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Space-time Topology Optimization For One-dimensional Wave Propagation

机译：一维波传播的时空拓扑优化

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摘要

A space-time extension of the topology optimization method is presented. The formulation, with design variables in both the spatial and temporal domains, is used to create structures with an optimized distribution of material properties that can vary in time. The method is outlined for one-dimensional transient wave propagation in an elastic rod with time dependent Young's modulus. By two simulation examples it is demonstrated how dynamic structures can display rich dynamic behavior such as wavenumber/fre-quency shifts and lack of energy conservation. The optimization method's potential for creating structures with novel dynamic behavior is illustrated by a simple example; it is shown that an elastic rod in which the optimized stiffness distribution is allowed to vary in time can be much more efficient in prohibiting wave propagation compared to a static bandgap structure. Optimized designs in form of spatio-temporal laminates and checkerboards are generated and discussed. The example lays the foundation for creating designs with more advanced functionalities in future work.
机译：提出了拓扑优化方法的时空扩展。该配方在空间和时间两个方面均具有设计变量，可用于创建具有随时间变化的最佳材料特性分布的结构。概述了该方法用于弹性杆中一维瞬态波传播的问题，该杆具有随时间变化的杨氏模量。通过两个仿真示例，证明了动态结构如何显示出丰富的动态行为，例如波数/频率偏移和缺乏能量守恒。一个简单的例子说明了优化方法在创建具有新颖动态行为的结构方面的潜力。结果表明，与静态带隙结构相比，允许优化的刚度分布随时间变化的弹性杆在阻止波传播方面更为有效。生成并讨论了时空层压板和棋盘格形式的优化设计。该示例为在将来的工作中创建具有更高级功能的设计奠定了基础。

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