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Phase-field based topology optimization with polygonal elements: a finite volume approach for the evolution equation

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Abstract

Uniform grids have been the common choice of domain discretization in the topology optimization literature. Over-constraining geometrical features of such spatial discretizations can result in mesh-dependent, sub-optimal designs. Thus, in the current work, we employ unstructured polygonal meshes constructed using Voronoi tessellations to conduct structural topology optimization. We utilize the phase-field method, derived from phase transition phenomenon, which makes use of the Allen-Cahn differential equation and sensitivity analysis to update the evolving structural topology. The solution of the Allen-Cahn evolution equation is accomplished by means of a centroidal Voronoi tessellation (CVT) based finite volume approach. The unstructured polygonal meshes not only remove mesh bias but also provide greater flexibility in discretizing complicated (e.g. non-Cartesian) domains. The features of the current approach are demonstrated using various numerical examples for compliance minimization and compliant mechanism problems.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 N. Mathews Ave., Urbana, IL, 61801, USA

    Arun L. Gain & Glaucio H. Paulino

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  1. Arun L. Gain
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  2. Glaucio H. Paulino
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Correspondence to Glaucio H. Paulino.

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Gain, A.L., Paulino, G.H. Phase-field based topology optimization with polygonal elements: a finite volume approach for the evolution equation. Struct Multidisc Optim 46, 327–342 (2012). https://doi.org/10.1007/s00158-012-0781-9

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