No abstract

In structural engineering, the analysis of plate elements is one of the important problems that based on theory of plates. The analytical solutions using traditional methods and manual calculations are determined in the cases with simple calculation schemes. It will be difficult to solve problems with the complicatedness in loading and boundary conditions. Thereof, the application of numerical methods is necessary to deal with that. The finite difference method and successive approximation method are popular numerical methods to solve relatively thoroughly the plate problems. In addition, with the development of construction technology, the dimensions of the current building projects become greater and lead to increase of building displacements that is required to take into account in analysis. The analysis of plates with non-linear geometrical is relatively complicated and iterative algorithms can help to solve this problem. In this paper, the authors used the difference equations of successive approximation method (MSA) and generalized equations of finite difference method (MFD) to solve the problems of non-linear plates with different boundary conditions and loading. From the comparison of obtained results with Volmir’s analytical results the conclusions and recommendations are proposed.

Currently, plates with characteristics of high thermal insulation, sound insulation and strength are sufficiently and widely used in structural engineering. To describing the connect of the plates with other elements, it is possible to give many calculation schemes on the different views. In this paper, it is considered the problem of rectangular plates, each side of which are fixed with hinged support or fixed support. This paper deals with the discontinuous points of boundary conditions with the use generalized equations of finite difference method. The obtained results of the analysis of stress state in discontinuous area of boundary conditions are compared with the results of work of Smirnov V.A.

The article proposes the development of a numerical method for calculating multilayer beams, based on the theory of composite rods by A.R. Rzhanitsyn. The modification of this theory is to simplify the calculation model for a determined class of structures. It is considered multilayer beams composed of same layers of rectangular cross section, with the same physical and mechanical characteristics. The stiffness of all connecting seams is taken equal. In the research the hypothesis of a functional relationship between shear forces in the seams of the structure is taken. This allows the authors to significantly reduce the dimension of the system of resolving differential equations, from n + 2 equations to three for any finite number of layers. Where n -is the number of seams, and, accordingly, the number of shear forces to find in the seams according to the A.R Rzhanitsyn model, n + 1 is the number of layers. A comparison of three models of the above dependence is given. The numerical methodology is based on the approximation of differential equations by difference equations of the method of successive approximations (MSA). This methodology has proven itself well in the calculation of beams, plates, shells for the action of static loads, in calculations in a dynamic setting and for stability, on an elastic foundation. Including multilayer beams and plates. It allows to take into account the finite discontinuities of the load parameters, stiffness parameters of the structure and foundation. The described methodology can find application in the practice of design organizations and enter the educational courses of higher educational institutions of the construction profile.

The problem considered in the article belongs to the class of geometrically nonlinear problems. A numerical method basing on the use of difference equations of successive approximation method (MSA) is proposed to solve the problem. The results obtaining from example of this article are compared with the results received by A.S. Volmir for confirmation of efficiency of methodology.