Virtual element method (VEM)-based topology optimization: an integrated framework

Heng Chi, Anderson Pereira, Ivan F.M. Menezes, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We present a virtual element method (VEM)-based topology optimization framework using polyhedral elements, which allows for convenient handling of non-Cartesian design domains in three dimensions. We take full advantage of the VEM properties by creating a unified approach in which the VEM is employed in both the structural and the optimization phases. In the structural problem, the VEM is adopted to solve the three-dimensional elasticity equation. Compared to the finite element method, the VEM does not require numerical integration (when linear elements are used) and is less sensitive to degenerated elements (e.g., ones with skinny faces or small edges). In the optimization problem, we introduce a continuous approximation of material densities using the VEM basis functions. When compared to the standard element-wise constant approximation, the continuous approximation enriches the geometrical representation of structural topologies. Through two numerical examples with exact solutions, we verify the convergence and accuracy of both the VEM approximations of the displacement and material density fields. We also present several design examples involving non-Cartesian domains, demonstrating the main features of the proposed VEM-based topology optimization framework. The source code for a MATLAB implementation of the proposed work, named PolyTop3D, is available in the (electronic) Supplementary Material accompanying this publication.

Original languageEnglish (US)
Pages (from-to)1089-1114
Number of pages26
JournalStructural and Multidisciplinary Optimization
Volume62
Issue number3
DOIs
StatePublished - Sep 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization

Keywords

  • MATLAB software
  • Polyhedral meshes
  • Topology optimization
  • Virtual element method

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