On design sensitivity analysis in linear elasticity by the boundary contour method

Abstract

A new derivation for design sensitivity analysis using the concept of the material derivative (or total derivative), and boundary contour conversion, is presented in this paper. This 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 equations into their boundary contour version. As expected, the final design sensitivity equations are identical to those presented in Ref. [1] in which the opposite process, namely, conversion of the BIE into a boundary contour version, followed by material differentiation, had been carried out.