Optimal truss and frame design from projected homogenization-based topology optimization
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In this article, we propose a novel method to obtain a near-optimal frame structure, based on the solution of a homogenization-based topology optimization model. The presented approach exploits the equivalence between Michell’s problem of least-weight trusses and a compliance minimization problem using optimal rank-2 laminates in the low volume fraction limit. In a fully automated procedure, a discrete structure is extracted from the homogenization-based continuum model. This near-optimal structure is post-optimized as a frame, where the bending stiffness is continuously decreased, to allow for a final design that resembles a truss structure. Numerical experiments show excellent behavior of the method, where the final designs are close to analytical optima, and obtained in less than 10 minutes, for various levels of detail, on a standard PC.
KeywordsOptimal frame design Optimal truss design Michell theory Topology optimization
The authors acknowledge the support of the Villum Fonden through the Villum investigator project InnoTop. The authors would also like to thank Andreas Bærentzen and Niels Aage for valuable discussions during the preparation of the work. Finally, the authors wish to thank Krister Svanberg for providing the MATLAB MMA code.
- Dobbs MW, Felton LP (1969) Optimization of truss geometry. J Struct Div 95(10):2105–2118Google Scholar
- Dorn WS, Gomory RE, Greenberg HJ (1964) Automatic design of optimal structures. Journal de Mecanique 3:25–52Google Scholar
- Groen JP, Sigmund O (2017) Homogenization-based topology optimization for high-resolution manufacturable micro-structures. Int J Numer Methods Eng :1–18. https://doi.org/10.1002/nme.5575
- Hemp WS (1973) Optimum structures. Clarendon Press, OxfordGoogle Scholar
- Pantz O, Trabelsi K (2010) Construction of minimization sequences for shape optimization. In: 15th international conference on methods and models in automation and robotics (MMAR), pp 278–283. https://doi.org/10.1109/MMAR.2010.5587222
- Pedersen P (1969) On the minimum mass layout of trusses. In: AGARD conference proceedings no 36, symposium on structural optimization, pp 36–70Google Scholar