Deformation of Elastic Spherical Shells with Random Initial Imperfections (O Deformatsii Uprugoi Afericheskoi Obolochki so Sluchainymi Nepravilnostyami),
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The equilibrium of a thin elastic spherical shell with small initial imperfections under the effect of a uniform pressure is investigated in a linearized position. It is assumed that deflections from the ideal form of the shell form a uniform random field with a correlation scale quite small as compared to the radius of the median surface. The mathematical expectation of the number of maximum, minimum and saddle points on a deformed surface is computed. An approximation equation for the number of overshoot of a deformed median surface for a given level is presented. The results obtained are used for the evaluation of reliability at limitations brought about in a full normal deflection of the shell.