Limiting the first principal stress in topology optimization: a local and consistent approach

Oliver Giraldo-Londoño, Jonathan B. Russ, Miguel A. Aguiló, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


The present study introduces a formulation for topology optimization of structures with constraints on the first principal stress. We solve the problem considering local stress constraints via the augmented Lagrangian method, which enables the solution of large-scale problems without the need for ad hoc aggregation schemes and clustering methods. Numerical examples are provided which demonstrate the effectiveness of the framework for practical problems with numerous (e.g., in the range of million(s)) local constraints imposed on the maximum principal stress. One of the examples is a three-dimensional antenna support bracket, which represents a realistic engineering design problem. This example, which has more than one million constraints, is proposed as a benchmark problem for stress-constrained topology optimization.

Original languageEnglish (US)
Article number254
JournalStructural and Multidisciplinary Optimization
Issue number9
StatePublished - Sep 2022

All Science Journal Classification (ASJC) codes

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


  • Augmented Lagrangian
  • Local stress constraints
  • Principal stresses
  • Topology optimization


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