【作者】 李挺；

【导师】 丁睿；

【作者基本信息】 苏州大学 ， 应用数学， 2002， 硕士

【摘要】 本文首先给出了常规边界元方法的一些结果及在Laplace变换区域中得到了由重调和算子基本解序列给出了粘弹性薄板动力响应问题的多重互易法(MRM方法)。并对粘弹性薄板的动力响应问题的MRM方法给出了收敛性分析，证明了MRM方法导出的边界积分方程的解与边值问题基本解导出的常规边界方程的解是相同的。采用变分方法系统分析了相应问题的边界变分方程，截断的MRM边界变分方程与近似截断MRM边界变分方程解的存在唯一性，解释了网格宽度与MRM方法中截断数的选取原则，讨论了MRM方法中的迭代误差估计，给出了数值算例。计算表明该方法具有较高精度和较快收敛性。说明了数值实验结果与理论分析是一致的。更多还原

【Abstract】 In this paper, firstly we present some results about of conventional BEM,and Multiple Reciprocity Method (MRM)for solving dynamics response of Viscoelastic thin plate is given the whole plane expression and boundary integral equation for MRM, next we prove that the solution of the boundary integral equation obtained by MRM is the same as the one derived from the conventional fundamental solution of boundary value problem. Applying variational method we analyze the existence and uniqueness for the solution of the corresponding boundary variational equation, truncated MRM boundary variational equation, and approximation truncated MRM boundary variational equation in detailed. We obtain the error estimation for various approximation solutions and construct the boundary integral method with constraint. We explain the principle for choosing the mesh size and the truncated number in MRM .Finally the numerical examples show that the theoretical analysis is accord with the numerical experiment result . By this way we perfectly discuss the MRM for the dynamic response of viscoelastic thin plate and its convergence analysis.更多还原