Combined shape and topology optimization for minimization of maximal von Mises stress

Haojie Lian, Asger N. Christiansen, Daniel A. Tortorelli, Ole Sigmund, Niels Aage

Research output: Contribution to journalArticlepeer-review


This work shows that a combined shape and topology optimization method can produce optimal 2D designs with minimal stress subject to a volume constraint. The method represents the surface explicitly and discretizes the domain into a simplicial complex which adapts both structural shape and topology. By performing repeated topology and shape optimizations and adaptive mesh updates, we can minimize the maximum von Mises stress using the p-norm stress measure with p-values as high as 30, provided that the stress is calculated with sufficient accuracy.

Original languageEnglish (US)
Pages (from-to)1541-1557
Number of pages17
JournalStructural and Multidisciplinary Optimization
Issue number5
StatePublished - May 1 2017
Externally publishedYes


  • Combined shape and topology optimization
  • Deformable simplicial complex method
  • Explicit surface representation
  • Stress minimization

ASJC Scopus subject areas

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


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