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Combining the complex variable reproducing kernel particle method and the finite element method for solving transient heat conduction problems

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Chinese Physics B 2013年第5期22卷 67-74页

作者：陈丽马和平程玉民 Department of Mathematics Shanghai University Department of Engineering Mechanics Chang'an University Shanghai Institute of Applied Mathematics and Mechanics Shanghai University

In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.

关键词： complex variable reproducing kernel particle method finite element method combined method,transient heat conduction

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The complex variable reproducing kernel particle method for two-dimensional elastodynamics

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Chinese Physics B 2010年第9期19卷 59-70页

作者：陈丽程玉民 Department of Engineering Mechanics Chang'an University Shanghai Institute of Applied Mathematics and Mechanics Shanghai University

On the basis of the reproducing kernel particle method （RKPM）, a new meshless method, which is called the complex variable reproducing kernel particle method （CVRKPM）, for two-dimensional elastodynamics is presented in this paper. The advantages of the CVRKPM are that the correction function of a two-dimensional problem is formed with one-dimensional basis function when the shape function is obtained. The Galerkin weak form is employed to obtain the discretised system equations, and implicit time integration method, which is the Newmark method, is used for time history analysis. And the penalty method is employed to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional elastodynamics are obtained. Three numerical examples of two-dimensional elastodynamics are presented, and the CVRKPM results are compared with the ones of the RKPM and analytical solutions. It is evident that the numerical results of the CVRKPM are in excellent agreement with the analytical solution, and that the CVRKPM has greater precision than the RKPM.

关键词： meshless method reproducing kernel particle method complex variable reproducing kernel particle method elastodvnamics

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The complex variable reproducing kernel particle method for bending problems of thin plates on elastic foundations

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COMPUTATIONAL MECHANICS 2018年第1期62卷 67-80页

作者： Chen, L. Cheng, Y. M. Changan Univ Dept Engn Mech Xian 710064 Shaanxi Peoples R China Shanghai Univ Shanghai Inst Appl Math & Mech Shanghai 200072 Peoples R China

In this paper, the complex variable reproducing kernel particle method (CVRKPM) for solving the bending problems of isotropic thin plates on elastic foundations is presented. In CVRKPM, one-dimensional basis function is used to obtain the shape function of a two-dimensional problem. CVRKPM is used to form the approximation function of the deflection of the thin plates resting on elastic foundation, the Galerkin weak form of thin plates on elastic foundation is employed to obtain the discretized system equations, the penalty method is used to apply the essential boundary conditions, and Winkler and Pasternak foundation models are used to consider the interface pressure between the plate and the foundation. Then the corresponding formulae of CVRKPM for thin plates on elastic foundations are presented in detail. Several numerical examples are given to discuss the efficiency and accuracy of CVRKPM in this paper, and the corresponding advantages of the present method are shown.

关键词： Meshless method complex variable reproducing kernel particle method Thin plate Elastic foundation Winkler model Pasternak model

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The complex variable reproducing kernel particle method for the analysis of Kirchhoff plates

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COMPUTATIONAL MECHANICS 2015年第3期55卷 591-602页

作者： Chen, L. Cheng, Y. M. Ma, H. P. Changan Univ Dept Engn Mech Xian 710064 Peoples R China Shanghai Univ Dept Math Shanghai 200072 Peoples R China Shanghai Univ Shanghai Inst Appl Math & Mech Shanghai 200072 Peoples R China

In this paper, the complex variable reproducing kernel particle method (CVRKPM) for the bending problem of arbitrary Kirchhoff plates is presented. The advantage of the CVRKPM is that the shape function of a two-dimensional problem is obtained one-dimensional basis function. The CVRKPM is used to form the approximation function of the deflection of a Kirchhoff plate, the Galerkin weak form of the bending problem of Kirchhoff plates is adopted to obtain the discretized system equations, and the penalty method is employed to enforce the essential boundary conditions, then the corresponding formulae of the CVRKPM for the bending problem of Kirchhoff plates are presented in detail. Several numerical examples of Kirchhoff plates with different geometry and loads are given to demonstrate that the CVRKPM in this paper has higher computational precision and efficiency than the reproducing kernel particle method under the same node distribution. And the influences of the basis function, weight function, scaling factor, node distribution and penalty factor on the computational precision of the CVRKPM in this paper are discussed.

关键词： Meshless method reproducing kernel particle method complex variable reproducing kernel particle method Kirchhoff plate

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