A Concurrent Topology Optimization Model for Dynamic Property of Structures with Connectable Graded Microstructures

Lattice structures composed of porous microstructures have attracted considerable attention due to their useful light-weight and multiphysical properties. Their mechanical properties are often a major concern in the design problem. However, unlike in the case of static stiffness maximization, few theoretical results can be used to guide the dynamic property design of such structures and their microstructures. In this paper, we present a numerical method of concurrent topology optimization for maximizing the natural frequencies of structures consisting of layer-wise graded microstructures. Both the configurations of graded microstructures and their spatial distribution in the macrostructural design domain are simultaneously optimized under constraints imposed on the macro- and microscales. The applied microscale design constraint still retains desired design space by allowing designable volume fractions of different microstructures under the total material usage restriction. The designable connective region technique is employed to guarantee the connectivity between different layers of microstructures. Numerical examples demonstrate the effectiveness of the proposed method. Compared to the uniform-lattice structural design, the proposed method is able to yield improved dynamic performance.

由多孔微结构组成的晶格结构因其有用的轻质和多物理特性而备受关注。它们的力学性能在设计问题中往往是一个主要关注点。然而，与静态刚度最大化的情况不同，很少有理论结果可用于指导此类结构及其微结构的动态特性设计。在本文中，我们提出了一种并行拓扑优化的数值方法，用于最大化由逐层渐变微结构组成的结构的固有频率。在宏观和微观尺度的约束下，同时优化渐变微结构的配置及其在宏观结构设计域中的空间分布。所应用的微观设计约束通过在总材料使用限制下允许不同微结构的可设计体积分数，仍然保留了所需的设计空间。采用可设计连接区域技术来保证不同层微结构之间的连接性。数值例子证明了所提方法的有效性。与均匀晶格结构设计相比，所提方法能够提高动态性能。