Stress-based shape and topology optimization with the level set method

Renato Picelli, Scott Townsend, C. Brampton, Julian Norato, H. A. Kim

Research output: Contribution to journalArticlepeer-review

165 Citations (SciVal)


This paper proposes a level set method to solve minimum stress and stress-constrained shape and topology optimization problems. The method solves a sub-optimization problem every iteration to obtain optimal boundary velocities. A p-norm stress functional is used to aggregate stresses in a single constraint. The shape sensitivity function is derived and a computational procedure based on a least squares interpolation approach is devised in order to compute sensitivities at the boundaries. Adaptive constraint scaling is used to enforce exact control of stress limits. Numerical results show that the method is able to solve the problem efficiently for single and multiple load cases obtaining solutions with smooth boundaries.

Original languageEnglish
Pages (from-to)1-23
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 1 Feb 2018


  • Level set method
  • Stress constraints
  • Stress minimization
  • Topology optimization

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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