The study of the problem of fretting damage to a mechanical assembly bolted in three dimensions requires the analysis of stress fields in Cartesian coordinates along the angle and radius of contact pads. It also requires determining the location of the crack initiation and propagation. In this study, we will focus on numerical simulation using ANSYS. The results obtained in the form of nodal solutions show in detail the positions of stress concentrations and the formation of the bolted assembly. The contact surface between plates (or contact elements) is characterized by contact pressure, adhesion and clearance. The results obtained made it possible to determine the stress that caused the initiation and propagation of a crack, as well as the position of the damaged area by fretting.

Keywords: bolt assembly, contact modeling, damage zone, fretting, Ramberg-Osgood law, Von Mises stresses

The article presents an analysis of existing methods for determining the stiffness parameters of bent reinforced concrete elements reinforced with external reinforcement based on carbon fibers. The results of comparing the results of the determination of stiffness by practical methods and laboratory tests are presented. As a result, general conclusions and recommendations were made for further research of this issue, as well as the general parameters of the carbon fiber-based reinforcement system needed to be taken into account.

Keywords: external reinforcement, carbon fiber, reinforcement, restoration

The calculation for progressive collapse with variation and comparison of different scenarios was carried out for the frame of a unique high-rise building of a multifunctional complex. At the first stage, the calculation was performed in a quasi-static formulation, the maximum deflections for two destruction scenarios were determined. The requirements for the state of limited operability in conditions of progressive collapse are completed. At the second stage, the calculation was made in a dynamic formulation. A modal analysis of the frame was previously performed in order to determine the forms of vibrations that will correspond to the expected deformations of the structure in the event of the occurrence and development of the process of progressive collapse. It is established that the maximum deflection of the plate when calculated in a dynamic formulation is 27.6% greater than in a quasi-static one. The residual deflection after the attenuation of the oscillatory process is 4.6% less than in the static calculation. Therefore, the object of study is safe from the point of view of the possibility of an emergency situation, accompanied by partial destruction of load-bearing structures.

Keywords: parametric architecture, evolution of shaping, aerodynamics, finite element method, analytical surfaces

The essence of the proposed is the arrangement of the frame from the channel around the coating beam. At the same time, the frame elements can be subjected to controlled effects, in the form of overvoltage in them, which is realized by specially installed traction brackets. The study of the proposed structural and technological solution, implemented by a channel frame, was carried out using digital technologies based on numerical modeling. In the proposed calculation model, the beam reinforcement area was changed due to the introduction of a reinforcement frame. In the Etabs software package, using the finite element method, transverse forces and moments were calculated in the newly formed system - a beam plus a channel frame. The paper considers the issue of the influence of the frame on the transverse force in the beam. Using the technology of processing large arrays of numbers, a mathematical model of the process was obtained when the beam was reinforced with a channel frame. A consistent analysis of the mathematical model was carried out, which allowed to state the correctness of the decision and assign the design dimensions of the device and its technological parameters.

Keywords: reinforced concrete beam, reinforcement, channel, reinforcement, shear force, load, numerical method, mathematical modeling, numerical modeling, mathematical model, Etabs software package

As part of the optimization of the design solution, studies of a cylindrical rod roof with increased rigidity of the support ribs and taking into account the reinforcement of the system with puffs were carried out. The required distance between the tension elements along the length of the structure is determined and the dimensions and shape of the section of the lower ribs are proposed. An optimality criterion with control parameters has been developed and three standard sizes of rods for the greatest efforts have been taken into account. Internal force factors and node movements with and without reinforcement are obtained. A positive redistribution of efforts on the surface and a decrease in the deformability of the roof were revealed. The dependence of the main geometric parameters on the mass is established.

Keywords: cylindrical rod roof, stiffness of support ribs, reinforcement by tightenings, optimization, forces, displacements, mass

Based on the beginning of the least work, theoretical dependencies were obtained to determine the internal forces in the elements of the combined trussed system. The analysis of the calculation results of a trussed beam with four posts was carried out and the physical side of the phenomenon of bending during the interaction of the main structure of the trussed beam with elements of a multi-post truss was revealed.

