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Local versus global stress constraint strategies in topology optimization: A comparative study
Author(s) -
da Silva Gustavo Assis,
Aage Niels,
Beck André Teófilo,
Sigmund Ole
Publication year - 2021
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6781
Subject(s) - topology optimization , mathematical optimization , continuation , augmented lagrangian method , constraint (computer aided design) , global optimization , topology (electrical circuits) , mathematics , parametric statistics , network topology , penalty method , optimization problem , computer science , finite element method , engineering , statistics , geometry , structural engineering , combinatorics , programming language , operating system
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 with 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.