This article gives a review of publications presenting analytical and numerical results on determining the lower limit of loss-of-stability loads of isotropic cylindrical shells under axial compression. The research was performed using the dynamic criterion in Chetaev's form and ideal shells perturbation equations, linearized in the vicinity of the considered equilibrium state. The stress calculation results corresponding to the limit in question considered as necessary conditions of compressed cylindrical shells instability are qualitatively and quantitatively close to the lower limit of experimentally determined critical stresses in the whole range of dimensionless parameters of similarity cylindrical shells.
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