Bending of an elastoplastic circular sandwich plate on an elastic foundation in a temperature field

Today, the development of the general theory of quasi-static deformation of three-layer structural elements, including plates, is not yet complete and is being intensively studied. Mathematical models of deformation under complex thermo-force and thermo-irradiation loads are created. The problems of strength, stability, and dynamic behaviour are considered. In strength calculations of three-layer structural elements, it is necessary to take kinematic hypotheses for each layer separately, which complicates the mathematical side of the problem but leads to significant refinement of the stress-strain state. The reaction of an elastic foundation is described by the Winkler model. The use of variational methods allows one to obtain a refined system of three differential equations of equilibrium in internal forces. The thermo-force bending of an elastoplastic circular sandwich plate with a light core connected to an elastic foundation is considered. The polyline normal hypotheses are used to describe the kinematics of a plate package that is not symmetric in thickness. In thin base layers, the Kirchhoff-Love hypotheses are accepted. In a light relatively thick core, the Timoshenko hypothesis is true, while the normal remains rectilinear, but rotates at some additional angle, the radial displacements change linearly in thickness. The differential equations of equilibrium are obtained using the Lagrange variation method. The statement of the boundary value problem in displacements is given in a cylindrical coordinate system. Numerical results for circular metal-polymer sandwich plates are presented.

BENDING OF AN ELASTIC THREE-LAYER PLATE WITH A HOLE CONNECTED TO THE SOIL FOUNDATION

The relevance of this paper is explained by a demand for the development of mechanical and mathematical models and methods for calculating the stress-strain state of the sandwich structural elements. The statement of the boundary value problem on the deformation of a circular sandwich plate with a central hole, connected to the soil foundation, was given. To describe the kinematics of an asymmetric plate pack, the broken line hypotheses are accepted. In a relatively thick lightweight core, the normal does not change its length, remains rectilinear, but rotates through some additional angle. Tuff, coarse grained soil, granite, and gneiss are accepted as the soil foundation. The bearing reaction is described by the Winkler model. The system of equilibrium equations is obtained by the variational method. Its solution is written in displacements through Kelvin functions. A numerical parametric analysis of displacements and stresses in the plate is carried out, their dependence on the type of soil foundation is shown.