CONSIDERATION OF THE PHYSICAL NONLINEARITY OF ORTHOTROPIC PLATE IN THE STATIC CALCULATION OF AN INFINITE REGULAR SYSTEM OF PLATES ON AN ELASTIC LAYER

Abstract

An infinite regular system of orthotropic plates on an elastic layer rigidly connected to a non-deformable base is considered. Nonlinear calculation of an infinite regular system of plates on an isotropic basis is performed by the variational-difference method (VRM), which is characterized by the replacement of differential equations by finite-difference approximations. The numerical solution of the resulting system of equations is performed using an iterative algorithm.
 When finding the variable stiffness of the plate on the elastic layer, the "stiffness – curvature" dependence on the Straw in the directions of the axes of inertia is used. According to the found cylindrical bending stiffness from the ratio of S.P. Timo-shenko, the torsion stiffness of the plate is determined for each iteration. The energy of deformation of the elastic base is replaced by the work of reactive pressures in the contact zone of the structure on the basis of the law of conservation of energy.
 The analysis of the results of elastic and nonlinear calculations (3rd iteration) was carried out for the values of the orthotropic plate sediment and contact stresses in the zone of interaction of the plate with the elastic base.