Abstract
A hierarchical structure is a structure that can be described by different characteristic lengths, and is such that its layout in the smaller scale (microscale) affects its behavior in the bigger scale (macroscale). Each hierarchical level is treated as a continuous medium composed of one or more materials. The simultaneous design of multiphase composite structures aims at finding the optimal distribution of materials such that one or more structural parameters are maximized (or minimized). In this work, the Bi-directional Evolutionary Structural Optimization method, BESO hereinafter, is applied to the maximization of the fundamental frequency of a structure subjected to a constraint on the total volume of materials used. Numerical experiments are made in order to validate the implementation and confirm the efficacy of the method in optimizing the topology of the structure.
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References
Huang, X., Xie, Y.M.: Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials. Comput. Mech. 43, 393–401 (2009)
Huang, X., Xie, Y.M.: Evolutionary Topology Optimization of Continuum Structures: Methods and Applications. Wiley, Chichester (2010)
Xu, B., Xie, M.: Concurrent design of composite macrostructure and cellular microstructure under random excitations. Compos. Struct. 123, 65–77 (2015)
Liu, Q., Chan, R., Huang, X.: Concurrent topology optimization of macrostructures and material microstructures for natural frequency. Mater. Des. 106, 380–390 (2016)
Long, K., Han, D., Gu, X.: Concurrent topology optimization of composite macrostructure and microstructure constructed by constituent phases of distinct Poisson’s ratios for maximum frequency. Comput. Mater. Sci. 129, 194–201 (2017)
Zuo, Z.H., Huang, X., Rong, J.H., Xie, Y.M.: Muti-scale design of composite materials and structures for maximum natural frequencies. Mater. Des. 51, 1023–1034 (2013)
Huang, X., Zuo, Z.H., Xie, Y.M.: Evolutionary topological optimization of vibrating continuum structures for natural frequencies. Comput. Struct. 88, 357–364 (2010)
Hassani, B., Hinton, E.: A review of homogenization and topology optimization I—homogenization theory for media with periodic structure. Comput. Struct. 69, 707–717 (1998)
Hassani, B., Hinton, E.: A review of homogenization and topology optimization II—analytical and numerical solution of homogenization. Comput. Struct. 69, 719–738 (1998)
Hassani, B., Hinton, E.: A review of homogenization and topology optimization III—topology optimization using optimality criteria. Comput. Struct. 69, 739–756 (1998)
Andreassen, E., Andreasen, C.S.: How to determine composite material properties using numerical homogenization. Comput. Mater. Sci. 83, 488–495 (2014)
Acknowledgements
The research described in this paper was financially supported by the National Council of Scientific and Technological Development CNPq-Brazil (grants 140081/2015-1, 148895/2016-6 and 148887/2016-3) from the Ministry of Science, Technology and Innovation.
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de Souza Lisboa, E., Moreira, J.B.D., Cesconeto, E.M., Casas, W.J.P. (2019). Optimization of the Fundamental Frequency of Mechanical Structures by Using the Bidirectional Evolutionary Structural Method. In: Fleury, A., Rade, D., Kurka, P. (eds) Proceedings of DINAME 2017. DINAME 2017. Lecture Notes in Mechanical Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-319-91217-2_10
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DOI: https://doi.org/10.1007/978-3-319-91217-2_10
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