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

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Article Navigation > Applied Mathematics and Mechanics > 2003 > 24(12): 1267-1275

DING Fang-yun, DING Rui, LI Bing-jie. Multiple Reciprocity Method With Two Series of Sequences of High-Order Fundamental Solution for Thin Plate Bending[J]. Applied Mathematics and Mechanics, 2003, 24(12): 1267-1275.

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Multiple Reciprocity Method With Two Series of Sequences of High-Order Fundamental Solution for Thin Plate Bending

1.
Department of Mathematics, Lanzhou University, Lanzhou 730000, P. R. China;
2.
School of Mathematical Sciences, Suzhou University, Suzhou 215006, P. R. China

Received Date: 2001-11-27
Rev Recd Date: 2003-07-02
Publish Date: 2003-12-15

Abstract

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

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References(8)

References

[1]	丁方允,吕涛涛.二维Helmholtz方程非线性边值问题的边界元分析[J].兰州大学学报,1994,30(2):25-30.
[2]	丁方允.三维Helmholtz方程Dirichlet问题的边界元法及其收敛性分析[J].兰州大学学报,1995,31(3):30-38.
[3]	Kamiya N,Andon E.A note on multiple reciprocity method integral formulation for the Helmholtz equation[J].Comm Numer Methods Engrg,1993,9(1):9-13.
[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.
[5]	Sladek V,Sladek J,Tanaka M.Multiple reciprocity method for harmonic vibration of thin elastic plates[J].Applied Mathemaics and Model,1993,17(4):468-476.
[6]	丁睿,朱正佑,程昌钧.粘弹性薄板动力响应的边界元方法(Ⅱ)——理论分析[J].应用数学和力学,1998,19(2):95-103.
[7]	丁睿,丁方允,张颖.屈曲特征值问题的边界元方法及收敛性分析[J].应用数学和力学,2002,23(2):144-156.
[8]	李正良,邓安福.双参数地基上板弯曲问题的边界积分方程[J].应用数学和力学,1992,13(7):633-644.