Internal variables and their sensitivities in three-dimensional linear elasticity by the boundary contour method

A variant of the usual boundary element method (BEM), called the boundary c ontour method (BCM), has been presented in the literature in recent years. In the BCM in three-dimensions, surface integrals on boundary elements of t he usual BEM are transformed, through an application of Stokes' theorem, in to line integrals on the bounding contours of these elements. A new formula tion for design sensitivities in three-dimensional linear elasticity, based on the BCM, has been recently presented in Ref. [12]. This challenging der ivation is carried out by first taking the material derivative of the regul arized boundary integral equation (BIE) with respect to a shape design vari able, and then converting the resulting equation into its boundary contour version. The focus of [12] is the boundary problem, i.e., evaluation of dis placements, stresses and their sensitivities on the bounding surface of a b ody. The focus of the present paper is the corresponding internal problem, i.e., analogous calculations at points inside a body. Numerical results for internal variables and their sensitivities are presented here for selected examples. (C) 2000 Elsevier Science S.A. All rights reserved.