The article presents a theoretical description and procedure for calculating the three-hinged arch parabolic outline. The technique of creation of the universal program in a computing complex of Mathcad for various options of vertical loading is in detail stated. The method of calculation of a three-hinged statically determined arch is considered in detail. The order of design calculation is given in the article. The technique of the automated creation of diagrams of internal power factors of an arch design is offered. A detailed description and analysis of the design scheme of three-hinged arch is given.

Keywords: three-hinged arch, statically definable arches, arched structures, parabolic outline, diagrams of internal power factor

The simulation variances of the final volume considerably simplifies the solution of certain problems of reliability. The collection of information for aggregates of large volumes is impractical because of the duration and high cost. Therefore, the analysis and calculation are subjected to a representative sample. To move from sample data to finite volume population parameters, an analytical method for determining the Weibull parameters for the population was used. Analysis of the analytical method for determining the parameters of the three-parameter Weibull distribution for the aggregate confirmed the possibility of using the method of modeling statistical data of strength and life of parts and components of machines. The calculations proved that in practice it is possible to use both the value of the shift parameter and the value of the extreme terms of a number of the population.

Keywords: reliability, analytical method, simulation, General population of finite volume, the sample, the Weibull law, strength, resource, detail, Assembly, machine

The possibility of using European standards, manuals and manuals for the calculation of elements of nodes of frame structures according to criteria that have not been reflected in Russian standards today is being considered. Numerical methods have been used to analyze the bearing capacity of frame nodes for various combinations of longitudinal forces and bending moments. The formation of residual plastic deformations in the elements of the nodes of the frame structures is considered. The nodes were calculated using the ANSYS software package, and a comparative analysis of the calculation results according to European and Russian standards was performed based on the results of the calculation. The question is raised about the need for further numerical studies of the work of steel frame assemblies, including the conduct of field tests, as well as the development of new methods for calculating frame assemblies with regard to plastic deformations. As a result of the calculations and calculations, the need to take into account the fatigue survivability of steel frame assemblies is established, which is associated with the probability of the occurrence of full design loads for the design life

Keywords: European standards, calculation of steel elements, nodes of frame structures, bearing capacity, plastic deformations, fatigue survivability, low-cycle design loads, full design load, redistribution of internal forces, flexibility of rigid nodes

The article conducts a study of the stress-strain state of the protective structure, taking into account temperature and radiation effects. Dry protection is a thick-walled cylindrical shell rigidly clamped at the base. The analysis is carried out in axisymmetric formulation. The calculation of the stress-strain state is preceded by the determination of the distribution of physical fields in the thickness of the structure. The stationary temperature field is considered taking into account internal sources of heat release. The diffusion approximation is used to determine the distribution of the neutron fluence. The calculation is performed numerically using the finite element method in the Matlab package. The results are compared with and without induced inhomogeneity. The significant influence of inhomogenity on stresses in the structure is shown. At the same time, taking into account heterogeneity does not lead to a significant change in displacements.

Keywords: thick-walled cylinders, stress-strain state, numerical methods, neutron fluence, temperature field, inhomogeneity, finite element method

The article deals with the principle of emulsion formation in mechanical absorbers, where the working body is presented in the form of a rotating cylinder. The analysis of interaction of liquids in the process of emulsion formation is made. The mutual influence of liquid layers is considered. The estimation of internal and external parameters characterizing the process of emulsion formation is obtained. The study given in the article will help in the preparation of engineering methods for calculating the operating and design parameters of devices.

Keywords: absorber, emulsion layer, viscosity, density, emulsion, surface contact area, energy dissipation, immiscible liquids, rotating cylinder, liquid

This paper deals with the investigation of crack strength of nuclear reactor cooling system wedge valve body. The main fracture mechanics expressions linking stress intensity factor with cracklike defect length are presented in the introduction. Analytical equations for reliability function evaluation are obtained, fracture toughness and stress intensity factor are viewed as Gaussian random values in the second part of the paper. The statistical linearization method is used to determine the distribution parameters (mean value, dispersion). The stress intensity was estimated by the finite element method with the use of SolidWorks Simulation system. Calculations are done for different types of cracks: throughwall, edge and semielliptic. It is shown that the presence of cracklike defects, even of small length, rather reduces the level of reliability function.