Keywords: truss beam, combined system, multi-column truss, relative eccentricity, potential energy

The objective need to improve information security systems in the conditions of information-telecommunication technologies developing is shown. A new area of NP-complete promplems of diophantine analisys is firstly researched, namely Tarry–Escott multigrade diophantine equation systems (MDES) of given dimension and degree. The theorems, that describe parametrical MDES parametric solution properties, required for the development of the algorythm of building of dissymmetric bigram cryptosystem, are given in the article. The author's theorem, which allows to develop information protection system (IPS) mathematical model as a cortege, containing diophantine probleme. A new approach to develop dissymmetric bigram cryptosystem(DBC) on the base of two-parametrical MDES solution, which generalize open key cryptosystem, is considered. Forward and reverse conversions based on parametrical solution are suggested tyo realize on such algorythm. A new concept of equivalence of ordered sets of numbers (parameters) of a given dimension and order is introduced to build DBC mathematical model, using two-parametrical MDES solution. Described mathematical model demonstrates application potential of diophantine equations for IPS with a high degree of reliability.

Keywords: NP-complete probleme, information protection system, symmetric (dissymmetric) cryptosystem, open key cryptosystem, forward and reverse information conversions, Tarry–Escott multigrade diophantine equation system, parametrical solution

Two-stage modeling of a parametric architecture object of a complex parametric architecture are considered in the article. At the first stage it was analyzed the evolution of the formation of an analytical surface obtained by rotating the Lame curve in a plane perpendicular to the axis of rotation. During the investigation were considered changes in the intensity of rounding of the corners of the shape in the horizontal plane. Study of screw parametric surfaces was carried out at the second stage. New forms of a superellipse were developed to solve the problem of determining the surface of an object of parametric architecture that is resistant to aerodynamic impact. Numerical experiment with use of the finite element method in the ANSYS PC allowed to construct a new analytical surface with a different angle of twisting of floor slabs along the height of a unique building. The proposed method of research and application of the possibilities of the evolution of shaping allows to proceed to the modernization of BIM technologies in the design of unique buildings and structures.

Keywords: parametric architecture, evolution of shaping, aerodynamics, finite element method, analytical surfaces

The article considers the possibility of using a new generation of thermal insulation materials in construction. The authors analyze the distinctive features of thermal insulation boards, reveal the advantages and disadvantages of insulation made of extruded polystyrene foam. Based on the analysis, it is concluded that these materials and technologies are a promising alternative to traditional ones.

Keywords: green roofs, thermal insulation, extruded polystyrene foam, fire hazard class, water absorption, biostability, strength, durability

Traditional analytical methods for determining critical forces lead to difficult solutions of transcendental equations, therefore they are not universal and are ineffective for rods with complex design schemes. The proposed numerical-graphical method for determining critical forces, can be easily adapted to complex non-classical problems.

Keywords: Euler problem, rod, critical force, stability, differential equations, boundary conditions, finite difference method, eigenvalues

This article discusses the theoretical order and practical solution of the problem of calculating the transverse vibrations of a thermosetting polymer self-supporting shell pipe " Furanflex».Сalculation scheme with a finite number of degrees of freedom.The pipe is evenly fixed in height.The procedure for creating a universal calculation algorithm for determining the natural frequencies of pipe vibrations is considered in detail.When creating an algorithm and calculating natural frequencies, determining coefficients, plotting plots, the Mathcad software package is used.When creating an algorithm and calculating natural frequencies, determining coefficients, plotting plots, the Mathcad software package is used. The article may be of interest to design engineers, specialists in calculating the dynamics and strength of structures and specialists of heat-generating companies and thermal power plants, teachers and students of universities in the construction industry.

Keywords: eigenvalues, polymer tube "furanflex", eigenvalues of the matrix

The purpose of our work was to search for possible options for the secondary use of destroyed brick buildings and structures. We conducted tests to verify the strength characteristics of bricks taken from the sites of reconstruction and complete demolition of buildings and structures. In the course of which, conclusions were drawn about the possibilities of further use of brick scrap from different places of demolition of building structures.

