Li Yang Fan, Huang Xiaodong, Zhou Shiwei
Centre for Innovative Structures and Materials, School of Engineering, RMIT University, GPO Box 2476, Melbourne 3001, Australia.
Key Laboratory of Advanced Technology for Vehicle Body Design & Manufacture, Hunan University, Changsha 410082, China.
Materials (Basel). 2016 Mar 10;9(3):186. doi: 10.3390/ma9030186.
This paper systematically investigated the topological design of cellular phononic crystals with a maximized gap size between two adjacent bands. Considering that the obtained structures may sustain a certain amount of static loadings, it is desirable to ensure the optimized designs to have a relatively high stiffness. To tackle this issue, we conducted a multiple objective optimization to maximize band gap size and bulk or shear modulus simultaneously with a prescribed volume fraction of solid material so that the resulting structures can be lightweight, as well. In particular, we first conducted the finite element analysis of the phononic band gap crystals and then adapted a very efficient optimization procedure to resolve this problem based on bi-directional evolutionary structure optimization (BESO) algorithm in conjunction with the homogenization method. A number of optimization results for maximizing band gaps with bulk and shear modulus constraints are presented for out-of-plane and in-plane modes. Numerical results showed that the optimized structures are similar to those obtained for composite case, except that additional slim connections are added in the cellular case to support the propagation of shear wave modes and meanwhile to satisfy the prescribed bulk or shear modulus constraints.
本文系统地研究了具有相邻两个能带之间最大间隙尺寸的蜂窝声子晶体的拓扑设计。考虑到所获得的结构可能承受一定量的静载荷，希望确保优化设计具有相对较高的刚度。为了解决这个问题，我们进行了多目标优化，以便在规定的固体材料体积分数下同时最大化带隙尺寸和体积模量或剪切模量，从而使所得结构也能轻量化。特别是，我们首先对声子带隙晶体进行了有限元分析，然后基于双向进化结构优化（BESO）算法结合均匀化方法，采用一种非常有效的优化程序来解决这个问题。针对面外和面内模式，给出了许多在体积模量和剪切模量约束下最大化带隙的优化结果。数值结果表明，优化后的结构与复合材料情况获得的结构相似，只是在蜂窝结构情况下增加了额外的细长连接，以支持剪切波模式的传播，同时满足规定的体积模量或剪切模量约束。