Keywords: fracture toughness, stress intensity factor, survival function

The article deals with the issues of dispersion of heterogeneous liquids by spray nozzles in order to divide them into components. The influence of various parameters on the size of the droplets obtained is investigated. For the mathematical description the probabilistic approach is applied, which allows to obtain a differential function of the particle size distribution, which can form the basis of the engineering method of calculation of this class of separators. An expression for determining the average value of the angular velocity of the internal flow is compiled. These dependences allow us to calculate the most probable value of the angular velocity corresponding to the decay of complex drops into secondary ones, which are the drops of the initial liquids.

Keywords: particle, emulsion, non-uniform liquid, droplets, jet, nozzle, velocity, flow, parameter, separator

The article deals with the transition from corrugated plates and shells to smooth structures of equivalent rigidity. An expression for the potential deformation energy of an infinitely small element of an equivalent smooth shell and formulas that establish a connection between internal forces and generalized deformations of a corrugated structure are given. A review of the formulas for the equivalent stiffness of the corrugated shell during bending, presented in the works of various authors, is carried out. In order to select the dependencies that provide the smallest error when replacing the corrugated shell with a smooth one, a numerical experiment is performed in the LIRA finite element complex. A corrugated plate hinged around the contour under the action of a uniformly distributed projective load is considered. The calculation of the structurally orthotropic construction is performed numerically by the finite difference method. It is also established that the monograph of S.G. Lekhnitsky contains an incorrect formula for the moment of inertia of a sinusoidal corrugation.

Keywords: corrugated structures, plates and shells, finite element method, finite difference method, orthotropy, equivalent stiffness

The well-known theoretical and experimental investigations of the stability of thin-sheeted shells of cylindrical storages are analyzed in the article. It was investigated the following problems concerning the stability of the wall of a spiral-bound granary and a cylindrical granary with a smooth wall, compressed by friction forces of the grain and load from the roof; stability of the wall of the cylindrical shell of containers for liquid and bulk materials when creating a prestress in them.

Keywords: stability calculation, wall stability, prestressing, internal lateral pressure, elastic rebound, cylindrical granary, grain friction force, load from the roof

Structurally heterogeneous materials, in particular polycrystalline materials, have wide application in construction and technics. The higher values of local microstress in comparison to the average values of stress lead to the faster exhaustion of bearing capacity and destruction. Therefore, nonuniformity of microstress and microstrain depending on structure, physical and mechanical properties, should be taken in consideration when estimating bearing capacity, especially for the elements of construction with different stress concentrators. On the base of the physico-mechanical model of structurally heterogeneous body stress concentration for small-scale plates , made of polycrystalline materials with hexagonal lattice, with circular holes, at the case of uniaxial stress state, is investigated. It is shown that coefficients of stress concentration depending on anisotropy of elastic properties of polycrystalline materials can take values which considerably differ from values for isotropic body. Physico-mechanical model developed for structurally heterogeneous body allows studying local microstress in the construction elements at various stress states, with different forms and kinds of stress concentrators, which is the subject of the further research

Keywords: stress distribution, structural heterogeneity of the material, polycrystalline metals,microstress and microstrain, stress concentration

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, cylindrical granary, grain friction force, load from the roof

