A one-dimensional model for elastic ribbons: A little stretching makes a big difference
A one-dimensional model for elastic ribbons: A little stretching makes a big difference
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DOI：
10.1016/j.jmps.2021.104457
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发表时间：
2021-05-10
影响因子：
5.3
通讯作者：
Neukirch, Sebastien
中科院分区：
文献类型：
--
作者：
Audoly, Basile;Neukirch, Sebastien
从弹性板理论出发，在假定t_t/a(2)的条件下，导出了厚度为t、宽度_a、长度为L的弹性带的一维非线性模型，指出即使对于截面很薄的弹性带(即t/a小到0.02)，Sadowsky的不可伸缩模型也可能是一个很差的近似。作为说明，将该一维模型应用于(I)带的弯扭不稳定，与实验和有限元壳体模拟结果吻合良好；(Ii)用于扭转带在拉力作用下的稳定性。讨论了一维模型的非凸性，并通过凸化论证加以说明。
Starting from the theory of elastic plates, we derive a non-linear one-dimensional model for elastic ribbons with thickness t, width a and length l, assuming t t/a(2); we point out that Sadowsky's inextensible model may be a poor approximation even for ribbons having a very thin cross-section (say, with t / a as small as 0.02). By way of illustration, the one-dimensional model is applied (i) to the lateral-torsional instability of a ribbon, showing good agreement with both experiments and finite-element shell simulations, and (ii) to the stability of a twisted ribbon subjected to a tensile force. The non-convexity of the one-dimensional model is discussed; it is addressed by a convexification argument.