https://ered.pstu.ru/index.php/mechanics/issue/feedPNRPU Mechanics Bulletin2020-02-05T14:44:45+05:00Dmitry A. Loevetspnrpu.mechanics@gmail.comOpen Journal SystemsPNRPU Mechanics Bulletin | Peer-review academic journalhttps://ered.pstu.ru/index.php/mechanics/article/view/543Dispersion and attenuation of a longitudinal wave propagating in a metamaterial defined as a mass-to-mass chain2020-01-28T14:42:39+05:00V I Erofeev-D A Kolesov-V L Krupenin-We study the features of propagation of a longitudinal wave in an acoustic (mechanical) metamaterial, modeled as a one-dimensional chain, containing equal masses, connected by elastic elements (springs), and having the same rigidity. Each mass contains within itself a series connection of another mass and viscous element (damper). The mass-to-mass model is free from the drawbacks of a number of other mechanical models of metamaterials: i.e. it eliminates the need to have the property of a deformable body to possess a negative mass, density, and (or) a negative elastic modulus. It is shown that the model under consideration makes it possible to describe the dispersion and frequency-dependent attenuation of a longitudinal wave, the character of which essentially depends on the ratio of the external and internal mass of the metamaterial. The behavior of the phase and group velocities of the wave is studied, as well as the evolution of its profile, both in the low-frequency and high-frequency ranges. The mass ratios were found at which the phase velocity exceeds the group velocity (normal dispersion) in magnitude and those at which the group velocity exceeds the phase velocity (anomalous dispersion) in a wide frequency range. Having the same asymptotic values when the frequency tends to infinity, the phase and group velocities have significant differences in behavior, namely, that the phase velocity is a monotonic function of frequency, and the group velocity has a maximum. In addition, in the region of normal dispersion, the group velocity may be negative, i.e. the so-called “reverse wave” effect is true, when, despite the fact that the phase velocity is directed in the positive direction of the spatial axis, the energy in such a wave is transferred in the negative direction.2019-12-15T00:00:00+05:00Copyright (c) 2019 Erofeev V.I., Kolesov D.A., Krupenin V.L.https://ered.pstu.ru/index.php/mechanics/article/view/544Experimental and theoretical study of mechanical deformation of freezing saturated soil2020-01-28T14:42:40+05:00M S Zhelnin-A E Prokhorov-A A Kostina-O A Plekhov-An intensive development of infrastructure in the far North and application of the artificial ground freezing technology for construction of civil and industrial buildings require an accurate description of frost heave caused by freezing of pore water in soils. It is important to understand this processes at the developing stage for the aim of safety exploitation of constructions. The present work is devoted to an experimental and theoretical study of the frost heave in laboratory samples of water saturated sand. Artificial freezing of the sample is performed in a chest freezer. During freezing measurements of temperature and strain are carried out by a control system consisting of a set of thermocouples and fiber optic sensors based on Bragg gratings. To analyze the obtained experimental data, a thermo-hydro-mechanical model has been developed. Water saturated soil is supposed to be three phase porous media consisting of a drained skeleton, water and ice. The model includes the energy conservation equation, the mass balance equations for moisture and ice content, the equilibrium equation and the constitutive relations taking into account an influence of the phase transition of water on heat and mass transfer and the additional volumetric strain. The numerical solution of the nonlinear partial differential equations of the model is performed by the finite element method. The feature of the model is a possibility to take into account the crystallization kinetics on the frost heave of the freezing saturated soil. As a result of the study, a good qualitative and quantitative agreement between a temperature measurement in the volume of the sample and the results of the simulation has been obtained. A comparison of the fiber-optic sensors readings with the results of the numerical simulation has shown that the calculated values are slightly deviated from the experimental ones. On the basis of the measurements analysis and the numerical results it can be concluded that the frost heave proceeds in a long time after the phase transition starts within the temperature range below the temperature of water freezing.2019-12-15T00:00:00+05:00Copyright (c) 2019 Zhelnin M.S., Prokhorov A.E., Kostina A.A., Plekhov O.A.https://ered.pstu.ru/index.php/mechanics/article/view/545The Torsion Problem of a Cylindrical Solid Taking Into Account the Material Weakening2020-01-28T14:42:40+05:00V E Wildemann-A I Mugatarov-The weakening of the material begins reaching a critical level of stress state, is characterized by a decrease in the level of stress during growing deformations and can develop with an equilibrium accumulation of structural damage. The equilibrium accumulation of damage is possible if the given displacements of the boundary points are provided (that is, with “hard” loading) and if the rigidity of the loading system is sufficient. The design becomes unable to withstand the load only when zones with weakened connections are developed enough. Therefore, taking into account the full deformation diagram in the calculations allows to more accurately determine the load bearing capacity of the design. This paper gives an analytical solution for the problem of a homogeneous cylindrical solid torsion with a circular cross section with its hard loading taking into account the material weakening. Piecewise linear approximations of elastic and elastoplastic medium with a linear weakening at the supercritical deformation stage are considered. The diagrams are plotted regarding stress distribution over the cross section are given; the graphs of the maximum torque value and the extreme value of the relative angle of rotation on the parameters of the deformation diagram. The dependences of the torque on the relative angle of rotation of the sections for the stage of initial supercritical deformation, as well as the stage of supercritical deformation and fracture are determined. The graphs of the dependence of torque on the angle of rotation of the section are given. Reserves of the load bearing capacity of the design are identified. It is noted that taking into account the weakening of the material is expedient in strength calculations and in determination of the