TThe article presents an algorithm for determining deflections in wooden beams of rectangular cross-section, taking into account the long load. The calculation algorithm is based on the proposed approach of D. Arleninov to specify the modulus of elasticity of wood, depending on the level of design stresses in tabular form. The aim of the research is to develop a software – oriented algorithm for calculating deflections of wooden beams under long-term loading. The object of study – a wooden beam of rectangular cross-section, located in a single load; the modulus of elasticity of the material varies both in length and height of the beam, depending on the level of design stresses. The algorithm uses the FEM of a mixed method with a variable length modulus of elasticity. The stiffness characteristics of the cross sections are refined during the calculation by a two-stage algorithm. Examples of the calculation of simply supported beams under various conditions of loading. The results of comparison with the experimental data of other authors indicate the correct operation of the proposed algorithm; the discrepancy between the numerical results and the experimental results is in the range from 0,31% to 11,6 %. This algorithm can also be used to clarify deflections and internal forces in flat statically indeterminate rod systems, whose modulus of elasticity varies depending on the acting stresses

Keywords: finite element of the mixed method, variable modulus of elasticity, deflection of wooden beams, long-term loading

Beams are structural elements subjected to bending loads transverse to their longitudinal axis. For steel beams, which compressed flange is not laterally restrained, checking loss of overall stability is often authoritative in determining their section. In engineering practice are known various approaches to verify the assurance of the steel beam against lateral-torsional buckling. In this article the attention is focused to the methods and their characteristics, described in actual version of the European standard EN1993-1-1.

Keywords: lateral-torsional buckling, steel beams, critical bending force, FEA

The theory of fractals is applicable for creating the real objects and for constructing the independent elements of the framework or the whole structure of the building. Innovative program was developed to research the shaping of the 3D fractal. The object of the study is 3D Mandelbrot fractal. External structures of various powers of 3D fractal were modeled and researched. New terminology has been developed which can be applied to 3D fractals. The power factor shows the ratio of the work of external forces to the total external. The concept of forming 3D fractal can be used in the design of unique buildings and structures.

Keywords: fractal, fractal geometry, Mandelbrot set, volumetric fractal, fractal structure, finite element method.

The problem of the impact of moving cars on the system "road structure – landslide slope"is considered. Adopted spatial continuum computational model. The inertial properties of vehicles and elements of the system "road structure - landslide slope"are taken into account.

Keywords: dynamic model, road construction, landslide slope, finite element method, nonlinear heredity theory, temperature-humidity factor

The article discusses the method for calculating beams with corrugated walls as three-layer structures of equivalent rigidity. The derivation of resolving equations for a one-dimensional finite element of a three-layer beam is given. A hypothesis is introduced that the shelves fully perceive normal stresses, and the wall only works on shear. When obtaining the basic equations, forced deformations are taken into account, which may include creep deformations, temperature deformations, shrinkage deformations, etc. The solution of the test problem for a beam hinged at the ends under the action of a load uniformly distributed over the length is presented. To control the reliability of the results, a finite element analysis was performed in a three-dimensional formulation in the LIRA software package. Shelves of the beam are modeled by flat triangular shell finite elements, and the wall is modeled by rectangular shell FE.

Keywords: corrugated wall beam, three-layer beam, finite element method, equivalent rigidity, stress-strain state

This article presents the basic assumptions and calculation scheme, allowing to obtain an approximate method of calculation of the filler of three-layer structures with a sufficiently large deformability, ie structures, deflections which are comparable to the thickness of the three-layer package as a whole.

Keywords: deformability, load, filler, load, energy, energy-absorbing element, hinge, travel speed, layer, elasticity

In this article, we propose a method for determining the reactive load for an element of the oval rod type with a rectangular or square cross-section, in which the diagrams of the moments of external forces and single loads are rectilinear. In this case, integration can be performed analytically

Keywords: energy-absorbing element, plot, rod, filler, load, beam, hinge, travel speed, layer

The problem of identification of defects in the construction in the form of a wall element is considered. Numerical simulation of the structure is carried out in the Ansys finite element complex. The investigated model of a wall structure has a defect in the form of a through crack, of a certain length. The edges of the cracks do not interact with each other. The excitation of the structure under pulsed loading is considered. Wave field displacements at control points are analyzed. Identified signs of identification of crack-like defect.

