板弯曲问题的具两组高阶基本解序列的MRM方法

基金项目: 国家自然科学基金资助项目(10201026);国家自然科学基金资助预研项目(T4107015)

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

摘要: 讨论了双参数地基上薄板弯曲问题.利用两组高阶基本解序列,即调和及重调和基本解序列,采用多重替换方法(MRM方法),得到了板弯曲问题的MRM边界积分方程.证明了该方程与边值问题的常规边界积分方程是一致的.因此由常规边界积分方程的误差估计即可得到板弯曲问题MRM方法的收敛性分析.此外该方法还可推广到具多组高阶基本解序列的情形.
- 板弯曲问题 /
- MRM方法 /
- 边界积分方程 /
- 高阶基本解序列
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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