Refined nonlinear deformation model of sandwich plates with composite facings and transversal-soft core

Following up on the results obtained earlier, a refined nonlinear model of static deformation of sandwich plates with transversal-soft core and facings with low transverse shear and transverse compression stiffness is constructed for the case of cylindrical bending. It is based on the use of linear approximations in thickness for deflections of the external layers, cubic approximation in thickness for tangential displacements and simplified three-dimensional equations of elasticity theory, that can be integrated along transverse coordinates and introduce two unknown function, representing constant transverse tangential stresses in thickness. The kinematic relations for the facings are constructed in a geometrically nonlinear quadratic approximation, which allows, take into account the physical nonlinear behavior of the material under transverse shear conditions, to describe in them non-classical transverse-shear forms of stability loss in both compression and bending conditions. To describe the static deformation process with high rates of variability of the parameters of the stress-strain state one-dimensional nonlinear equations of equilibrium and conjugation of the facings with the core by tangential displacements are constructed, which based on the generalized Lagrange variational principle.