Boundary Integral Equations for Recovery of Design Sensitivities in Shape Optimization

A new formulation for obtaining design sensitivities in shape optimization has been developed. The formulation is based on a direct application of the material derivative concept to the appropriate boundary integral equations for displacements and stresses in an elastic solid. As a check on accuracy, the approach was applied to a uniformly loaded infinite plate containing an elliptical hole. In this case, the availability of an analytical solution made it possible to calculate errors exactly. Furthermore, a wide range of stress states could be considered simply by varying the aspect ratio of the elliptical hole. For convenience, the design sensitivities were calculated with respect to changes in the major axis. Numerical convergence was established by comparing results based on four successive boundary meshes. In general, the predictions for both displacement and stress sensitivities were remarkably accurate.