Research on multistable characteristics of inclined self-supporting cosine-curved shell structures

CHEN Zhuo; WANG Xin; WANG Shuai; HE Jialu; LI Xiangyuan

doi:DOI：10.16579/j.issn.1001.9669.2025.11.010

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Research on multistable characteristics of inclined self-supporting cosine-curved shell structures

·Design·Calculation· | 更新时间：2025-11-26

- Research on multistable characteristics of inclined self-supporting cosine-curved shell structures
- Journal of Mechanical Strength Vol. 47, Issue 11, Pages: 79-88(2025)
- 作者机构：
  
  1.重庆交通大学土木工程学院，重庆 400074
  2.重庆交通职业学院智能制造与汽车学院，重庆 402274
- 作者简介：
  
  CHEN Zhuo, E-mail: zhuochen@cqjtu.edu.cn
- 基金信息：
  
  Chongqing Postdoctoral Science Foundation Project(CSTB2023NSCQ-BHX0185)
- DOI：DOI：10.16579/j.issn.1001.9669.2025.11.010
  CLC： TB34
- Received：03 February 2024，
  
  Revised：2024-04-19，
  
  Published：15 November 2025
- 稿件说明：
移动端阅览
陈卓，王鑫，王帅，等. 斜向自支撑余弦曲壳结构多稳态特性研究［J］. 机械强度，2025，47（11）：79-88.

CHEN Zhuo，WANG Xin，WANG Shuai，et al. Research on multistable characteristics of inclined self-supporting cosine-curved shell structures［J］. Journal of Mechanical Strength，2025，47（11）：79-88.
陈卓，王鑫，王帅，等. 斜向自支撑余弦曲壳结构多稳态特性研究［J］. 机械强度，2025，47（11）：79-88. DOI： DOI：10.16579/j.issn.1001.9669.2025.11.010.

CHEN Zhuo，WANG Xin，WANG Shuai，et al. Research on multistable characteristics of inclined self-supporting cosine-curved shell structures［J］. Journal of Mechanical Strength，2025，47（11）：79-88. DOI： DOI：10.16579/j.issn.1001.9669.2025.11.010.

摘要

负刚度多稳态结构具有可调节性和可恢复性，因而广泛应用于各个领域。现有负刚度多稳态曲壳结构形式较为单一、组装灵活度不足，为此设计了一种基于余弦函数的斜向自支撑多稳态曲壳结构。利用有限元仿真，探究单胞和串联双胞的反力-位移、稳态与刚度的变化规律，分析曲壳高度、斜支撑高度对结构稳态特性的影响，最后利用响应面优化算法确定单胞最优参数。另一方面，借助3D打印技术制作TPU材料的双胞结构实物，进行准静态压缩试验，并将试验结果与仿真数据进行对比。研究表明，与已有的厚围环曲壳结构相比，斜向自支撑曲壳结构更易实现双稳态；通过合理控制曲壳高度与支撑结构高度，可以得到具有双稳态单胞，以及三稳态的串联双胞结构；在压缩过程中各个稳态之间可以实现跳跃切换，且正刚度随压缩过程增大；平行串联与翻转串联在加载中均可以体现每个胞元的屈曲过程，具有三稳态，比现有厚围环曲壳结构更易实现多胞元的任意、灵活组合叠加。斜向自支撑余弦曲壳结构为结构性能可调节及能量吸收与自锁提供了新结构，也为多稳态结构领域发展提供了新的方向。

Abstract

Negative stiffness multistable structures are widely utilized across various fields due to their adjustability and recoverability. However

the existing negative stiffness multistable curved dome is limited in its form and assembly flexibility. Therefore

this study proposes a design for a self-supporting negative stiffness multistable curved dome based on the cosine function. Finite element simulation was employed to investigate the force-displacement characteristics

steady-state behavior

and stiffness of individual units and the overall system. Furthermore

the impact of the curved dome’s height and the supporting part’s height on the steady-state properties of the structure was analyzed. Subsequently

an optimization algorithm based on response surface methodology was utilized to determine the optimal parameters for the unit. Additionally

3D printing technology was employed to fabricate a twin-unit system using TPU material

followed by conducting quasi-static compression experiments and comparing the results with simulation data. The results indicate that the self-supporting curved dome

compared to the existing thick-encircled curved dome

facilitates easier attainment of a bistable state. By effectively controlling the height of the curved dome and the supporting structure

a bistable as well as a tri-stable state can be achieved. During the compression process

the system’s stable state can be altered

and the positive stiffness increases as compression progresses. Both parallel and flipped connections demonstrate the buckling process of each unit during loading and its tri-stable state. The self-supporting cosine curved dome enables more flexible combinations and superposition of multiple units compared to the existing thick encircled curved dome. The self-supporting cosine curved dome provides a new structure for programmable and intelligent control of structural performance and offers a promising direction for the advancement of multistable structures.

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references

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