PolyStress: a Matlab implementation for local stress-constrained topology optimization using the augmented Lagrangian method

Oliver Giraldo-Londoño, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


We present PolyStress, a Matlab implementation for topology optimization with local stress constraints considering linear and material nonlinear problems. The implementation of PolyStress is built upon PolyTop, an educational code for compliance minimization on unstructured polygonal finite elements. To solve the nonlinear elasticity problem, we implement a Newton-Raphson scheme, which can handle nonlinear material models with a given strain energy density function. To solve the stress-constrained problem, we adopt a scheme based on the augmented Lagrangian method, which treats the problem consistently with the local definition of stress without employing traditional constraint aggregation techniques. The paper discusses several theoretical aspects of the stress-constrained problem, including details of the augmented Lagrangian-based approach implemented herein. In addition, the paper presents details of the Matlab implementation of PolyStress, which is provided as electronic supplementary material. We present several numerical examples to demonstrate the capabilities of PolyStress to solve stress-constrained topology optimization problems and to illustrate its modularity to accommodate any nonlinear material model. Six appendices supplement the paper. In particular, the first appendix presents a library of benchmark examples, which are described in detail and can be explored beyond the scope of the present work.

Original languageEnglish (US)
Pages (from-to)2065-2097
Number of pages33
JournalStructural and Multidisciplinary Optimization
Issue number4
StatePublished - Apr 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


  • Aggregation-free approach
  • Augmented Lagrangian
  • Local stress constraints
  • Matlab
  • Topology optimization


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