静力学
本构方程
引力奇点
非线性系统
材料科学
简单(哲学)
正规化(语言学)
弯曲
数学
数学分析
复合材料
丝带
应用数学
经典力学
统计物理学
物理
计算机科学
几何学
热力学
哲学
人工智能
有限元法
认识论
量子力学
作者
Sébastien Neukirch,Basile Audoly
标识
DOI:10.1098/rspa.2021.0548
摘要
Elastic ribbons are elastic structures whose length-to-width and width-to-thickness aspect ratios are both large. Sadowsky proposed a one-dimensional model for ribbons featuring a nonlinear constitutive relation for bending and twisting: it brings in both rich behaviours and numerical difficulties. By discarding non-physical solutions to this constitutive relation, we show that it can be inverted; this simplifies the system of differential equations governing the equilibrium of ribbons. Based on the inverted form, we propose a natural regularization of the constitutive law that eases the treatment of singularities often encountered in ribbons. We illustrate the approach with the classical problem of the equilibrium of a Möbius ribbon, and compare our findings with the predictions of the Wunderlich model. Overall, our approach provides a simple method for simulating the statics and the dynamics of elastic ribbons.
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