examples are presented to demonstrate the effectiveness of the method in geometrically nonlinear problems analysis. Numerical results show that the MLPG method is an effective one and that the values of the unknown variable are quite accurate.

关键词： local Petrov-Galerkin method moving least square approximation total Lagranian method geometrically nonlinear problems

Improved non-singular local boundary integral equation method

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Applied Mathematics and Mechanics(English Edition) 2007年第8期28卷 1093-1099页

作者：付东杰陈海波张培强 Department of Modern Mechanics University of Science and Technology of China Hefei 230026 P.R.China CAS Key Laboratory of Mechanical Behavior and Design of MaterialsUniversity of Science and Technology of ChinaHefei 230026P.R.China

When the source nodes are on the global boundary in the implementation of local boundary integral equation method （LBIEM）, singularities in the local boundary integrals need to be treated specially. In the current paper, local integral equations are adopted for the nodes inside the domain and moving least square approximation （MLSA） for the nodes on the global boundary, thus singularities will not occur in the new al- gorithm. At the same time, approximation errors of boundary integrals are reduced significantly. As applications and numerical tests, Laplace equation and Helmholtz equation problems are considered and excellent numerical results are obtained. Furthermore, when solving the Helmholtz problems, the modified basis functions with wave solutions are adapted to replace the usually-used monomial basis functions. Numerical results show that this treatment is simple and effective and its application is promising in solutions for the wave propagation problem with high wave number.

关键词： meshless method local boundary integral equation method moving least square approximation singular integrals

ICM Method Combined with Meshfree approximation for Continuum Structure

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Journal of Beijing Institute of Technology 2010年第3期19卷 279-285页

作者：龙凯左正兴肖涛 Rehan H.Zuberi School of Mechanical Engineering Beijing Institute of Technology School of Renewable Energy North China Electric Power University Shanghai Diesel Engine Co. Ltd

The independent continuous mapping（ICM） method is integrated into element free Galerkin method and a new implementation of topology optimization for continuum structure is *** facilitate the enforcement of the essential boundary condition and derivative of various sensitivities,a singular weight function in element free Galerkin method is *** point variable is defined to illustrate the condition of material point and its vicinity instead of element or *** topological variables field is constructed by moving least square approximation which inherits the continuity and smoothness of the weight *** to reciprocal relationships between the topological variables and design variables,various structural responses sensitivities are derived according to the method for calculating the partial derivatives of compound *** examples indicate that checkerboard pattern and mesh-dependence phenomena are overcome without additional restriction methods.

关键词： topology optimization independent continuous mapping method continuum structure,meshfree method moving least square approximation

Homogenization Topology Optimization Method Based on Continuous Field

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Homogenization Topology Optimization Method Based on Continu...