This work analyzes buckling under action of external lateral pressure of a thin cylindrical shell with a curvelinear edge stiffened by identical rings. It is assumed that the rings may be considered as circular beams. A combination of asymptotic methods is applied to get approximate formulas for the critical pressure. The usage of asymptotic formulas for critical pressure allows obtaining the approximate relations for calculation of optimal stiffened shell parameters corresponding to the minimal value of its weight.
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