The physically nonlinear deformation of circular sandwich plates with a compressible filler | Mekhanika | kompozitsionnykh | materialov i konstruktsii
> Volume 26 > №1 / 2020 / Pages: 58-73

The physically nonlinear deformation of circular sandwich plates with a compressible filler



Three-layer structural elements are used in aerospace and transport engineering, construction, production and transportation of hydrocarbons. The theory of deformation of three-layer plates with incompressible fillers is currently developed under external force influences quite well. Here is the formulation of the boundary value problem on the bending of an elastoplastic circular three-layer plate with a compressible filler. For thin bearing layers, the Kirchhoff hypothesis is accepted. In a relatively thick lightweight filler, the hypothesis of Tymoshenko 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 contour is assumed to have a rigid diaphragm that prevents the relative shift of the layers. The physical equations of state in the bearing layers correspond to the theory of small elastic-plastic deformations of Ilyushin. The filler is nonlinear elastic. 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. The method of successive approximations based on the method of elastic solutions is applied for the solution. The General iterative analytical solution of the boundary value problem in Bessel functions is obtained. Its parametric analysis is carried out at uniformly distributed load and rigid sealing of the plate contour. The influence of the compressibility of the filler on the stress-strain state of the plate is numerically investigated. The comparison of the calculated deflection values obtained by the traditional model with incompressible filler and in the case of its compression is given.