Abstract The quasistatic elastic problem is formulated as an elliptic system for the displacements coupled with a parabolic equation for the damage field. The corresponding inverse problem is reformulated as an optimal control problem to find a stable traction, by a given observation data. Firstly, a convex functional is constructed with Tikhonov regularization, and a stable approximation of surface traction is obtained by minimizing it. Then a finite element discretization of the inverse elastic problem is analyzed. Moreover, the error estimation of the numerical solutions is deduced. At last, a numerical algorithm is detailed and three examples illustrate the efficiency of the algorithm.
ZHENG Cong, CHENG Xiao-liang, LIANG Ke-wei. Numerical analysis of inverse elastic problem with damage. Applied Mathematics A Journal of Chinese Universities, 2016, 31(4): 476-490.
