Abstract
Abstract. The paper presents the results of a study of the stress-strain state of a circular plate of constant cylindrical stiffness, which lies on a variable elastic foundation and is under the influence of a continuously distributed transverse load. Twelve variants of calculation are considered ‒ six for a steel round plate and six more ‒ for a concrete round plate under two conditions of fixing and three different laws of variation of the bed coefficient. To solve the problem, the finite element method implemented in the LIRA-SAPR software package is used. It is noted that in the case when the bedding coefficient is a variable value depending on the coordinate in which the foundation settlement is determined, the analytical approach leads to the need to solve the corresponding differential equations with variable coefficients. Therefore, calculations of circular and annular plates lying on a variable elastic foundation by means of analytical solutions of differential equations are extremely rare in scientific periodicals and are of a private nature. An effective method for the analytical solution of differential equations with variable coefficients for a number of problems in mechanics was proposed by one of the authors of the article, however, the application of the method to the calculation of a circular plate on an elastic foundation with a variable bed coefficient requires verification, therefore, here we consider the features of the finite element analysis of such a plate under different boundary conditions and different laws of variation of the bed coefficient. In all versions, the results completely coincide with the known results of bending of slabs that do not have an elastic base and in the case when this base exists and its resistance is constant. The discrepancy here is very insignificant ‒ in the third significant digit after the decimal point for deflection when hinged and in the second for moments. In case of rigid clamping, the deflections and moments also differ from the corresponding values of the known solutions in the second significant digit after the decimal point.
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