Topology optimization for minimum weight with compliance and stress constraints
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The paper deals with a formulation for the topology optimization of elastic structures that aims at minimizing the structural weight subject to compliance and local stress constraints. The global constraint provides the expected stiffness to the optimal design while a selected set of local enforcements require feasibility with respect to the assigned strength of material. The Drucker–Prager failure criterion is implemented to handle materials with either equal or unequal behavior in tension and compression. A suitable relaxation of the equivalent stress measure is implemented to overcome the difficulties related to the singularity problem. Numerical examples are presented to discuss the features of the achieved optimal designs along with performances of the adopted procedure. Comparisons with pure compliance–based or pure stress–based strategies are also provided to point out differences arising in the optimal design with respect to conventional approaches, depending on the assumed material behavior.
KeywordsTopology optimization Stress constraints Compliance constraint Singularity problem Drucker–Prager failure criterion
Part of the work has been supported by the “9th Executive Programme for Scientific Cooperation between the Francophone Belgian Community and Italy”, that is gratefully acknowledged.
- Bendsøe M, Sigmund O (2003) Topology optimization—theory, methods and applications, Springer, EUA, New YorkGoogle Scholar
- Chang CJ, Zheng B, Gea HC (2007) Topology optimization for tension/compression only design. In: Proc. of the 7th WCSMO. COEX Seoul, Korea, pp 2488–2495Google Scholar
- Dorn WS, Gomory RE, Greenberg HJ (1964) Automatic design of optimal structures. J Méc 3:25–52Google Scholar
- Duysinx P (1999) Topology optimization with different stress limits in tension and compression. In:Proceedings of the 3rd World Congress of Structural and Multidisciplinary Optimization WCSMO3Google Scholar
- Duysinx P, Sigmund O (1998) New developments in handling stress constraints in optimal material distribution. 7th Symposium on Multidisciplinary Analysis and Optimization AIAA–98–4906: pp 1501–1509Google Scholar
- Fancello E and Pereira JT (2003) Structural topology optimization considering material failure constraints and multiple load cases. Lat Amer J Solids Struct 1:3–24Google Scholar
- Fleury C (2007) Structural optimization methods for large scale problems: status and limitations. In: Proceedings of the ASME2007 IDERTC/CIE DETC2007/VIB-34326Google Scholar
- Haftka RT and Gürdal Z (1992) Elements of structural optimization, third revised and expanded edition. Academic publishers, Dordrecht, KluwerGoogle Scholar