The thin revolution shell of corrugated by forming was selected as the object of the study. The new form of the equilibrium equations of revolution shells was obtained in the theory of Kirchhoff-Love's. The stability of axisymmetric equilibrium state is investigated on basis of the perturbation theory methods. At the ends of the shell is performed the hinge resistance, external and internal hydrostatic pressure is considered as the external load. A new, in this class of problems, the method based on the theory of Floquet-Lyapunov to determine the critical value of the load at which the axisymmetric stress-strain state loses stability was developed. The influence of the kind of "edge effect" on the critical values of the external load was carried out. In addition to the proposed method, the method of initial parameters to study the stability is used. The comparison of the obtained results using these two methods was conducted. Forms of stability loss for the two types of shells of revolution was constructed.

Для исследования устойчивости тонких гофрированных оболочек в рамках теории Киргхгофа-Лява, приведены новые, по форме уравнения равновесия оболочки вращения. Исследование устойчивости оболочек проведено при шарнирном опирании обоих торцов. Для определения критических значений внешнего и внутреннего гидростатического давления, при которых осесимметричное напряженно-деформированное состояние теряет устойчивость, разработаны алгоритмы, опирающиеся на метод начальных параметрах и новый в данном классе задач метод — метод Флоке-Ляпунова. Для найденных значений критической нагрузки построены формы потери устойчивости.