A boundary element approach to identify static boundary conditions in elastic solids from stresses at internal points

The paper deals with the reconstruction of static boundary conditions for three-dimensional elastic solids when there are not enough known boundary conditions but the stress tensor in an adequate number of internal points is known. To tackle this inverse problem numerically, a B-spline boundary element discretization is performed and, successively, a direct relation between the known stresses and boundary conditions to be reconstructed is obtained eliminating unknown boundary conditions not relevant for the analysis. The ill-conditioning of the derived algebraic system of equations, which tends to magnify the errors contained in its known term, is treated using the Tikhonov regularization method. To make the whole regularization algorithm automatic, the generalized cross validation criterion is used for choosing the regularization parameter. Some numerical results allow an analysis of the algorithm's performance.