Assembly complexity and manufacturing costs of engineering structures can be significantly reduced by using periodic mechanical components, which are defined by combining multiple identical unit cells into a global topology. Additionally, the superior energy-absorbing properties of lattice-based periodic structures can potentially enhance the overall performance in crash-related applications. Recent research developments in periodic topology optimization (PTO) have shown its efficacy for tackling new design problems and finding advanced novel structures. However, most of these methods rely on gradient information in the optimization process, which poses difficulties for crash problems where analytical sensitivities are usually not directly applicable. In this paper, we present an effective periodic evolutionary level set method (P-EA-LSM) for the optimization of periodic structures. P-EA-LSM uses a low-dimensional level-set representation based on moving morphable components to parametrize a single unit cell, which is replicated in the design domain according to a predefined pattern. The unit cell is optimized using an evolutionary algorithm and the structural responses are calculated for the entire system. We initially assess the performance of P-EA-LSM using three 2D minimum compliance test cases with varying periodicities. Our results demonstrate that our approach produces solutions comparable to other state-of-the-art methods for PTO while keeping a low dimensionality of the optimization problem. Subsequently, we effectively evaluate the capabilities of P-EA-LSM in a crashworthiness scenario. This particular application highlights the significant potential of the method, which does not rely on analytical sensitivities.

通过使用周期性机械部件可以显着降低工程结构的装配复杂性和制造成本，这些部件是通过将多个相同的单元组合成全局拓扑来定义的。此外，基于晶格的周期性结构卓越的能量吸收特性可以潜在地提高碰撞相关应用的整体性能。周期性拓扑优化（PTO）的最新研究进展已显示出其在解决新设计问题和寻找先进新颖结构方面的功效。然而，这些方法大多数依赖于优化过程中的梯度信息，这给分析灵敏度通常不能直接应用的碰撞问题带来了困难。在本文中，我们提出了一种有效的周期性进化水平集方法（P-EA-LSM）来优化周期性结构。P-EA-LSM 使用基于移动可变形组件的低维水平集表示来参数化单个晶胞，该晶胞根据预定义的模式在设计域中复制。使用进化算法对晶胞进行优化，并计算整个系统的结构响应。我们最初使用不同周期的三个 2D 最小合规性测试用例来评估 P-EA-LSM 的性能。我们的结果表明，我们的方法产生的解决方案与其他最先进的 PTO 方法相当，同时保持优化问题的低维度。随后，我们有效评估了 P-EA-LSM 在耐撞场景中的能力。这一特殊应用凸显了该方法的巨大潜力，该方法不依赖于分析灵敏度。