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Title of the article COMPARISON OF SOLUTIONS TO THE BENDING PROBLEMS OF THREE-LAYER PLATES ON THE WINKLER AND PASTERNAK FOUNDATIONS
Authors

KOZEL Anastasiya G., M. Sc. in Eng., Senior Lecturer of the Department “Structural Мechanics”, Belarusian State University of Transport, Gomel, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.
In the section MECHANICS OF DEFORMED SOLIDS
Year 2021
Issue 1
Pages 30–37
Type of article RAR
Index UDK 539.3
DOI https://doi.org/10.46864/1995-0470-2021-1-54-30-37
Abstract Solutions of problems on axisymmetric bending of an elastic three-layer circular plate on the Winkler and Pasternak foundations are given. The bearing layers are taken as isotropic, for which Kirchhoff’s hypotheses are fulfilled. In a sufficiently thick lightweight, incompressible in thickness aggregate, the Timoshenko model is valid. The cylindrical coordinate system, in which the statements and solutions of boundary value problems are carried out, is connected with the median plane of the filler. On the plate contour, it is assumed that there is a rigid diaphragm that prevents the relative shear of the layers. The system of differential equations of equilibrium is obtained by the variational method. Three types of boundary conditions are formulated. One- and two-parameter Winkler and Pasternak models are used to describe the reaction of an elastic foundation. The solution to the boundary value problem is reduced to finding three desired functions, plate deflection, shear, and radial displacement in the filler. The general analytical solution to the boundary value problem is written out in the case of the Pasternak model in Bessel functions. At the Winkler foundation, the known solution is given in Kelvin functions. A numerical comparison of the displacements and stresses obtained by both models with a uniformly distributed load and rigid sealing of the plate contour is carried out.
Keywords three-layer circular plate, elasticity, bending, stress-strain state, Pasternak and Winkler foundation
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