The bending of an elastic circular sandwich plate on the pasternak foundation | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 24 > №3 / 2018 / Pages: 392-406

### The bending of an elastic circular sandwich plate on the pasternak foundation

#### Abstract:

Due to the wide application of composite, including three-layer, structural elements in construction and machine building, it is necessary to create appropriate mathematical models and methods for calculating their stress-strain state under different operating conditions. Here is the statement of the boundary value problem of axisymmetric deformation of an elastic three-layer circular plate on the two-parameter basis of Pasternak. This allows the influence of shear properties of the base material on the stress-strain state of the calculated design to take into account. To describe kinematics of asymmetrical on the thickness of the plate pack is adopted the hypothesis of a broken line. The Kirchhoff hypothesis of incompressibility, straightness and perpendicular to the normal to the deformed median surface is valid in thin bearing layers. In a relatively thick incompressible thickness of the filler is performed Tymoshenko hypothesis with a linear approximation of the displacements in the thickness of the layer. The contour assumes the presence of a rigid diaphragm that prevents the relative displacement of the layers. A non-uniform system of ordinary linear differential equations of equilibrium by the variational method is obtained. Three types of boundary conditions are formulated. The solution of the boundary value problem is reduced to finding three required functions – plate deflection, shear and radial displacement in the filler. The General analytical solution of the boundary value problem in Bessel functions is obtained. The numerical analysis is carried out at evenly distributed load and rigid filling of the plate contour. The influence of shear properties of the base on the stress-strain state of the plate at different compression ratios is studied numerically. The calculated values of displacements and shear in the filler obtained using Pasternak and Winkler models are compared.

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