THE REFINED MODELING IN THE PROBLEMS DEFORMATION OF MULTILAYERED COVERINGS ON A RIGID FOUNDATION UNDER LOCAL LOADING

Abstract

Multilayered coverings can be considered as thick plates resting on a rigid substrate. For investigating the stress-strain state (SSS) of multilayered plates on a rigid foundation, a refined models of 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. In such a way, only unflexural deformation can be modeled, which reduces the number of unknowns and the general order of differentiation of the resolving system of equations. Such a diagram is modelling frictionless slip of the plate over surface of its contact with the foundation. The rigid contact of the initial plate with the foundation is modelled by introducing an additional thin practically nondeformable layer.The refined continual models are used takes into account the deformations of transverse shear and transverse compression in high iterative approximation. Two variants of refined models are considered. In the first variant, the load function is given explicitly,whereas in the second variant it is replaced by an unknown desired function of compression. Numerically, the models are 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. The advantages of the second variant of the refined model in the problems where the load function has gaps is demonstrated. The features of SSS plates on a rigid foundation under the action of local distributed loads are shown.