Thermal-elastic-plastic bending

of circular three-layer plate on deformable foundation

E.I.Starovoytov, D.V.Leonenko, A.V.Yarovaya

Byelorussian State University of Transport

In a number of papers deformation of three-layer plates was examined in thermal-radiation field and also - on deformable foundation at isothermal loading. Transversally loaded elastic-plastic circular three-layer plate with light aggregate resting on a deformable foundation in temperature field is considered in this work. For problem statement and solution let us consider the problem in cylindrical coordinates r, φ, z. For isotropic bearing layers with thickness h₁, h₂ Kirchhoff hypotheses is accepted. An aggregate being incompressible along its thickness (h₃ љ= 2У) is light; and it is supposed, under deformation the normal turns on some angle ψ. The displacements at layer boundaries are continuous. A rigid diaphragm preventing the layers from relative shear is supposed to exist at the plate contour.

Due to loading symmetry the tangential displacements in layers are absent: u_φ^(k) = 0 (k is number of a layer), and the plate deflection, relative shift in the aggregate and radial displacement of a coordinate plane are independent of φ, i.e. u(r), ψ(r), w(r). These functions are here considered as unknown quantities. All displacements and linear sizes of the plate are the quantities relative to its radius r₀.

Here the formulated boundary value problem is essentially nonlinear, therefore we cannot indicate its exact solution. And it was considered the procedure of application of Ilyushin's method of elastic solutions to the studied problem. Numerical research of elastic-plastic bending was carried out for the foundation of medium rigidity (k₀=100MPa/m). It showed fast convergence of the method of elastic solutions. The general solution obtained in this work can be used for research of any case of bending of three-layer circular plate with light aggregate on the elastic foundation with or without an orifice.