An effective algorithm for reconstructing boundary conditions in elastic solids Original Research Article

This paper discusses the reconstruction of boundary conditions for linear elastic solids when there are not enough known boundary conditions but the stress tensor is known in a sufficient number of internal points. Starting with a refined boundary elements discretization of the elastic solid, an iterative strategy based on the conjugate gradient method is presented. This iterative strategy uses a Monte-Carlo simulation of the generalized cross-validation criterion to select the optimal solution. The proposed algorithm possesses some advantages with respect to direct approaches. Indeed, it furnishes almost as accurate results but at a low computational cost. Some numerical results allow an analysis of the algorithmʹs performance.