An inverse method of fundamental solutions for the identification of 2D elastic properties of anisotropic solids

There are six elastic constants for an anisotropic body in plane strain/stress conditions. In the inverse problem of this study, it is assumed that the elastic constants of an anisotropic body are unknown, while the displacements or strains at several sampling points of the body under static loading are provided. For the first time, the method of fundamental solutions is used for solving the problem, where the sensitivity analysis is performed by direct differentiation of the discretized equations. For that, the closed-form relations for sensitivity of the displacements/strains with respect to the elastic constants are analytically derived. Using a numerical study, it is shown that the proposed sensitivity analysis is more advantageous compared to the traditional finite difference approximation. A simple method for the proper selection of the initial guesses is also proposed. Two different example problems under plane strain and plane stress conditions are examined to investigate the accuracy of the proposed method. Moreover, the effects of the number of measurement data, the measurement error, and the configuration of sampling points on the solution of the inverse problem are studied. It is observed that the solutions are more accurate in the cases where the sampling points are located at different parts of the body.