Polygonal finite elements for topology optimization: A unifying paradigm

Cameron Talischi, Glaucio H. Paulino, Anderson Pereira, Ivan F.M. Menezes

Research output: Contribution to journalArticle

Abstract

In topology optimization literature, the parameterization of design is commonly carried out on uniform grids consisting of Lagrangian-type finite elements (e.g. linear quads). These formulations, however, suffer from numerical anomalies such as checkerboard patterns and one-node connections, which has prompted extensive research on these topics. A problem less often noted is that the constrained geometry of these discretizations can cause bias in the orientation of members, leading to mesh-dependent sub-optimal designs. Thus, to address the geometric features of the spatial discretization, we examine the use of unstructured meshes in reducing the influence of mesh geometry on topology optimization solutions. More specifically, we consider polygonal meshes constructed from Voronoi tessellations, which in addition to possessing higher degree of geometric isotropy, allow for greater flexibility in discretizing complex domains without suffering from numerical instabilities.

Original languageEnglish (US)
Pages (from-to)671-698
Number of pages28
JournalInternational Journal for Numerical Methods in Engineering
Volume82
Issue number6
DOIs
StatePublished - May 7 2010

Keywords

  • Polygonal elements
  • Topology optimization
  • Unstructured meshing
  • Voronoi tessellations

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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