A BOUNDARY-ELEMENT SOLUTION OF AN INVERSE ELASTICITY PROBLEM AND APPLICATIONS TO DETERMINING RESIDUAL-STRESS AND CONTACT STRESS

A boundary element solution is developed for an inverse elasticity pro blem. In this inverse problem, boundary conditions are incompletely sp ecified. Strains can be determined experimentally, in practice, al a n umber of internal points and used as input to completely resolve these boundary conditions. In this paper, these strains, including random e rrors, are numerically simulated. This inverse problem finds applicati ons in the evaluation of residual stress and contact stress. In contra st to previous studies, the construction of the sensitivity matrix is embedded in the boundary element formulation thereby avoiding the solu tion of a series of forward problems. Further, the effects of prescrib ed non-zero boundary conditions and body forces are included in the re lation between measured strains and the primary traction unknowns. Unf ortunately, the inverse problem is still ill-posed. Physical constrain ts are introduced to stabilize the solution. As a result, the algorith m presented here has reasonable tolerance to error in the measurement of strains. Numerical examples are given to validate the inverse algor ithm;In these examples, the input strains are numerically simulated, a nd stable and accurate solutions are obtained with up to +/- 5% random error in the input. (C) 1997 Elsevier Science Ltd.