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Mechanics of Machines, Mechanisms and Materials

3_2019_sen_3

Title of the article

NONLINEAR DEFORMATION OF CIRCULAR SANDWICH PLATES WITH COMPRESSIBLE FILLER
Authors

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

ZAKHARCHUK Yuliya V., Ph. D. in Phys. and Math., Senior Lecturer of the Department “Building technologies and constructions”, 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 2019 Issue 3 Pages 26–33
Type of article RAR Index UDK 539.3 Index BBK  
Abstract

Here is the formulation of the boundary value problem on the bending of an elastoplastic three-layer circular plate with a compressible filler. To describe the kinematics of the package, the hypotheses of the polyline are accepted. For thin bearing layers, the Kirchhoff hypothesis is accepted. In a relatively thick lightweight filler, the Tymoshenko hypothesis is performed with a linear approximation of radial displacements and deflection along the layer thickness. The work of shear stresses and compression stresses is assumed to be small and is not taken into account. The physical equations of state in the bearing layers correspond to the nonlinear theory of elasticity. The inhomogeneous system of ordinary nonlinear differential equations of equilibrium is obtained by the Lagrange variational method. Boundary conditions are formulated. The solution of the boundary value problem is reduced to finding the four desired functions – the deflection of the lower layer; shear, radial displacement and compression function in the filler. These functions satisfy an inhomogeneous system of ordinary nonlinear differential equations. Here is the formulation of the boundary value problem on the bending of an elastoplastic three-layer circular plate with a compressible filler. To describe the kinematics of the package, the hypotheses of the polyline are accepted. For thin bearing layers, the Kirchhoff hypothesis is accepted. In a relatively thick lightweight filler, the Tymoshenko hypothesis is performed with a linear approximation of radial displacements and deflection along the layer thickness. The work of shear stresses and compression stresses is assumed to be small and is not taken into account. The physical equations of state in the bearing layers correspond to the nonlinear theory of elasticity. The inhomogeneous system of ordinary nonlinear differential equations of equilibrium is obtained by the Lagrange variational method. Boundary conditions are formulated. The solution of the boundary value problem is reduced to finding the four desired functions – the deflection of the lower layer; shear, radial displacement and compression function in the filler. These functions satisfy an inhomogeneous system of ordinary nonlinear differential equations.
Keywords

nonlinear elasticity, three-layer circular plate, compressible filler, deformation
   
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