Keywords: demolition, scrap, building, structure, brick, recycling, testing, strength, recycling, iron concrete

This article discusses the theoretical order and practical solution of the problem of calculating the beam by the initial parameters method using the Mathcad calculation complex. The article describes in Detail and proposes the procedure for creating a universal calculation algorithm and program for any combination of vertical load. . Программа автоматизировано создает эпюры. The program automatically creates diagrams of internal force factors, displacements, rotation angles of beam sections.The article may be of interest to design engineers, specialists in calculating the dynamics and strength of structures, teachers and students of engineering Universities and the construction industry.

Keywords: method of initial parameters, beams, diagrams of internal force factors, beam movement, angles of rotation of sections

When designing joints for flooring with supporting structures of roofs and floors in the form of carbon fiber strips, one of the main tasks is to determine the load acting on the joint. The article discusses the results of the calculated determination of the forces in the elements of the connection of metal beams with the flooring, depending on the value of the initial curvature as standard and over-standard. The research results can be used to design the fastening of steel decks to the load-bearing steel elements of coatings and floors made of composite materials.

Keywords: carbon fiber composite, composite materials, fiber reinforced polymers (FRP), strengthening, initial deflection, metallic structures, reconstruction, structural connections, loads and actions

The stress-strain state of a two-phase body under the action of a load is described using a system of partial differential equations (Lame equations), the analytical solution of which can be obtained for a narrow class of problems. To apply one of the variational methods to solving the generalized Lamé system, a functional is written based on the potential energy of deformations, which allows us to expand the range of tasks for the study of mechanical processes in soil foundations under engineering structures.

Keywords: two-phase body, water-saturated soil base, potential energy of a two-phase body, stress-strain state

The article presents a description of the computational model and the results of modeling the stress-strain condition of cable-stayed structures. The calculations are performed in a geometrically nonlinear formulation.

Keywords: stress-strain condition, cable-stayed structure, geometric nonlinearity, flexible cable system, spatial framed system

The article presents theoretical calculations and studies of the possibility of parametric oscillations and parametric resonance arising in a polymer self-supporting thermoplastic pipe "Furanflex". Тheoretical calculations of the possibility of asymmetric parametric oscillations and parametric resonance are considered.The Furanflex thermoplastic, polymer liner is offered as a variant of a separate gas exhaust trunk during the reconstruction of boiler rooms and thermal power plants by heat generating companies.The description and calculation of resonant phenomena for asymmetric parametric oscillations are described in detail.Detailed mathematical transformations of differential equations of parametric oscillations are given.The article provides a detailed description and analysis of the occurrence of parametric oscillations. Examples of symmetric and asymmetric parametric oscillations are considered.Information and conclusions of the presented work are intended for a different range of readers, teachers, designers, students of construction specialties.This article should be of interest to utility managers and heat generating companies .

Keywords: chimney, ventilation duct, repair, restoration of the chimney,protection of the chimney, lining, furanflex, thermoplastic liner,perimetric oscillation

This work is carried out as part of the study of the frame-rod structure with elements of thin-walled profiles. The results of a numerical study of a three-bolt connection of a thin-walled galvanized plate 1.5 mm thick with a plate of 3 mm thick on adjustable voltage bolts are presented. The calculation models are created by volume elements in Ansys software taking into account the strength properties of materials.

Keywords: galvanized thin-walled profiles, bolted joints, rod structures, thin-walled profiles, finite element method

The calculation algorithm is given and various options for solving the problem are considered when changing the parameters of the design scheme of the rod system on the example of a beam in the MS Excel software environment together with the MathCAD package. The proposed approach allows you to combine formulas, graphics, and calculation results on a single sheet, which is especially useful in the educational process. It contributes to a more conscious perception of the calculation process by students, allows them to implement various forms of distance learning in information technologies.

