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Numerical Analysis of Inverse Elasticity Problemwith Signorini's Condition

Part of:Special kinds of problemsPartial differential equations, boundary value problemsPartial differential equations, initial value and time-dependent initial-boundary value problemsNumerical methods

Published online by Cambridge University Press:  05 October 2016

Cong Zheng,
Xiaoliang Cheng and
Kewei Liang
Cong Zheng*
Affiliation:
School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, P.R. China
Xiaoliang Cheng*
Affiliation:
School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, P.R. China
Kewei Liang*
Affiliation:
School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, P.R. China
*
*Corresponding author. Email addresses:congzheng@zju.edu.cn (C. Zheng), xiaoliangcheng@zju.edu.cn (X. Cheng), matlkw@zju.edu.cn (K. Liang)
*Corresponding author. Email addresses:congzheng@zju.edu.cn (C. Zheng), xiaoliangcheng@zju.edu.cn (X. Cheng), matlkw@zju.edu.cn (K. Liang)
*Corresponding author. Email addresses:congzheng@zju.edu.cn (C. Zheng), xiaoliangcheng@zju.edu.cn (X. Cheng), matlkw@zju.edu.cn (K. Liang)

Abstract

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An optimal control problem is considered to find a stable surface traction, which minimizes the discrepancy between a given displacement field and its estimation. Firstly, the inverse elastic problem is constructed by variational inequalities, and a stable approximation of surface traction is obtained with Tikhonov regularization. Then a finite element discretization of the inverse elastic problem is analyzed. Moreover, the error estimation of the numerical solutions is deduced. Finally, a numerical algorithm is detailed and three examples in two-dimensional case illustrate the efficiency of the algorithm.

Keywords

Optimal controlvariational inequalityinverse elastic problemfinite elementerror estimatesnumerical simulations

MSC classification

Secondary:65M15: Error bounds65N21: Inverse problems65N22: Solution of discretized equations74M15: Contact74S05: Finite element methods

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 4 , October 2016, pp. 1045 - 1070
Copyright
Copyright © Global-Science Press 2016 

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