Abstract
Abstract : The small-deflection theory of plates under lateral loads and the laws of the theory of plastic deformations are used in the analysis instead of elastic stress-strain relationships. Four approximate methods are applied to obtain numerical results for a simply supported, uniformly loaded plate. The Sokolovsky method reduces the equations relating the moments, curvatures, and plate loads to 2 simultaneous first-order nonlinear differential equations which are solved numerical integration. The Ilyushin (iteration) method separates a nonlinear second-order differential equation into a linear and nonlinear portion. The effect of the nonlinear portion on the solution is determined by iteration. A third method utilizes the principle of minimum potential energy to estimate the circumferential curvature of the plate, while a fourth method employs the principle of minimum complementary potential energy to estimate the radial bending moment in the plate. The estimates in these 2 methods are evaluated by Galerkin's method. Numerical examples are furnished for each case. A comparison of the first 3 methods is discussed, and applications of the iteration and the potential-energy methods are developed for rectangular plates, but no numerical results are obtained.
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