Topology optimization using regularized intermediate density control

Abstract

We consider topology optimization of elastic continua. The elasticity tensor is assumed to depend linearly on the design function (density) as in the variable thickness sheet problem. In order to get “black–white” design pictures, the intermediate density values are controlled by an explicit constraint. This constraint is regularized by including a compact and linear operator S to guarantee existence of solutions. A proof of convergence of the finite element (FE) discretized optimization problem's solutions to exact ones is also given, so the method is not prone to numerical anomalies such as mesh dependence or checkerboards. The procedure is illustrated in some minimum compliance examples where S is chosen to be a classical convolution-type operator. The FE-discretized optimization problems are solved by sequential convex approximations.