晶格结构中的最佳异质结
Towards Optimal Heterogeneity in Lattice Structures
摘要：
我们提出了一个多阶段的设计参数化，以获得优化的异质晶格结构。3D域被离散成立方体网格，其中每个立方体具有八个不同的单位单元类型或相。当所有相位都存在时，域类似于密集连接的接地结构。格构单元中梁段的横截面积是设计变量，采用Kroshenko梁理论建模。在一个特定的晶格相位的所有梁段具有相同的横截面面积，以保持设计变量的数量低。刚性结构的优化问题，制定和解决使用的最优性准则算法。我们提出了一个案例研究，以显示拓扑优化的异质结构的优越性，在一个单一的相位均匀的晶格。为了解释相组成，我们进行了四个基本的负载测试上的单相，即，拉伸或压缩，剪切，弯曲和扭转。根据对应于各个载荷条件的刚度对相位进行排序。结果表明，在优化后的结构中，局部内部负载的配置驱动相的选择。我们还注意到，微极弹性捕获的散装行为的异质晶格结构，不仅有助于解释的最优相位，但也提高了计算效率的建议的优化技术。
英文摘要：
We present a multi-phase design parameterization to obtain optimized heterogeneous lattice structures. The 3D domain is discretized into a cubical grid wherein each cube has eight distinct unit cell types or phases. When all phases are present, the domain resembles a densely connected ground structure. The cross-section area of beam segments in lattice units, modelled using Timoshenko beam theory, are the design variables. All beam segments in a particular lattice phase have the same area of cross-section to keep the number of design variables low. The optimization problem is formulated for stiff structures and is solved using the optimality criteria algorithm. We present a case study to show the superiority of topology-optimized heterogeneous structures over uniform lattices of a single phase. In order to interpret the phase composition, we perform four basic load tests on single phases, namely, tension or compression, shear, bending, and torsion. The phases are ranked based on the stiffness corresponding to individual loading conditions. The results show that in the optimized structure, the local internal load configuration drives the selection of phases. We also note that micropolar elasticity captures the bulk behaviour of heterogeneous lattice structures, and helps not only to interpret the optimality of phases but also to improve the computational efficiency of the proposed optimization technique.
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