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Volume 20, Issue 4
Numerical Analysis of Inverse Elasticity Problem with Signorini's Condition

Cong Zheng, Xiaoliang Cheng & Kewei Liang

DOI: 10.4208/cicp.120715.010216a

Commun. Comput. Phys., 20 (2016), pp. 1045-1070.

Published online: 2018-04

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  • Abstract

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.

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@Article{CiCP-20-1045, author = {Cong Zheng, Xiaoliang Cheng and Kewei Liang}, title = {Numerical Analysis of Inverse Elasticity Problem with Signorini's Condition}, journal = {Communications in Computational Physics}, year = {2018}, volume = {20}, number = {4}, pages = {1045--1070}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.120715.010216a}, url = {http://global-sci.org/intro/article_detail/cicp/11182.html} }
TY - JOUR T1 - Numerical Analysis of Inverse Elasticity Problem with Signorini's Condition AU - Cong Zheng, Xiaoliang Cheng & Kewei Liang JO - Communications in Computational Physics VL - 4 SP - 1045 EP - 1070 PY - 2018 DA - 2018/04 SN - 20 DO - http://doi.org/10.4208/cicp.120715.010216a UR - https://global-sci.org/intro/article_detail/cicp/11182.html KW - AB -

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.

Cong Zheng, Xiaoliang Cheng and Kewei Liang. (2018). Numerical Analysis of Inverse Elasticity Problem with Signorini's Condition. Communications in Computational Physics. 20 (4). 1045-1070. doi:10.4208/cicp.120715.010216a
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