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A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems

Chinese Physics B 2013年第8期22卷 238-244页

作者：王启防戴保东栗振锋 Department of Engineering Mechanics Taiyuan University of Science & Technology College of Transportation & Logistics Taiyuan University of Science & Technology

On the basis of the complex variable moving least-square （CVMLS） approximation, a complex variable meshless local Petrov-Galerkin （CVMLPG） method is presented for transient heat conduction problems. The method is developed based on the CVMLS approximation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for a domain integral in symmetric weak form. In the construction of the well-performed shape function, the trial function of a two-dimensional （2D） problem is formed with a one-dimensional （1D） basis function, thus improving computational efficiency. The numerical results are compared with the exact solutions of the problems and the finite element method （FEM）. This comparison illustrates the accuracy as well as the capability of the CVMLPG method.

关键词： meshless method complex variable moving least-square method complex variable meshless localPetrov-Galerkin method transient heat conduction problems

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The complex variable meshless local Petrov-Galerkin method of solving two-dimensional potential problems

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Chinese Physics B 2012年第10期21卷 49-55页

作者：杨秀丽戴保东张伟伟 Department of Engineering Mechanics Taiyuan University of Science&Technology

Based on the complex variable moving least-square（CVMLS） approximation and a local symmetric weak form,the complex variable meshless local Petrov-Galerkin（CVMLPG） method of solving two-dimensional potential problems is presented in this *** the present formulation,the trial function of a two-dimensional problem is formed with a one-dimensional basis *** number of unknown coefficients in the trial function of the CVMLS approximation is less than that in the trial function of the moving least-square（MLS） *** essential boundary conditions are imposed by the penalty *** main advantage of this approach over the conventional meshless local Petrov-Galerkin（MLPG） method is its computational *** numerical examples are presented to illustrate the implementation and performance of the present CVMLPG method.

关键词： meshless method complex variable moving least-square method complex variable meshless local Petrov-Galerkin method potential problems

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The complex variable meshless local Petrov-Galerkin method for elasticity problems of functionally graded materials

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APPLIED MATHEMATICS AND COMPUTATION 2015年 268卷 1140-1151页

作者： Wei, Dandan Zhang, Weiwei Wang, Linghui Dai, Baodong Taiyuan Univ Sci & Technol Dept Engn Mech Taiyuan 030024 Peoples R China

This paper proposed the complex variable meshless local Petrov-Galerkin (CVMLPG) method for the static analysis of functionally graded materials (FGMs). In the presented method, the complex variable moving least-square (CVMLS) approximation, which is established based on the moving least-square (MLS) approximation by introducing the complex variable theory, is adopted for construction of the field approximation function. Compared with the conventional MLS method, the number of the unknown coefficients in the trial function of the CVMLS method is less than that of the MLS approximation, thus higher efficiency and accuracy can be achieved under the same node distributions. One advantage of the CVMLPG method for the FGMs is that the variations of the functionally graded material properties are simulated by using material parameters at Gauss points, so it totally avoids the issue of the assumption of homogeneous in each element in the finite element method (FEM) for the FGMs. Some of selected benchmark examples are considered to confirm the validity and accuracy of the proposed method. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Meshless method complex variable moving least-square method complex variable meshless local Petrov-Galerkin method Functionally graded materials Elasticity

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The complex variable meshless local Petrov-Galerkin method for elastodynamic problems

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APPLIED MATHEMATICS AND COMPUTATION 2014年 243卷 311-321页

作者： Dai, Baodong Wang, Qifang Zhang, Weiwei Wang, Linghui Taiyuan Univ Sci & Technol Dept Engn Mech Taiyuan 030024 Peoples R China

The complex variable meshless local Petrov-Galerkin (CVMLPG) method is further developed for structural dynamic analyses of two-dimensional (2D) solids. The complex variable moving least-square (CVMLS) approximation is used to construct the shape function and the Heaviside step function is chosen for representing the test function. In the construction of the well-performed shape function, the trial function of 2D problem is formed with a one-dimensional (1D) basis function, thus improving computational efficiency. The governing elastodynamic equations are transformed into a standard local weak formulation, and then it is discretized into a meshfree system of time-dependent equations, which are solved by the standard implicit Newmark time integration scheme. Numerical results obtained from the proposed CVMLPG method are compared with the exact solutions and those of the conventional MLPG method and excellent agreement is achieved. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Meshless method complex variable moving least-square method complex variable meshless local Petrov-Galerkin method Elastodynamics

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