Rigorous Derivation of the Formula for the Buckling Load in Axially Compressed Circular Cylindrical Shells
Rigorous Derivation of the Formula for the Buckling Load in Axially Compressed Circular Cylindrical Shells
复制标题
轴向受压圆柱壳屈曲载荷公式的严格推导
DOI：
10.1007/s10659-015-9513-x
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发表时间：
2014
影响因子：
2
通讯作者：
D. Harutyunyan
中科院分区：
文献类型：
--
作者：
Y. Grabovsky;D. Harutyunyan
本文的目的是将最近发展的任意细长体屈曲理论应用于轴向压缩圆柱壳（视为三维超弹性体）屈曲的一个易处理但非平凡的例子。该理论是基于一个严格的数学渐近分析的第二个变化的三维，完全非线性弹性能量，作为壳的厚度趋于零。本文的主要结果是对经典的屈曲载荷公式的严格证明，以及用Koiter圆描述波数的单次Fourier谐波屈曲模态中位移分量相对振幅的显式表达式。这项工作也是努力了解轴向压缩圆柱壳的屈曲载荷对载荷和形状缺陷的高度敏感性的根本原因的一部分。
The goal of this paper is to apply the recently developed theory of buckling of arbitrary slender bodies to a tractable yet non-trivial example of buckling in axially compressed circular cylindrical shells, regarded as three-dimensional hyperelastic bodies. The theory is based on a mathematically rigorous asymptotic analysis of the second variation of 3D, fully nonlinear elastic energy, as the shell’s thickness goes to zero. Our main results are a rigorous proof of the classical formula for buckling load and the explicit expressions for the relative amplitudes of displacement components in single Fourier harmonics buckling modes, whose wave numbers are described by Koiter’s circle. This work is also a part of an effort to understand the root causes of high sensitivity of the buckling load of axially compressed cylindrical shells to imperfections of load and shape.