The regulation of the stress-strain state of the floor slab is considered in order to choose the optimal design solution for the frame of a unique building. Three variants of design solutions with varying reinforcement of the plate and cross sections of the vertical elements of the frame are proposed. The numerical experiment was performed by the finite element method using the Lira-CAD software package. To improve the accuracy of the results obtained, calculations were made taking into account the nonlinear operation of materials. The computational model of the floor slab includes physically nonlinear shell finite elements. Nonlinear loading was modeled taking into account the creep of concrete. Based on the results of the calculations, the analysis of the deflections of the floor slab and the consumption of materials was performed. The numerical experiment allowed us to propose an optimal design solution for the frame of a unique building.

Keywords: stress-strain state, finite element method, unique building, physical nonlinearity, deformation law, building frame

Flat bending stability problem of constant rectangular transverse section wooden beam, loaded by a concentrated force in the middle of the span is considered. Differential equation is provided for the cases when force is located not in the center of gravity. The solution of the equation is generated numerically by the method of finite differences. For the case of applying a load at the center of gravity, the problem reduces to a generalized secular equation. In other cases, the iterative algorithm developed by the authors is implemented, in the package Matlab. A relationship is obtained between the value of the critical force and the position of the load application point. For this dependence, a linear approximating function is chosen. A comparison of the results obtained by the authors with an analytical solution using the Bessel functions is performed.

Keywords: flat bending stability, secular equation, finite difference method, iteration process

The problem of the stability of E.Reyssner plate on the three-dimensional elastic layer with predetermined constant elasticity. The end surfaces are smooth, communications holding layer. It is believed that the plate is in a flat stress-strain state of the effects on its cylindrical surface of the self-balanced load, with some numerical parameter characterizing the magnitude of the load at loss of stability of the plate. From the conditions of restraint ties, a system of equations for determining the numerical parameter. We give a method for calculating the lowest value of the parameter at which the fixed loss of stability of the plate. As special cases, the results of the classical theory and model of Winkler foundation.

Keywords: the self-balance loading, strained state, stress functions, stability loss

Construction of three-dimensional structures faces the need to cover the hard concrete layer with lightweight insulation and waterproof carpet. This combination of materials with different mechanical and physical properties requires the creation of methods for determining the stress-strain state of elastic composite layer lying on absolutely solid. According to these criteria the general solution of elasticity theory problem for each layer has been calculated. The system of differential equations is solved. A homogeneous solution can be used to study various problems of stress state in a layer. Formation of the problem of infinitely extending beamless surface has been drawn as an example. These solutions can be used in studding various problems of stress state layer. The solutions of engineering problems require the definition of complex roots of transcendental characteristic equation. In this paper, the roots were determined by Newton`s method. The obtained roots of the characteristic equation determine the stress and displacements in each point of a composite layer.

Keywords: eigenvalues, eigenfunctions, boundary conditions, a potential solution, vortex solution, differential operators, homogeneous system, the voltage of the plate