Stresses, stress sensitivities and shape optimization in two-dimensional linear elasticity by the Boundary Contour Method

This paper presents new formulations for computing stresses as well as their sensitivities in two-dimensional (2-D) linear elasticity by the Boundary Contour Method (BCM). Contrary to previous work (e.g. Reference 1), the formulations presented here are established directly from the boundary contour version of the Hypersingular Boundary Integral Equation (HBIE) which can provide accurate numerical results and is very e cient with regard to numerical implementation as well as computational time. The Design Sensitivity Coe cients (DSCs) computed from the above formulations are then coupled with a mathematical programming method, here the Successive Quadratic Programming (SQP) algorithm, in order to solve shape optimization problems. Numerical examples are presented to demonstrate the validity of the new formulations for calculation of DSCs. Also, based on these formulations, shape optimization examples by the BCM are presented here for the rst time.