A multiple-data-based direct method for inverse problem in three-dimensional linear elasticity

Abstract

Estimating the unknown Young’s modulus and boundary conditions of an elastic object from locally observed boundary data is an inverse problem which is usually solved by iterative methods. In this paper, a multiple-data-based direct (MD) method is proposed to solve this inverse problem without iterations. The proposed method applies a global normalized objective function and a global regularization coefficient τg for energy-like regularization to ensure the convergence of the unknown displacement boundary conditions. A coarse-mesh based preprocessing algorithm is proposed to speed up the determination of the regularization coefficient. A multi-force-position method is proposed to obtain observation data, which improves accuracy of the MD method when the number of experiments is limited. Both numerical and physical experiments were conducted. Compared with the single-data-based direct (SD) methods proposed in our previous work, the MD method yields more accurate estimation of Young’s modulus and boundary conditions in both numerical and physical experiments.