Combined mesh and penalization adaptivity based topology optimization

Topology optimization (TO) allows to produce efficient structural designs subjected to certain constraints. With the recent developments in additive manufacturing, it is now possible to realize functional components with complex geometries using high quality materials. However, for such geometries to be successfully fabricated, it is important that the designs generated from TO are black-white in nature. A black-white design consists of only solids and voids with no intermediate density (gray) values. From the point of view of the associated computational costs, designing such complex structures should be cheap as well. This paper introduces a novel adaptivity scheme for TO that can be used to produce optimal structures with reduced gray areas at relatively low computational costs. A new mesh refinement indicator is introduced which efficiently selects the finite elements to be refined/coarsened during the course of the optimization. The filter radius is also adapted and the proposed method is coupled with penalization continuation to generate well performing designs. The proposed approach is used to optimize the design of a cantilever beam for compliance minization. The results show that the mesh refinement indicator helps to generate high resolution areas and suppresses the intermediate densities at low computational costs. Also, the designs obtained using penalization adaptivity are found to resemble the analytical solution of a similar problem.