Topology optimization with local stress constraints: a stress aggregation-free approach

Fernando V. Senhora, Oliver Giraldo-Londoño, Ivan F.M. Menezes, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


This paper presents a consistent topology optimization formulation for mass minimization with local stress constraints by means of the augmented Lagrangian method. To solve problems with a large number of constraints in an effective way, we modify both the penalty and objective function terms of the augmented Lagrangian function. The modification of the penalty term leads to consistent solutions under mesh refinement and that of the objective function term drives the mass minimization towards black and white solutions. In addition, we introduce a piecewise vanishing constraint, which leads to results that outperform those obtained using relaxed stress constraints. Although maintaining the local nature of stress requires a large number of stress constraints, the formulation presented here requires only one adjoint vector, which results in an efficient sensitivity evaluation. Several 2D and 3D topology optimization problems, each with a large number of local stress constraints, are provided.

Original languageEnglish (US)
Pages (from-to)1639-1668
Number of pages30
JournalStructural and Multidisciplinary Optimization
Issue number4
StatePublished - Oct 1 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


  • Aggregation-free
  • Augmented Lagrangian
  • Consistent topology optimization
  • Stress constraints
  • Stress relaxation
  • von Mises stress


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