Quasi-zero stiffness (QZS) is highly demanded in passive vibration isolators. Most of the existing design methods of QZS vibration isolators are typically based on mechanism designs, where pre-defined structural configurations, components, or mechanisms with certain features, such as negative stiffness, are required to synthesize the designs. This work introduces topology optimization for QZS structure designs, enabling the design of structures without pre-definitions and resulting in single-part designs rather than structural assemblies. We propose novel mathematical formulations of the objective function based on the QZS force-displacement curve and generic mathematical formulations of the optimization problem. An extended moving isosurface threshold method is used to solve the formulated optimization problem. In addition, topology optimization of metastructures with snap-through features and an alternative design method that synthesizes QZS metastructures by combining snap-through structures with positive stiffness elements are also presented. The optimized snap-through metastructures are numerically validated by nonlinear finite element analysis (NFEA) and experiment, which shows negative stiffness and snap-through characteristics. Numerical examples and investigations are presented for the QZS structures designed by both optimization and synthesis methods. The NFEA results reveal the QZS designs obtained from the two methods can achieve approximately constant stiffness of 0.502 N/mm over a 17 mm displacement range and 0.402 N/mm over a 12 mm displacement range, respectively.

中文翻译：

---

具有准零刚度和突弹跳变特征的超结构的拓扑优化


被动隔振器对准零刚度 （QZS） 的要求很高。QZS 隔振器的大多数现有设计方法通常基于机构设计，其中需要预定义的结构配置、组件或具有某些特征（如负刚度）的机构来综合设计。这项工作介绍了 QZS 结构设计的拓扑优化，无需预定义即可进行结构设计，并产生单零件设计而不是结构装配。我们提出了基于 QZS 力-位移曲线的目标函数的新颖数学公式和优化问题的通用数学公式。使用扩展移动等值面阈值方法求解公式化的优化问题。此外，还提出了具有突弹跳变特征的超结构的拓扑优化，以及通过将突弹跳变结构与正刚度单元相结合来合成 QZS 超结构的替代设计方法。优化的突弹跳动超结构通过非线性有限元分析 （NFEA） 和实验进行数值验证，显示出负刚度和突弹跳变特性。本文为通过优化和综合方法设计的 QZS 结构提供了数值示例和研究。NFEA 结果表明，从这两种方法获得的 QZS 设计可以在 17 mm 位移范围内实现 0.502 N/mm 的近似恒定刚度，在 12 mm 位移范围内分别实现 0.402 N/mm 的近似恒定刚度。