Topology optimization driven by anisotropic mesh adaptation: Towards a free-form design

Abstract

We propose the new adaptive algorithm SIMPATY for topology optimization to design lightweight and stiff structures exhibiting free-form features. This is achieved by properly combining the classical SIMP method with an anisotropic mesh adaptation strategy based on a recovery-based a posteriori error estimator. Mesh adaptivity allows us to contain (and, for simple structures, even to eliminate) the filtering usually adopted in a topology optimization context. Thus, the final layout is intrinsically smooth, so that the post-processing phase can be strongly reduced (or even skipped), and the structure can directly move on to the production manufacturing phase. A free-form design is also enhanced by anisotropic mesh adaptivity. An extensive numerical validation supports these remarkable properties.