Applied Mathematics and Mechanics

, Volume 19, Issue 2, pp 101–110

# Boundary element method for solving dynamical response of viscoelastic thin plate(II)—Theoretical analysis

• Ding Rui
• Zhu Zhengyou
• Cheng Changjun
Article

## 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 and the 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 is shown that the theoretical analysis in this paper are consistent with the numerical results in [1].

### Key words

dynamic response viscoelasticity approximate boundary element method error estimation

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### References

1. [1]
Ding Rui, Zhu Zhengyou and Cheng Changjun, Boundary element method for solving dynamic response of viscoelastic thin plate (I),Applied Mathematics and Mechanics (English Ed.),18, 3 (1997), 229–235.Google Scholar
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Ding Fangyun, The BEM for Dirichlet problems of three dimensional Helmholtz equation and its convergence,J. Lanzhou Univ.,31, 3 (1995), 30–38. (in Chinese).Google Scholar
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Zhu Jialin,Boundary Element Analysis for Elliptic Boundary Value Problem, Science Press, Beijing (1987). (in Chinese)Google Scholar
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K. Ruotsalainen and W. Wendland, On the boundary element method for some nonlinear boundary value problem,Numer. Math.,53, 1 (1988), 229–314.
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R. Bellman,Numerical Inversion of the Laplace Transform, Amer. Elsevier Publ. Co. (1966), 624–635.Google Scholar

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## Authors and Affiliations

• Ding Rui
• 1
• Zhu Zhengyou
• 2
• Cheng Changjun
• 2
1. 1.Mechanical Postdoctoral StationSouthwestern Jiaotong UniversityChengduP. R. China
2. 2.Shanghai Institute of Applied Mathematics and MechanicsShanghaiP. R. China