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A novel single variable based topology optimization method for band gaps of multi-material phononic crystals

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2022年第9期65卷 1-19页

作者： Chen, Hongfang Fu, Yu Hu, Yujin Ling, Ling Huazhong Univ Sci & Technol Sch Mech Sci & Engn State Key Lab Digital Mfg Equipment & Technol Wuhan 430074 Peoples R China

Multi-material phononic crystals have the potential to not only provide wide enough band gaps to fulfill sound insulation and shock isolation, but also reduce cost, weight, or enhance rigidity. A single variable based topology optimization method for band gaps of multi-material phononic crystals is proposed in this paper. Compactly supported radial basis functions (CSRBF) integrated with a variant of Heaviside functions are utilized to describe the multiple materials fields, which can make the method free from traditional filtering procedures. An adjustable stair form interpolation model is adopted to construct the mapping from the single design variable field to the multi-material physical parameter field. It reduces the dependency of the dimension of design variables on the number of material types, which can significantly decrease the number of design variables and improve the computational efficiency. A nested form avoiding overlap among each material is adopted to characterize the multiple material phases. Several numerical examples are used to demonstrate the effectiveness of the presented method.

关键词： Multi-material topology optimization Phononic crystal band gaps single variable-based stair form Compactly supported radial basis functions

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Topological optimization design of multi-material phononic crystals with floating projection constraints to achieve ultra-wide band gap

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COMPOSITE STRUCTURES 2024年 346卷

作者： Liao, Lin Yao, Song Li, Yingli Cent South Univ Sch Traff & Transportat Engn Key Lab Traff Safety Track Minist Educ Changsha 410075 Peoples R China Cent South Univ Joint Int Res Lab Key Technol Rail Traff Safety Changsha 410075 Peoples R China Cent South Univ Natl & Local Joint Engn Res Ctr Safety Technol Rai Changsha 410075 Peoples R China

The multi-material phononic crystals (PnCs) not only has the potential to achieve broadband vibration reduction and noise control, but also has the capability to reduce costs and weight. This paper proposes a single variable based topological optimization method for widening the band gaps (BGs) in multi-material PnCs. The method combines the floating projection topology optimization (FPTO) method, and utilizes an adjustable stair form interpolation model is used to construct a mapping from a single design variable field to a multi-material field. It avoids the nested form of overlap between different materials to characterize multiple material phases, and the parameter self adaptability of FPTO solves the problem of multiple parameters in univariate optimization methods. Floating projection constraint is used to improve the projection strategy for intermediate densities to obtain a 0/1 design, resulting in a final design with a clear topological structure. Optimized PnCs using various engineered materials are generated to improve BG performance which can rival Au/Epoxy systems. And the effects of mass and cost constraints is also considered to achieve multi-material PnCs by maximizing the BG. The results also indicate that the resulting multi-material PnCs may achieve ultra-wide BG characteristics.

关键词： Multi-material Phononic crystal Floating projection topology optimization Ultra-wide band gap single variable-based stair form

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