Surface variables and their sensitivities 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 and curvatures, at suitable points on the boundary of a body, can be easily obtained from a post-processing step of the standard BCM. A new formulation for design sensitivities in three-dimensional linear elasticity, based on the BCM, is presented in this paper. This challenging derivation is carried out by first taking the material derivative of the regularized boundary integral equation (BIE) with respect to a shape design variable, and then converting the resulting equation into its boundary contour version. Finally, numerical results for surface variables, as well as their sensitivities, are presented for selected illustrative examples.