Shape optimization in three-dimensional linear elasticity by the boundary contour method

Abstract

A variant of the usual boundary element method (BEM), called the boundary contour method (BCM), has been presented in the literature in recent years. In the BCM in three dimensions, surface integrals on boundary elements of the usual BEM are transformed, through an application of Stokes’ theorem, into line integrals on the bounding contours of these elements. The BCM employs global shape functions with the weights, in the linear combinations of these shape functions, being defined piecewise on boundary elements. A very useful consequence of this approach is that stresses, at suitable points on the boundary of a body, can be easily obtained from a post-processing step of the standard BCM. The subject of this paper is shape optimization in three-dimensional (3D) linear elasticity by the BCM. This is achieved by coupling a 3D BCM code with a mathematical programming code based on the successive quadratic programming (SQP) algorithm. Numerical results are presented for several interesting illustrative examples.