Development of new inverse boundary element techniques in photoelasticity

This paper presents a number of possible algorithms for inverse boundary el ement (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 un connected points rather than by discretized elements. From the photoelastic principal stress information obtained at a sufficient number of internal p oints, the unknown boundary conditions can be reconstructed using the inver se boundary element method (BEM). The inverse BE theory and numerical formu lation 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 th e differences in principal stresses and their directions at the interior po ints are used to compute the unknown boundary conditions on the surface. In stage 2, the individual stress components are calculated by the forward BE M using the computed boundary conditions from stage 1. The effect of scatte r 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 agre ement with other solutions.