皱曲弹性薄板能量的下界--最小脊
Lower bounds for the energy in a crumpled elastic sheet - A minimal ridge
摘要：
本文研究了一个长而薄的矩形弹性薄膜的线性化Fopl - von Karman理论，该薄膜弯曲成一个角$2 α$。我们证明严格的界限，这种配置的最小能量的板厚度$σ$和弯曲角度。我们证明了最小能量标度为$σ^{5/3} α^{7/3}$。这种缩放与先前获得的结果与各向同性压缩边界条件下的薄板的线性化理论，其中的能量尺度为$σ$形成鲜明对比。
英文摘要：
We study the linearized Fopl - von Karman theory of a long, thin rectangular elastic membrane that is bent through an angle $2 α$. We prove rigorous bounds for the minimum energy of this configuration in terms of the plate thickness $σ$ and the bending angle. We show that the minimum energy scales as $σ^{5/3} α^{7/3}$. This scaling is in sharp contrast with previously obtained results for the linearized theory of thin sheets with isotropic compression boundary conditions, where the energy scales as $σ$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
