Internal 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. A new formulation for design sensitivities in three-dimensional linear elasticity, based on the BCM, has been recently presented in Ref. [12]. 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. The focus of [12] is the boundary problem, i.e., evaluation of displacements, stresses and their sensitivities on the bounding surface of a body. 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.