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Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (12): 1431-1440.

• 论文 • 上一篇    下一篇

MULTIPLE RECIPROCITY METHOD WITH TWO SERIES OF SEQUENCES OF HIGH-ORDER FUNDAMENTAL SOLUTION FOR THIN PLATE BENDING

丁方允1, 丁睿2, 李炳杰1   

  1. 1. Department of Mathematics, Lanzhou University, Lanzhou 730000, P.R.China;
    2. School of Mathematical Sciences, Suzhou University, Suzhou 215006, P.R.China
  • 收稿日期:2001-11-27 修回日期:2003-07-02 出版日期:2003-12-18 发布日期:2003-12-18
  • 通讯作者: CHENG Chang-jun
  • 基金资助:
    the National Natural Science Foundation of China(10201026);the National Natural Science Foundation Pre-Research Project(T4107015)

MULTIPLE RECIPROCITY METHOD WITH TWO SERIES OF SEQUENCES OF HIGH-ORDER FUNDAMENTAL SOLUTION FOR THIN PLATE BENDING

DING Fang-yun1, DING Rui2, LI Bing-jie 1   

  1. 1. Department of Mathematics, Lanzhou University, Lanzhou 730000, P.R.China;
    2. School of Mathematical Sciences, Suzhou University, Suzhou 215006, P.R.China
  • Received:2001-11-27 Revised:2003-07-02 Online:2003-12-18 Published:2003-12-18
  • Supported by:
    the National Natural Science Foundation of China(10201026);the National Natural Science Foundation Pre-Research Project(T4107015)

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摘要： 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.

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.

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