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.
Highlights
The problem of bending elastic round plates of initial curvature is one of the actual problems of the technical theory of elasticity
A round plate with an initial curvature as a structural element is widely used, which is calculated by many questions related to the design of round Foundation plates, turbine disks, flexible shaft connections, hydraulic machine blades, disk springs, etc. [1], The development of modern practice requires researchers and designers to create methods for solving a large number of strength problems related to the variability of thickness, elastic modulus, Poisson's ratio, and the presence of initial curvature in aggregates
Existing studies of symmetrical bending of round plates with initial curvature are of a particular nature
Summary
The problem of bending elastic round plates of initial curvature is one of the actual problems of the technical theory of elasticity. Asymmetric bending of round plates of variable thickness has been studied even less; here, in addition to solutions for hyperbolic profile plates, there are practically no solutions for any other profiles of practical significance. These problems are mathematically reduced to differential equations with variable coefficients, the exact solution of which, as a rule, does not exist. Using the method of partial discretization of differential equations, based on the theory of generalized functions, an analytical solution to the problem of bending elastic round plates with account for the initial curvature is obtained
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