A level set method for shape and topology optimization of both structure and support of continuum structures

Qi Xia, Michael Yu Wang, Tielin Shi

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74 Citations (Scopus)


We present a level set method for the shape and topology optimization of both structure and support. Two level set functions are used to implicitly represent a structure. The traction free boundary and the Dirichlet boundary are represented separately and are allowed to be continuously changed during the optimization. The optimization problem of minimum compliance is considered. The shape derivatives of both boundaries are derived by using a Lagrangian function and the adjoint method. The finite element analysis is done by modifying a fixed background mesh, and we do not use the artificial weak material. Numerical examples in two dimensions are investigated.

Original languageEnglish
Pages (from-to)340-353
Number of pages14
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 15 Apr 2014
Externally publishedYes


  • Dirichlet boundary
  • Homogeneous Neumann boundary
  • Level set method
  • Shape and topology optimization
  • Shape derivative

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