Shape optimization in elasticity and elasto-viscoplasticity by the boundary element method

Abstract

This paper is concerned with the optimal shape design of solids undergoing small-strain, small-rotation, elasto-viscoplastic deformation. Shape sensitivities for this class of problems are determined by using a direct differentiation approach (DDA) to the governing boundary element method (BEM) equations of the problem. The standard BEM and the sensitivity equations are discretized and solved numerically. Shape optimization is carried out by coupling the standard and sensitivity analyses with an optimizer. The optimization algorithm chosen here uses sequential quadratic programming to obtain the desired optimal shape of a body in an iterative manner. Numerical solutions for optimal shapes of cutouts in plates (two-dimensional plane stress) are presented. The difference between optimal shapes of solids undergoing purely elastic and elasto-viscoplastic deformation is shown clearly in these examples.