中国物理B ›› 2010, Vol. 19 ›› Issue (9): 90204-090204.doi: 10.1088/1674-1056/19/9/090204

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

陈丽1, 程玉民2   

  1. (1)Department of Engineering Mechanics, Chang'an University, Xi'an 710064, China; (2)Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • 收稿日期:2010-01-28 修回日期:2010-02-24 出版日期:2010-09-15 发布日期:2010-09-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 10871124), and the Innovation Program of Shanghai Municipal Education Commission, China (Grant No. 09ZZ99).

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

Chen Li(陈丽)a) and Cheng Yu-Min(程玉民)b)†   

  1. a Department of Engineering Mechanics, Chang'an University, Xi'an 710064, China; b Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • Received:2010-01-28 Revised:2010-02-24 Online:2010-09-15 Published:2010-09-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 10871124), and the Innovation Program of Shanghai Municipal Education Commission, China (Grant No. 09ZZ99).

摘要: 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.

Abstract: 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.

Key words: meshless method, reproducing kernel particle method, complex variable reproducing kernel particle method, elastodynamics

中图分类号: 

  • 0260