Keywords: numerical modeling, wall element, defect, crack, identification, finite element modeling, dynamic analysis, oscillations, displacement wave field

The problem of identification of defects in the construction in the form of a wall element is considered. Numerical simulation of the structure is carried out in the Ansys finite element complex. The investigated model of a wall structure has a defect in the form of a through crack, of a certain length. The edges of the cracks do not interact with each other. The excitation of the structure under pulsed loading is considered. Wave field displacements at control points are analyzed. Identified signs of identification of crack-like defect.

Keywords: numerical modeling, wall element, defect, crack, identification, finite element modeling, dynamic analysis, oscillations, displacement wave field

The purpose of the study is to develop a software – oriented algorithm for calculating flat rod systems with variable length modulus of elasticity. The object of study – a flat rod system, located in a single load, the elements of which are interfaced at the nodes rigidly or pivotally; the shape of the axes and the conditions of the support are set. A special finite element is developed on the basis of the finite element method in the form of a mixed method. To calculate the elements of the response matrix and the vector of freight coefficients, a numerical integration procedure is used. Examples of calculation of cantilever rods in two variants are given: with a variable length modulus of elasticity; and a rod having three, five and seven sections along the length made of different materials. The comparison with the results of other authors is given. A flat frame of four finite elements with variable modulus of elasticity is calculated. The results of solving the examples indicate the correct operation of the proposed algorithm. It is shown that the parameters of the stress-strain state of the structure can be adjusted by changing the properties of the material.

Keywords: mixed method, finite element, variable modulus of elasticity, response matrix

The paper deals with statically determinate and statically indeterminate reinforced beams of a rectangular cross-section of bimodule material loaded with a uniformly distributed load. Since for heterogeneous materials, the elastic modulus for tension and compression are different, the work aimed to study the influence of different boundary conditions in statically indeterminate beams on SSS. It is shown that the magnitude of the maximum normal stresses is less than the stresses found without taking into account the bimodule nature of the beam material, both in statically determinate and in statically indeterminate beams. The maximum normal stress and maximum deflection decrease with the transition to a statically indeterminate beam from a similarly statically determined beam by replacing the supports. The method used in work makes it possible to clarify the calculation of strength and rigidity, taking into account the bimodule nature of the material of the reinforced beams, and also to select the optimal fastening of the beams that ensure the bearing capacity of the structure with material saving.

Keywords: reinforced beam, heterogeneity, bimodule material, stress-strain state, normal stresses, deflection, statically indeterminate scheme, bearing capacity, strength, deformability

The technique of calculating the metal corrugated structures using the finite element method for an axisymmetric load is considered in the article. One-dimensional finite elements in the form of truncated cones are used. Calculations are performed using the program developed by the authors in the Matlab package. An example of calculation of a ground well rigidly clamped in the base under the action of ground pressure is given. The sinusoidal profile of the corrugation is considered. The graphs of changes in bending moments and ring forces are presented. For a smooth shell of the same thickness, the bending moment in the pinch was 30.3% higher compared to the corrugated, and the maximum value of the ring force was 15.7% higher.

Keywords: metal corrugated structures, cylindrical shell, finite element method, axisymmetric problem, soil well, shell theory, edge effect

In this paper, various methods were used to calculate the flexion plate, obtained approximating the function of the deflection plate, numerical values and diagrams of displacements and moments, conclusions are drawn from the results of the methods.

Keywords: plate, approximating function, curvature, energy functionality

dependences of value distribution of hardness of an armature of the class A500C of different diameters are constructed. For determination of the minimum values the method of graphic transition from selective data to set is used. Calculation of the smallest values of hardness using the shift received in the analysis of set is carried out.

Keywords: selection, armature, population of final volume