粘弹性薄板动力响应的边界元方法(Ⅱ)——理论分析<sup>*</sup>

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粘弹性薄板动力响应的边界元方法(Ⅱ)——理论分析^*

基金项目: *国家自然科学基金;教委博士点基金

1.
Mechanical Postdoctoral Station, Southwestern Jiaotong University, Chengdu 610031, P. R. China;
2.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P. R. China

摘要: 本文中,对[1]中提出的粘弹性结构动力响应的近似边界元方法给出了必要的理论分析,得到了近似解的存在唯一性定理和误差估计.基于这些结论给出了网格宽度与基本解中截断项数的选取原则.本文中得到的理论结果和[1]中数值实验结果是一致.
- 动力响应 /
- 粘弹性 /
- 近似边界元法 /
- 误差估计
Abstract: In this paper,the necessary theoretical analysis for the approximation boundary element method to solve dynamical response of viscoelastic thin plate presented in [1] is.discussed.The theorem of existence and uniqueness of the approximate solution andthe error estimation are also obtained.Based on these conclusions,the principle for choosing the mesh size and the number of truncated terms in the fundamental solution are given.It isshown that the theoretical ana analysis in this paper are consistent with thenumerical results in [1].
- dynamic response /
- viscoelasticity /
- approximate boundary elementmethod /
- error estimation

[1]	丁睿、朱正佑、程昌钧,粘弹性薄板动力响应的边界元法(Ⅰ),应用数学和力学,18(3)(1997),211-216.
[2]	丁方允,三维Helmholtz方程Dirichlet问题的边界元法及其收敛性分析,兰州大学学报,31(3)(1995),30-38.
[3]	祝家麟,《椭圆边值问题的边界元分析》,科学出版社(1987).
[4]	K.Ruotsalainen and W.Wendland,On the boundary element method for somenonlinear boundary value problem,Numer Math.53,1(1988),229-314.
[5]	R.Bellman.Numerical Inversion of the Laplace Transform,Amer.Elsevier.Publ.Co,(1966).624-635.