A boundary element solution of an inverse elasticity problem and applications to determining residual stress and contact stress

Abstract

A boundary element solution is developed for an inverse elasticity problem. In this inverse problem, boundary conditions are incompletely specified. Strains can be determined experimentally, in practice, at a number of internal points and used as input to completely resolve these boundary conditions. In this paper, these strains, including random errors, are numerically simulated. This inverse problem finds applications in the evaluation of residual stress and contact stress. In contrast to previous studies, the construction of the sensitivity matrix is embedded in the boundary element formulation thereby avoiding the solution of a series of forward problems. Further, the effects of prescribed non-zero boundary conditions and body forces are included in the relation between measured strains and the primary traction unknowns. Unfortunately, the inverse problem is still ill-posed. Physical constraints are introduced to stabilize the solution. As a result, the algorithm presented here has reasonable tolerance to error in the measurement of strains. Numerical examples are given to validate the inverse algorithm. In these examples, the input strains are numerically simulated, and stable and accurate solutions are obtained with up to ±5% random error in the input.