Deformation of multilayered plates on a rigid foundation under local loading

Refined models of symmetrical stress-strain state have been used for studying the stress-strain state (SSS) of multilayered plates on a rigid foundation. The design diagram of a transversely loaded plate is formed by symmetric supplementing it with regard to the contact surface and the foundation. The load on the double-thickness plate is applied bilaterally and symmetrically to its mid-surface. In such a way, only unflexural deformation can be modeled, which reduces the number of unknowns and the general order of differentiation of the calculating system of equations. Such a diagram models the frictionless slip of the plate over the surface of its contact with the foundation. The rigid contact of the plate with the foundation is modelled by introducing an additional thin practically undeformed layer.

The refined continual models have been used to take into account the deformations of transverse shear and transverse compression in high iterative approximation. Two variants of refined models have been 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 calculating system of algebraic equations of VDM, the Lagrange variation functional is integrated on a half step of discretization, with a simultaneous use of backward and forward differences for the first derivatives of the displacement functions. The advantages of the second variant of the refined model has been demonstrated in the problems where the load function has gaps. The features of SSS plates on a rigid foundation under the action of local distributed loads have been presented.

Keywords: multilayered plate, a refined model, transverse shear, transverse compression, variational-difference method.