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

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 Stokesʹ 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. . 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 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.