论文标题
Wang Tilings的模块化优化:用于桁架结构的应用
Modular-topology optimization with Wang tilings: An application to truss structures
论文作者
论文摘要
模块化吸引了解决优化方面的许多问题。它为结构优化带来了可制造性和可重构性的好处,并可以在周期性单元电池(PUC)的计算性能与在多尺度材料优化中的不均匀设计的功效之间进行权衡。在这里,我们介绍了一种新颖的策略,用于同时使用Wang Tilling编码的桁架模块拓扑的最小符合性设计及其宏观组装,这种形式主义提供了对模块及其界面数量的独立控制。我们通过元数据和数学编程的结合来解决新兴的双层优化问题。在高层,我们采用遗传算法来优化模块组件。对于每个组件,我们将获得最佳模块拓扑作为凸二阶锥形程序的解决方案,该圆锥形程序利用了基础模块,并结合了应力限制,多个负载案例以及用于各种结构的模块的重复使用。提出的策略的优点用三个代表性的例子说明了,清楚地表明,通过我们的方法获得的最佳设计表现出了降低的依从性:与PUC设计相比,从56%到69%。
Modularity is appealing for solving many problems in optimization. It brings the benefits of manufacturability and reconfigurability to structural optimization, and enables a trade-off between the computational performance of a Periodic Unit Cell (PUC) and the efficacy of non-uniform designs in multi-scale material optimization. Here, we introduce a novel strategy for concurrent minimum-compliance design of truss modules topologies and their macroscopic assembly encoded using Wang tiling, a formalism providing independent control over the number of modules and their interfaces. We tackle the emerging bilevel optimization problem with a combination of meta-heuristics and mathematical programming. At the upper level, we employ a genetic algorithm to optimize module assemblies. For each assembly, we obtain optimal module topologies as a solution to a convex second-order conic program that exploits the underlying modularity, incorporating stress constraints, multiple load cases, and reuse of module(s) for various structures. Merits of the proposed strategy are illustrated with three representative examples, clearly demonstrating that the best designs obtained by our method exhibited decreased compliance: from 56% to 69% compared to the PUC designs.