Abstract
In this article, an analytical solution of the problem of bending a round plate with an initial curvature is obtained. A round plate with an initial curvature as a structural element is widely used, the calculation of which leads to many questions related to the design of round Foundation plates, turbine disks, flexible shaft connections and other. The nonlinear theory of round flexible plates provides the key to explaining the process of loss of stability, which often leads to complete destruction of the structure. Therefore, there is a high need for analytical methods for solving problems of calculating the stress-strain state of round flexible plates, taking into account the initial curvature. These problems are mathematically reduced to differential equations with variable coefficients, the exact solution of which, as a rule, does not exist. Therefore, the construction of analytical solutions to these problems is very relevant.