Application of generalized equations of the method of finite differences to the calculation of continuous orthotropic plates

The paper considers the calculation of continuous orthotropic plates under various boundary conditions. The numerical solution is constructed using generalized equations of the finite difference method (FDM), which allow solving the problem within the integrable domain, taking into account the discontinuities of the required function, its first derivative and the right-hand side of the original differential equation without special reduction of the grid pitch. The differential equation for the equilibrium of orthotropic plates in fourth-order partial derivatives is written as a second-order differential equation with respect to the second partial derivatives of the deflection function, the difference approximation of which follows from the general difference approximation of the partial differential equation. The second difference equation is obtained by considering the compatibility of deformations. The results of the calculation of continuous slabs for hinged support and for rigid jamming are given. The reliability of the calculation was confirmed by comparing the solutions on several grids, performing static and kinematic checks. (paper)