A modified Q4/Q4 element for topology optimization

Glaucio H. Paulino, Chau H. Le

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


Design variable and displacement fields are distinct. Thus, their respective material and finite element meshes may also be distinct, as well as their actual location of nodes for the two fields. The proposed Q4/Q4M element possesses design variable nodes and displacement nodes which are not coincident. The element has been implemented using different approaches, including continuous approximation of material distribution and nodal approaches. The results obtained demonstrate that the element is effective in generating structural topologies with high resolution. From a numerical point of view, mesh independent solutions can be obtained by means of projection.

Original languageEnglish (US)
Pages (from-to)255-264
Number of pages10
JournalStructural and Multidisciplinary Optimization
Issue number3
StatePublished - Jan 2009
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


  • Displacement mesh
  • Material mesh
  • Node-based design variables
  • Q4/Q4
  • Q4/Q4M
  • Q4/U
  • Topology optimization


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