The goal of this paper is to apply the recently developed theory of bucklingof arbitrary slender bodies to a tractable yet non-trivial example of bucklingin axially compressed circular cylindrical shells, regarded asthree-dimensional hyperelastic bodies. The theory is based on a mathematicallyrigorous asymptotic analysis of the second variation of 3D, fully nonlinearelastic energy, as the shell's slenderness parameter goes to zero. Our mainresults are a rigorous proof of the classical formula for buckling load and theexplicit expressions for the relative amplitudes of displacement components insingle Fourier harmonics buckling modes, whose wave numbers are described byKoiter's circle. This work is also a part of an effort to quantify thesensitivity of the buckling load of axially compressed cylindrical shells toimperfections of load and shape.
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