Rigorous Derivation of the Formula for the Buckling Load in Axially Compressed Circular Cylindrical Shells
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.
KeywordsBuckling Cylindrical shell Instability Second variation Critical load Imperfection sensitivity
Mathematics Subject Classification74K25 26D10 35A23 49S05
The authors are grateful to Eric Clement and Mark Peletier for their valuable comments and suggestions. This material is based upon work supported by the National Science Foundation under Grant No. 1412058.
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