Analytical Calculation of Annular Plates Supported on an Elastic Foundation with Power-Law Inhomogeneity

Abstract:

The problem of axisymmetric bending of a ring plate, which is under the influence of a constant uniformly distributed transverse load and rests on a non-uniform elastic Winkler foundation, is considered. The inhomogeneity of the elastic foundation is given by a power function with an arbitrary non-negative power exponent . In analytical form, the fundamental functions and a partial solution of the corresponding differential equation are found. These functions are dimensionless and are represented by absolutely and uniformly convergent power series. In turn, formulas for the parameters of the stress-strain state of the plate are expressed through the specified functions. In fact, the calculation of the plate is reduced to the procedure of numerical implementation of explicit analytical formulas. The practical application of the obtained solutions is demonstrated using the example of a concrete slab with both fixed contours, resting on a cubic-variable elastic foundation

• Periodical: Advances in Science and Technology (Volume 170)
• Pages: 27-36
• DOI: https://doi.org/10.4028/p-y3oYhW
• Online since: November 2025
• Authors: Yurii Krutii, Mykola Surianinov*, Hanna Karnaukhova, Alla Perperi, Oleksiy Klymenko
• Keywords: Analytical Method, Inhomogeneous Elastic Foundation, Ring Plate, Variable Coefficient of Subgrade Resistance, Winkler Hypothesis

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