Objective. A family of multilayer finite elements designed for calculating reinforced concrete slabs and shells of variable thickness is described. The features of the formation of stiffness matrices associated with the variability of the cross-section of elements are considered.Methods. The family is based on the simplest planar triangular element constructed using the Kirchhoff hypothesis. The transverse displacements in this element are approximated by an incomplete cubic polynomial. This element is not suitable for practical use, but it is based on improved elements of three- and foursided shape in the plan. Special attention is paid to the consideration of cross-section variability.Results. The results of testing the developed elements are presented and the advantages of their use in the practice of design and calculation of structures are shown.Conclusion. The developed PRINCE software package can be useful in the design and calculation of structures containing plates of variable thicknesses.

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Objectives. The need to ensure the reliable functioning of expensive airfield structures poses great challenges for surveyors, designers, builders and operators of these structures. These tasks are complicated by the continuous development of aircraft, an increase in the intensity of their movement, an increase in mass, take-off and landing characteristics of aircraft and the degree of operational impact of aircraft on airfield structures. The aim of the study is the technological solution model proposed by the authors for the carrier layer of artificial runway pavement in the form of a honeycomb structure of closed steel sheets filled with concrete along with a method for assessing the strength and determining the rigidity of its aggregate.Method. A method is proposed for assessing the ultimate strength and determining the real stiffness parameters of structural layers of a runway with a constructive solution to the question of concrete work in cramped conditions (“cage effect”) from the impact of manifold repeated operational aircraft loads. This method is based on the fundamental principles of the deformation theory of reinforced concrete, developed by V.M. Bondarenko and elaborated in relation to the volumetric stress state of reinforced concrete structures in the works by G.A. Geniev, K.L. Surov and V.I. Rimshin.Result. An analytical dependency is obtained for establishing a discrete value, a generalised (integral) parameter of the material deformation of the carrier layer, i.e. the equation of the mechanical state of steel-reinforced concrete in a complex stress state, as well as the repeated application of an operational aircraft load at an arbitrary stress point of the artificial runway pavement taking into account the influence of changes in strength, reinforcement, temperature, humidity and rheological factors.Conclusion. The introduction of new technological principles for reinforcing and concrete laying into the design solutions of the bearing layers of artificial runway pavement allows their bearing capacity and rigidity to be significantly increased due to the redistribution of impact energy and the efficient use of the properties of structural materials during loading.

Objectives To study the problem of determining the degree of stress at the apex of a wedge-shaped area in cases where the sides (or one of them) are covered with a thin flexible coating.Method It is assumed that the coating is not stretchable. On the other side of the wedge-shaped area, the same coating is assumed to be present; it is either fixed, stress-free or in smooth contact with a rigid base. Mathematically, the problem is reduced to the task of determining the roots of characteristic transcendental equations arising from the existence of a nontrivial solution to the system of linear homogeneous equations.Results Values for the specific characteristics of the radial component of a stress tensor are determined for different combinations of boundary conditions and solution angles. In particular, the angles at which the singular behaviour of stresses occurs are determined. The case is considered when a special boundary condition is given on the edge surface, simulating the overlay. Characteristic equations are obtained to determine the index of the degree dependency of the asymptotic solution in its vicinity for four variants of boundary conditions. In two cases, transcendental equations are obtained, which are solved numerically.Conclusion Calculations of the first positive roots of the equations depending on the angle of the edge solution and Poisson's ratio are presented. The values of the angles, at which the singular behaviour of stresses occurs, are determined. In the case of a combination of boundary conditions (III – IV), the singular stress behaviour is observed for the angle ???? = ????/8, while in the case of (III – III) this value is equal to ????/4.

Objective. The purpose of the study is to determine the group of the limiting state according to the condition of loss of stability of the equilibrium form of structures. Method. The study is based on the provisions of the theory of stability of equilibrium states of building structures; branching theory of solutions of nonlinear equations; perturbation method; methods of catastrophe theory.Result. The results of the analysis of the post-critical behavior of structures based on the solution of the problem in higher approximations and from the fundamental provisions of the theory of catastrophes are generalized. It is proved that the study of the stability of equilibrium forms of structures using algebraic means and geometric images of the theory of catastrophes makes it possible to unambiguously determine the type of critical bifurcation points, predict the nature of the behavior of the structure, and determine the limit state group to which the state reached by the structure should be attributed. Conclusion. It seems necessary to rename the ordinal numbers of the types of critical points of bifurcations so that they coincide with the numbers of the groups of limit states corresponding to them.