Development of new inverse boundary element techniques in photoelasticity

This paper presents a number of possible algorithms for inverse boundary element (BE) techniques applied to photoelastic analysis. The BE technique is shown to be an ideal companion to photoelastic analysis since, unlike the finite element (FE) method, the interior solutions can be represented by unconnected points rather than by discretized elements. From the photoelastic principal stress information obtained at a sufficient number of internal points, the unknown boundary conditions can be reconstructed using the inverse boundary element method (BEM). The inverse BE theory and numerical formulation are presented for problems involving Cartesian stress components and are then extended to photoelastic stress analysis. The inverse BE approach follows two stages. In stage 1, the photoelastic stress measurements of the differences in principal stresses and their directions at the interior points are used to compute the unknown boundary conditions on the surface. In stage 2, the individual stress components are calculated by the forward BEM using the computed boundary conditions from stage 1. The effect of scatter of the experimental results is also included in the analysis. A number of examples are presented in this paper and are shown to be in excellent agreement with other solutions.