Advertisement

Applied Mathematics and Mechanics

, Volume 24, Issue 12, pp 1431–1440 | Cite as

Multiple reciprocity method with two series of sequences of high-order fundamental solution for thin plate bending

  • Ding Fang-yun
  • Ding Rui
  • Li Bing-jie
Article
  • 29 Downloads

Abstract

The boundary value problem of plate bending problem on two-parameter foundation was discussed. Using two series of the high-order fundamental solution sequences, namely, the fundamental solution sequences for the multi-harmonic operator and Laplace operator, applying the multiple reciprocity method (MRM), the MRM boundary integral equation for plate bending problem was constructed. It proves that the boundary integral equation derived from MRM is essentially identical to the conventional boundary integral equation. Hence the convergence analysis of MRM for plate bending problem can be obtained by the error estimation for the conventional boundary integral equation. In addition, this method can extend to the case of more series of the high-order fundamental solution sequences.

Key words

plate bending problem multiple reciprocity method boundary integral equation high-order fundamental solution sequence 

Chinese Library Classification number

O175.8 

2000 Mathematics Subject Classification

65M28 65N38 74S15 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    DING Fang-yun, LÜ Tao-tao. Boundary element analysis for two dimensional Helmholtz equation nonlinear boundary value problem[J].J Lanzhou University, 1994,30(2):25–30. (in Chinese)Google Scholar
  2. [2]
    DING Fang-yun. Boundary element method for three dimensional Helmholtz equation Dirichlet problem and its convergence analysis[J],J Lanzhou University, 1995,31(3):30–38 (in Chinese)Google Scholar
  3. [3]
    Kamiya N, Andon E. A note on multiple reciprocity method integral formulation for the Helmoltz equation[J].Comm Numer Methods Engrg, 1993,9(1):9–13.zbMATHCrossRefGoogle Scholar
  4. [4]
    Sladek V, Sladek J, Tanaka M. Boundary element solution of some structure-acoustic coupling problems using the multiple reciprocity method[J].Comm Mumer Methods Engrg, 1994,10(2):237–248.zbMATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    Sladek V, Sladek J, Tanaka M. Multiple reciprocity method for harmonic vibration of thin elastic plates[J].applied Mathematics and Model, 1993,17(4):468–476.zbMATHCrossRefGoogle Scholar
  6. [6]
    DING Rui, ZHU Zheng-you, CHENG, Chang-jun. Boundary element method for solving dynamical response of viscoelastic thin plate (II)—Theoretical analysis[J].Applied Mathematics and Mechanics (English Edition), 1998,19(2):101–110.MathSciNetGoogle Scholar
  7. [7]
    DING Rui, DING Fang-yun, ZHANG Yin. Boundary element method for buckling eigenvalue problem and its convergence analysis[J].Applied Mathematics and Mechanics (English Edition), 2002,23(2):155–168.MathSciNetGoogle Scholar
  8. [8]
    LING Zhengh-liang, Deng An-fu. Boundary integral equation of the bending-plate problem on the two-parameter foundation[J].Applied Mathematics and Mechanics (English Edition), 1992,13(7):657–667.Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

  • Ding Fang-yun
    • 1
  • Ding Rui
    • 2
  • Li Bing-jie
    • 1
  1. 1.Department of MathematicsLanzhou UniversityLanzhouP.R. China
  2. 2.School of Mathematical SciencesSuzhou UniversitySuzhouP.R. China

Personalised recommendations