Numerical Analysis of Inverse Elasticity Problemwith Signorini's Condition. (5th October 2016)

• Record Type: Journal Article
• Authors: Zheng, Cong; Cheng, Xiaoliang; Liang, Kewei
• Is Part Of: Communications in computational physics. Volume 20:Number 4(2016:Oct.)
• Page Start: 1045
• Page End: 1070
• Publication Date: 2016-10-05
• Subjects: 65M15, -- 65N21, -- 65N22, -- 74M15, -- 74S05; Optimal control, -- variational inequality, -- inverse elastic problem, -- finite element, -- error estimates, -- numerical simulations; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.120715.010216a
• Languages: English
• ISSNs: 1815-2406

Abstract

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.