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Tristability of thin orthotropic shells with uniform initial curvature

机译:具有均匀初始曲率的正交异性薄壳的可拉伸性

摘要

Composite shells show a rich multistable behaviour of interest for the design of shape-changing (morphing) structures. Previous studies have investigated how the initial shape determines the shell stability properties. For uniform initial curvatures and orthotropic material behaviour, not more than two stable equilibria have been reported. In this paper, we prove that untwisted, uniformly curved, thin orthotropic shells can have up to three stable equilibrium configurations. Cases of tristability are first documented using a numerical stability analysis of an extensible shallow shell model. Including mid-plane extension shows that the shells must be sufficiently curved in relation to their thickness to be multistable. Thus, an inextensible model allows us to perform an analytical stability analysis. Focusing on untwisted initial configurations, we illustrate with simple analytical results how the material parameters of the shell control the dependence of its multistable behaviour on the initial curvatures. In particular, we show that when the bending stiffness matrix approaches a degeneracy condition, the shell exhibits three stable equilibria for a wide range of initial curvatures. © 2008 The Royal Society.
机译:复合材料壳体在设计变形(变形)结构时表现出令人感兴趣的丰富多稳态行为。先前的研究已经研究了初始形状如何确定壳的稳定性。对于均匀的初始曲率和正交异性材料行为,已经报道了不超过两个稳定的平衡。在本文中,我们证明了不扭曲,均匀弯曲的薄正交异性壳最多可以具有三个稳定的平衡构型。首先使用可扩展浅壳模型的数值稳定性分析记录了三态性的情况。包括中平面延伸在内,表明壳必须相对于其厚度充分弯曲以使其具有多重稳定性。因此,不可扩展的模型使我们能够执行分析稳定性分析。着眼于未扭转的初始构型,我们用简单的分析结果说明了壳体的材料参数如何控制其多稳态行为对初始曲率的依赖性。特别是,我们显示出,当弯曲刚度矩阵接近简并条件时,壳体在很宽的初始曲率范围内会表现出三个稳定的平衡。 ©2008皇家学会。

著录项

  • 作者

    Vidoli Stefano; Maurini C.;

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  • 年度 2008
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  • 原文格式 PDF
  • 正文语种 eng
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