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 Relative Articles Scaling instability of the buckling load in axially compressed circular cylindrical shells Experimental and numerical study on buckling of axially compressed composite cylinders Rigorous asymptotic analysis of buckling of thin-walled cylinders under axial compression ANALYSIS AND CALCULATION METHODS FOR BUCKLING STRENGTH OF DOME-ROOF TANK SHELLS WITH IMPERFECTIONS UNDER AXIAL COMPRESSION含缺陷罐壁轴压失稳临界应力计算方法 The secondary buckling transition: wrinkling of buckled spherical shells Post-Buckling Behavior of Laminated Composite Cylindrical Shells Subjected to Axial, Bending and Torsion Loads Dynamics and statics of flexible axially symmetric shallow shells Dynamics and statics of flexible axially symmetric shallow shells Experimental - theoretical study of axially compressed cold formed steel profiles Experimental Investigation on the Buckling Process of Water-filled Metal Cylindrical Shells under Axial Impact充满水的金属圆柱壳经受轴向撞击时屈曲过程的实验研究 More...
Mathematics  2014

# Rigorous derivation of the formula for the buckling load in axially compressed circular cylindrical shells

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Abstract:

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 slenderness parameter 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 quantify the sensitivity of the buckling load of axially compressed cylindrical shells to imperfections of load and shape.

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