Analytical Method for Calculating Ring Plates on an Elastic Foundation with an Arbitrary Continuously Variable Bedding Factor

An analytical method for calculating the bending of ring plates resting on a non-homogeneous elastic Winkler foundation has been developed for the case when the bedding factor and load are given by any continuous functions. The method is based on the exact solution of the corresponding differential equation. Calculation formulas for the parameters of the stress-strain state of the plate are given in closed form. An example illustrates the practical application of the developed method. The case is considered when the bedding factor changes according to the parabolic law, and the load is given by the sine law. Calculation results are presented in numerical and graphic formats. For comparison, the calculation results obtained by the finite element method are also provided.