Local versus global stress constraint strategies in topology optimization: a comparative study

Gustavo Assis da Silva*, Niels Aage, André Teófilo Beck, Ole Sigmund

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


Stress-constrained topology optimization requires techniques for handling thousands to millions of stress constraints. This work presents a comprehensive numerical study comparing local and global stress constraint strategies in topology optimization. Four local and four global solution strategies are presented and investigated. The local strategies are based on either the Augmented Lagrangian or the pure Exterior Penalty method, whereas the global strategies are based on the P-mean aggregation function. Extensive parametric studies are carried out on the L-shaped design problem to identify the most promising parameters for each solution strategy. It is found that: (1) the local strategies are less sensitive to the continuation procedure employed in standard density-based topology optimization, allowing achievement of better quality results using less iterations when compared to the global strategies; (2) the global strategies become competitive when P values larger than 100 are employed, but for this to be possible a very slow continuation procedure should be used; (3) the local strategies based on the Augmented Lagrangian method provide the best compromise between computational cost and performance, being able to achieve optimized topologies at the level of a pure P-continuation global strategy with P = 300, but using less iterations.
Original languageEnglish
JournalInternational Journal for Numerical Methods in Engineering
Publication statusAccepted/In press - 2021


  • Augmented lagrangian
  • Global stress constraint
  • Local stress constraints
  • Stress aggregation function
  • Topology optimization


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