Non-probabilistic robust continuum topology optimization with stress constraints
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This paper proposes a non-probabilistic robust design approach, based on optimization with anti-optimization, to handle unknown-but-bounded loading uncertainties in stress-constrained topology optimization. The objective of the proposed topology optimization problem is to find the lightest structure that respects the worst possible scenario of local stress constraints, given predefined bounds on magnitudes and directions of applied loads. A solution procedure based on the augmented Lagrangian method is proposed, where worst-case local stress constraints are handled without employing aggregation techniques. Results are post-processed, demonstrating that maximum stress of robust solutions is almost insensitive with respect to changes in loading scenarios. Numerical examples also demonstrate that obtained robust solutions satisfy the stress failure criterion for any load condition inside the predefined range of unknown-but-bounded uncertainties in applied loads.
KeywordsTopology optimization Stress constraints Uncertainties Non-probabilistic Robust Worst case
The authors received financial support from CNPq (National Council for Research and Development), grant number 306373/2016-5, FAPESP (São Paulo Research Foundation), grant number 2015/25199-0, and FAPESC, grant numbers 2017TR1747 and 2017TR784. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.
- Arora J S (2012) Introduction to optimum design, 3rd edn. Academic Press, BostonGoogle Scholar
- Birgin E, Martínez J (2014) Practical augmented lagrangian methods for constrained optimization society for industrial and applied mathematics, Philadelphia, PA. https://doi.org/10.1137/1.9781611973365
- Duysinx P, Bendsøe MP (1998) Topology optimization of continuum structures with local stress constraints. Int J Numer Methods Eng 43 (8):1453–1478. https://doi.org/10.1002/(SICI)1097-0207(19981230)43:8<1453::AID-NME480>3.0.CO;2-2 MathSciNetCrossRefzbMATHGoogle Scholar
- Fancello E A, Pereira J T (2003) Structural topology optimization considering material failure constraints and multiple load conditions. Lat Am J Solids Struct 1(1):3–24Google Scholar
- Le C, Norato J, Bruns T, Ha C, Tortorelli D (2010) Stress-based topology optimization for continua. Struct Multidiscip Optim 41(4):605–620. https://doi.org/10.1007/s00158-009-0440-y
- Thore CJ (2016) On a nash game for topology optimization under load-uncertainty: Finding the worst load. In: VII European congress on computational methods in applied sciences and engineering, pp 5–10Google Scholar
- Wang F, Jensen JS, Sigmund O (2011a) Robust topology optimization of photonic crystal waveguides with tailored dispersion properties. J Opt Soc Am B 28(3):387–397. https://doi.org/10.1364/JOSAB.28.000387
- Wang F, Lazarov BS, Sigmund O (2011b) On projection methods, convergence and robust formulations in topology optimization. Struct Multidiscip Optim 43(6):767–784. https://doi.org/10.1007/s00158-010-0602-y