- STRUCTURAL MECHANICS
- The Use of Generalized Equations of Finite Difference Method for Calculation of Orthotropic Plates
- UDC 624.072

**Nataliya B. UVAROVA**, e-mail: nbuvarova@yandex.ru

**Vladimir V. FILATOV**, e-mail: fofa@mail.ru

Moscow State University of Civil Engineering (National Research University), Yaroslavskoe shosse, 26, Moscow 129337, Russian Federation

**Anastasia A. CHUBAROVA**, e-mail: achubarova@yandex.ru

Terra Auri Proekt, ul. Leninskaya Sloboda, 19, str. 6, Moscow 115280, Russian Federation

**Abstract**. The article deals with the calculation of orthotropic plates for a range of loads. The resolving differential equilibrium equation of orthotropic plates in partial derivatives of the fourth order is reduced to the differential equation of the second order concerning the second partial derivative functions of deflections. To construct the numerical solution, the modified differential equation is approximated by the generalized equation of the method of finite differences. The second difference equation for the unknowns is the equation resulting from the consideration of compatibility of deformations of the elements, on which the grid of coordinate lines divides the region of integration. The finite differences method algorithm makes it possible to take into account the finite discontinuities of the right part of differential equation, calculate the plates for linear and concentrated impacts without the involvement of peripheral points and condensation of the grid at discontinuous impacts. On the basis of equations obtained, the calculations of hinged orthotropic plates under the effect of uniformly distributed load, simple bending, and strip load have been made. The reliability of the solutions is confirmed by the study of convergence of results on several meshes, comparing the obtained solutions with some existing data, executing static and kinematic tests.

**Key words**: orthotropic plate, differential equation, numerical solution, generalized equations of finite difference method, hinge support, boundary conditions. - REFERENCES

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