Sandwich Shells with Composite Facings and a Transversally Flexible Core: Refined Equations and Buckling Modes of Specimens Under Four-Point Bending Tests

Abstract

In order to develop the previously obtained results for the case of medium bending, a refined geometrically nonlinear theory of static deformation has been developed for sandwich plates and shells with a transversely flexible core and composite facings having low stiffness on transverse shear and transverse compression. This theory is based on a refined Timoshenko shear model taking into account the transverse compression to describe the mechanics of facings. For a transversally flexible core, simplified three-dimensional equations of elasticity theory have been used. These equations allow integration along the transverse coordinate with the introduction into consideration of two two-dimensional unknown functions in the role of which constant in thickness transverse tangential stresses are used. Based on the generalized Lagrange variational principle, two-dimensional geometrically nonlinear equations of equilibrium as well as coupling conditions of facings with a core via tangential displacements are constructed to describe the static deformation process with high rates of variability of stress–strain state parameters. Based on them, an approximate analytical solution of the linearized problem of possible buckling modes has been found for a sandwich beam of a symmetrical in thickness structure under four-point bending.