Keywords: the core of the system, algorithm, modelling, integration, information technology

The article presents theoretical calculations and studies of the possibility of parametric oscillations and parametric resonance arising in a polymer self-supporting thermoplastic pipe "Furanflex". The Furanflex thermoplastic, polymer liner is offered as a variant of a separate gas exhaust trunk during the reconstruction of boiler rooms and thermal power plants by heat generating companies.The article provides a detailed description and analysis of the occurrence of parametric oscillations. Examples of symmetric and asymmetric parametric oscillations are considered.Information and conclusions of the presented work are intended for a different range of readers, teachers, designers, students of construction specialties.This article should be of interest to utility managers and heat generating companies .

Keywords: chimney, ventilation duct, corrosion, repair, restoration of the chimney, condensate,protection of the chimney, lining, furanflex, thermoplastic liner,perimetric oscillation

The article discusses the most common schemes of direct integration of equations of motion in engineering practice, and gives basic formulas. An analysis of the accuracy of these methods is made on the example of solving a test problem

Keywords: structural dynamics, structural mechanics, direct methods for integrating equations of motion, Newmark's method, Habolt's method, Wilson's method

The article is considered the wall stability of a steel cylindrical pre-stressed granary, compressed by the friction forces of grain and shell, taking into consideration the influence of the grain internal pressure, its elastic resistance from the inside and the elastic resistance of the pre-stressed shell outside. In this case, the initial and subcritical deflection of the shell is assumed to be axisymmetric, and the loss of the shell stability occurs with the formation of asymmetric deflection. The given solution of the problem allows to determine the magnitude of the critical efforts taking into consideration the influence of the grain internal pressure, its elastic repulsion, the magnitude of the initial deflections and the ratio of shell dimensions.

Keywords: stability calculation, wall stability, prestressing, internal lateral pressure, elastic rebound

Mathematical models with analytical properties are needed to create modern stabilization systems for various objects and technical systems. This is due to the fact that most of the existing methods for the synthesis of automatic systems are based on mathematical transformations of models of control objects. However, for complex objects and systems, these models are obtained experimentally. Moreover, the experimental data are approximated by various well-known methods. If the dependences are essentially nonlinear in nature, they are approximated by sections. Such a fragmented model as a whole is not analytical, which excludes the use of many well-known methods for the synthesis of nonlinear stabilization systems. In these cases, it is advisable to use the new Cut-Glue approximation method developed at DSTU, which allows one to obtain an analytical model of an object from piecewise approximations. This analytical model allows you to apply the analytical method for the design of quasilinear control systems for nonlinear objects. In this paper the propoused approach is illustrated by example of the design of a nonlinear system for stabilizing the flight altitude of an airship.

Keywords: stabilization system, analytical synthesis, nonlinear control object, mathematical model, quasilinear form, experimental data, fragmentary model, multiplicatively additive approximation

The work of a metal cylindrical mesh shell with support ribs of increased rigidity is investigated. The rational variant of the profile of longitudinal elements is determined and the recommended parameters of the cross-section of the rods in the place of strengthening of the lower faces are proposed. Several approaches to circuit design were tested and cross-sections were calculated for three blocks of design solutions. It is recommended to use the I-beam profile as the optimal option to increase the coefficient of stability of the structure. Due to the increased rigidity of the support ribs, a significant unloading of dangerous areas was obtained and the form of possible deformation of the system was reconstructed. Qualitative regularities of distribution of longitudinal forces and displacements reflecting positive changes of the general state of the grid surface are revealed. The obtained numerical values of the calculated parameters showed the presence of reserves of the bearing capacity of the structure.

Keywords: cylindrical mesh shell, roof, reinforcement, stiffness of supporting ribs, force factor, deformation parameter

Operational characteristics of reinforced concrete bending elements under low-cycle impact are considered. The residual deformations and deflections of partially prestressed structures exposed to repeated static loads are investigated, the dependences for estimating the residual deformations and deflections of partially prestressed structures under the action of low-cycle loads are Given. On the basis of the analysis, the dependence of the relative increase in deflections on the coefficient of partial prestressing with repeated application of static loads was established.

Keywords: partially prestressed elements, repeated loads, residual deformations, non-stressed reinforcement, low-cycle impact, residual deformations and deflections