The method of fundamental solutions for solving scattering problems from infinite elastic thin plates

Abstract

We investigate different variants of the method of fundamental solutions for solving scattering problems from infinite elastic thin plates. These provide novelty and desirable ease of implementation as direct accurate and fast solvers to be used iteratively in solving the corresponding inverse problems. Various direct problems associated with physical states of clamped, simply supported, roller–supported and free plates can be solved efficiently using the proposed meshless method. In particular, the numerical implementation performed for clamped plates leads to results showing very good agreement with the analytical solution, where available, and with previously obtained boundary integral method solutions. As for the inverse obstacle identification, the study further develops a constrained nonlinear regularization method for identifying a cavity concealed in an infinite elastic thin plate that has important benefits to the structural monitoring of aircraft components using non–destructing material testing.