Topology Optimization Assisted by Automatic Level Set-Fitted Polygonal Meshes
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Topology Optimization (TO) is widely considered as a powerful and flexible mathematical technique to optimally place void and material areas inside a design domain, with the goal of meeting specific requirements in possibly diverse multiphysics and multiscale scenarios. Among the mathematical models for TO available in the literature, level set techniques conveniently represent the material/void alternation (i.e., the topology) by the zero level set of a signed distance function, which is evolved according to the required optimization setting [1]. The discretization of a level set TO problem typically involves a finite element scheme. In this framework, computational grids can be customized by means of mesh adaptation or body-fitting techniques to properly resolve the evolving level set contour and to accurately approximate the problems constraining the optimization. In particular, body-fitted meshes represent a promising solution for TO discretization, aligning the element edges with respect to the topology contour, thus reducing approximation errors and providing crisp optimized configurations [2]. We propose to frame the TO problem in the context of a Discontinuous Galerkin discretization on grids composed by generic polygons and to introduce an ad hoc level set-fitting procedure. This choice leverages the capabilities of polytopal meshes in handling arbitrary elemental shapes without introducing mesh quality issues, and turns out to be ideal in capturing sharply the topology under optimization at a reasonable computational cost. In this communication, we present the proposed TO technique based on level set-fitted polygonal meshes customized to the minimum compliance structural problem in linear elasticity, by showing both the theoretical backbone and the corresponding numerical tests. The obtained results highlight that the automatic level set-fitting procedure provides layouts characterized by highly resolved contours that are comparable with the reference literature. REFERENCES [1] P. Wei and G.H. Paulino, A parameterized level set method combined with polygonal finite elements in topology optimization. Struc. Multidisc. Optim., 61:1913–1928, 2020. [2] C. Nardoni, D. Danan, C. Mang, F. Bordeu and J. Cortial, A R&D Software Platform for Shape and Topology Optimization Using Body-Fitted Meshes. Springer Cham, Mesh Generation and Adaptation, Sevilla, R., Perotto, S., Morgan, K. (eds), Vol. 30, 2022.