SIM-AM 2023

Body-Fitted Polygonal Meshes for Topology Optimization

  • Antonietti, Paola Francesca (Politecnico di Milano)
  • Ferro, Nicola (Politecnico di Milano)
  • Micheletti, Stefano (Politecnico di Milano)
  • Parolini, Nicola (Politecnico di Milano)
  • Perotto, Simona (Politecnico di Milano)
  • Verani, Marco (Politecnico di Milano)

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Topology Optimization (TO) consists in the mathematically-guided allocation of void and material areas inside a design domain, so that a given objective functional is minimized and suitable constraints are met. This technique has encountered great popularity in the last decades both for research and industrial purposes, especially thanks to the spread of additive manufacturing techniques that fully exploit the potentiality of TO in terms of allowed and manufacturable optimized shapes. Among the different mathematical approaches for TO, level set techniques are commonly employed to model the topology changes. Specifically, the material/void interface is identified by the zero level set of a signed distance function, which is evolved in order to match the imposed optimization criteria [1]. With a view to a finite element discretization, triangular/tetrahedral grids, customized by means of mesh adaptation or body-fitting techniques, have been exploited in order to properly resolve the evolving level set and to accurately approximate the considered physics. In fact, body-fitted meshes correctly align the elements of the tessellation to the topology changes, thus limiting approximation errors and providing reliable optimized configurations [2]. Nevertheless, triangular/tetrahedral grids typically require local control at each body-fitting step to avoid the deterioration of the overall quality of the resulting mesh. To overcome this drawback, we propose to couple a level set-based topology optimization to a body-fitted approach on polygonal meshes. The goal of this algorithm is to sharply capture the topology interface under optimization, while leveraging the benefits of polytopal grids that can handle arbitrary elemental shapes and do not suffer from quality issues. In this communication, we present the novel TO workflow on polygonal meshes. In particular, we highlight that the use of elements characterized by generic shapes and sizes ensures that the body-fitted grid generation can be easily automatized without requiring any local remeshing operations for mesh quality preservation. Successively, the derived algorithm is challenged onto some benchmark cases and the computational performance is assessed in comparison with the state-of-the-art literature.