Asymptotic derivation of a higher-order one-dimensional model for tape springs
Asymptotic derivation of a higher-order one-dimensional model for tape springs
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DOI：
10.1098/rsta.2022.0028
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发表时间：
2023-04-03
期刊：
影响因子：
5
通讯作者：
Lestringant, Claire
中科院分区：
文献类型：
--
作者：
Kumar, Arun;Audoly, Basile;Lestringant, Claire
我们推导出一个一维模型的带状弹簧。推导从非线性薄壳理论开始，并使用降维技术，该技术将带弹簧中表面的基于中心线的参数化与应变沿带弹簧长度沿着缓慢变化的假设相结合。一维模型实际上是一个高阶杆模型：在首阶，应变能取决于拉伸，弯曲和扭转应变，并与文献中的经典结果一致;以下两个订单是新颖的，并捕获应变能对应变梯度的依赖性。作为降维过程的一部分，横截面位移被求解，使得一维模型渐近精确。我们期望该模型能准确有效地捕捉带状弹簧的变形和不稳定性，包括高度局部化的变形。本文是“冲击敏感壳的探测和动力学”专题的一部分。
We derive a one-dimensional model for tape springs. The derivation starts from nonlinear thin-shell theory and uses a dimension reduction technique that combines a centreline-based parametrization of the tape-spring midsurface with the assumption that the strain varies slowly along the length of the tape spring. The one-dimensional model is effectively a higher-order rod model: at leading order, the strain energy depends on the extensional, bending and twisting strains and is consistent with classical results from the literature; the two following orders are novel and capture the dependence of the strain energy on the strain gradients. The cross-sectional displacements are solved as part of the dimension reduction process, making the one-dimensional model asymptotically exact. We expect that the model will accurately and efficiently capture the deformations and instabilities in tape springs, including those involving highly localized deformations.This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.