Design sensitivity analysis using the boundary element method

Abstract

A directly differentiated form of boundary integral equation with respect to geometric design variables is used to calculate shape design sensitivities. This allows the coupling of an optimizing technique and a boundary element elastic stress analyser to form an optimum shape design algorithm in two dimensions. Hermitian cubic spline functions used to represent boundary shapes offer considerable advantages in fitting a wide range of curves, and in the automatic remeshing process. They also reduce the need for optimization constraints to avoid impractical designs during the optimization procedure. The boundary element method offers advantages over the finite element method, and is applicable to a wide range of shape optimization problems.