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Title of the article BENDING OF AN ELASTOPLASTIC FIVE-LAYER CIRCULAR PLATE SYMMETRIC IN THICKNESS
Authors

STAROVOITOV Eduard I., D. Sc. in Phys. and Math., Prof., Professor of the Department “Structural Mechanics, Geotechnical and Structural Engineering”, Belarusian State University of Transport, Gomel, Republic of Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.

SALICKI Vladislav S., PhD Student, Belarusian State University of Transport, Gomel, Republic of Belarus,  This email address is being protected from spambots. You need JavaScript enabled to view it.
In the section MECHANICS OF DEFORMED SOLIDS
Year 2026
Issue 2(75)
Pages 62–70
Type of article RAR
Index UDK 539.3
DOI https://doi.org/10.46864/1995-0470-2026-2-75-62-70
Abstract The problem of bending of a five-layer circular plate symmetric in thickness by axisymmetric distributed load is considered. The central and outer layers are assumed to be load-bearing, thin, and of increased rigidity. They perceive the main part of the force load and can exhibit elastoplastic properties. Their deformation follows the Kirchhoff hypotheses. Two relatively thick nonlinearly elastic fillers are used to connect the load-bearing layers. They provide redistribution of forces between the layers and are used to protect against unwanted external influences such as temperature and radiation. The deformation of the fillers is described by Timoshenko hypotheses, which take into account the relative shift, the additional rotation of the normal to the middle surface of the layer. The system of differential equations of equilibrium for the considered plate is obtained using the variational method of Lagrange. It includes a system of two nonlinear differential equations. The sought-for functions are the deflection of the plate, the radial displacement of the midplane of the central supporting layer, and two relative shear displacements in the fillers. The Ilyushin method of elastic solutions is used to solve the corresponding boundary value problem. The general solution is obtained in a recursive form. Formulas are provided for calculating the sought-for displacements and relative shear displacements under the boundary conditions of rigid clamping of the plate contour. The convergence of the method and the dependence of the solution on the physical nonlinearity of the layer materials are numerically investigated.
Keywords five-layer circular plate, physical nonlinearity, bending, analytical solution, numerical results
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