Deformation of Homogeneous and Multilayered Coverings with Longitudinal Defects on a Rigid Foundation

For investigating the stress-strain state (SSS) of multilayered plates on a rigid foundation, a refined structural-continual model of momentless symmetrical SSS is offered. The design diagram of a transversely loaded plate is formed by supplementing it with a plate symmetric about the contact surface with the foundation. The load to the double-thickness plate is applied bilaterally and symmetrically about its midsurface. The SSS of the plate becomes symmetric (unflexural). Numerically, the model is realized by the variational-difference method (VDM). To derive the resolving system of algebraic equations of VDM, the Lagrange variational functional is integrated on a half step of digitization, with a simultaneous use of backward and forward differences for the first derivative of displacement functions. Calculations confirmed the efficiency of such an approach, which allows one to obtain solutions qualitatively and quantitatively close to three-dimensional ones. Problems with a discretely changing rigidity of the plate in its plane due to the occurrence of longitudinal planar defects are solved.