system’s safety factor.2019-12-15T00:00:00+05:00Copyright (c) 2019 Wildemann V.E., Mugatarov A.I.https://ered.pstu.ru/index.php/mechanics/article/view/546Nonstationary 1D Dynamics Problems for Heteromodular Elasticity with Piecewise-Linear Approximation of Boundary Conditions2020-01-28T14:42:40+05:00O V Dudko-A A Lapteva-V E Ragozina-The paper provides the investigation of a heteromodular elastic medium under dynamic loading. The heteromodularity (when the stress - strain relation depends on the deformation direction) is a distinctive feature of many natural and structural materials: rocks, porous and cohesive bulk media, fibrous and granular composites, some metal alloys, etc. The fact that the listed materials show the heteromodular property at the stage of elastic deformation should be especially taken into account when solving problems of their shock dynamics. To describe the heteromodular behavior of an elastic medium in terms of small strains we use the physically nonlinear model of V.P. Myasnikov. The accepted assumption about the one-dimensional straining reduces the nonlinear relationship of stresses and small strains to piecewise linear equations. In the case of dynamic shock deformation, the initial nonlinearity of the model is concentrated in the equations which define the velocity of the shock wave abruptly transforming the heteromodular medium from a stretched to a compressed state. In this paper we investigate the processes of generation, motion, and possible interactions of plane one-dimensional deformation waves (including shock ones) in a heteromodular elastic half-space. The points of the half-space boundary undergo one-dimensional motions according to a given non-linear law corresponding to the “stretching-compression” mode. We suggest replacing the nonstationary boundary condition of the problem by its piecewise linear approximation and constructing a connected sequence of analytical solutions with a linear boundary condition at each local time interval. The proposed approach is the basis of the numerical solving algorithm for a boundary value problem with a given nonlinear condition. It is shown that the general solution behind the shock wave consists of several local layers, which number is related to the quantity of nodes in the piecewise linear decomposition of the boundary condition. In these layers, the compression deformation is defined by the relevant part of the boundary condition and simultaneously “stores” information on the preliminary tension, which should be considered an important feature of the heteromodular medium dynamics.2019-12-15T00:00:00+05:00Copyright (c) 2019 Dudko O.V., Lapteva A.A., Ragozina V.E.https://ered.pstu.ru/index.php/mechanics/article/view/547Energy product in a crack-like defect model under loading of mode II type2020-01-28T14:42:41+05:00V V Glagolev-L V Glagolev-A A Markin-The loading of a crack-like defect in mode II is considered. In contrast to the classical representation of a crack in the form of a mathematical cut, the proposed model defines a crack in the form of a physical cut with a characteristic linear size. The mental continuation of a physical cut in a solid forms an interaction layer. It is significant that the stress-strain state of the layer does not introduce a singularity to the crack model. The product of the increment of the specific free energy in the face square element of the layer by the linear size determines its energy product. The object of the study is a double-cantilever sample, and the subject of study is the energy product in the face element of the interaction layer. The external load of the cantilevers leads to their horizontal antisymmetric displacements, which form uniform shear deformations in the interaction layer. From the equilibrium conditions of the cantilevers in the variation form, taking into account the hypothesis of axial deformation homogeneity and their reduction, a system of differential equations is obtained, which relates the stress state in the layer and the cantilevers. The solution of the characteristic equation of the system is investigated for various ratios of layer thickness and cantilevers. It is shown that when the relationship is less than a certain value, depending on the Poisson's ratio, real roots take place. In the framework of the real roots of the characteristic equation, an analytical solution of the problem is obtained. Subject to the neglect of compression cantilevers found a simplified solution. The deformations in the layer are determined taking into account the compression of the consoles and without it. The analysis of the dependence of the energy product on the relationship of the thickness of the layer and cantilevers. It is shown that with a thickness ratio of 10-6 or less, the energy product practically does not change its value. Accounting for the compression of cantilevers gives a difference in the values of the energy product of the order of 20 % in relation to the simplified solution of the problem.2019-12-15T00:00:00+05:00Copyright (c) 2019 Glagolev V.V., Glagolev L.V., Markin A.A.https://ered.pstu.ru/index.php/mechanics/article/view/548About a new approach to calculating spiral clamps2020-01-28T14:42:41+05:00A N Danilin-S I Zhavoronok-L N Rabinsky-The bearing capacity of spiral clamps, which are mounted on wires (cables) for their tension, connection, repair, etc., is studied. The design of spiral clamps is formed from stretched spirals that are wound onto conductors with an interference fit, which makes it possible to obtain tensile connections practically inseparable. The general problem of the interaction of spiral clamps and overhead line conductor layers is formulated. Different asymptotic solutions are given for initial and boundary value problems, and the design parameters of spiral clamps are determined to provide their carrying capacity. A wire layer is represented by the energy approach as an equivalent anisotropic elastic cylindrical shell, and wire construction as a whole is considered as a system of cylindrical shells inserted each other and interacting by forces of pressure and friction. The equivalence of the elastic properties of the shell to the properties of the wire layer is established using energy averaging. The constitutive relations obtained using the Castigliano theorem relate the generalized displacements and the corresponding forces. The matrix in these ratios is a stiffness matrix or flexibility matrix of a spiral wire structure. Such approach allows variety of interaction problems for spiral clamps with conductor layers to be solved, and the force transfer mechanism to be investigated from common positions. Static equations are written from the equilibrium of the elementary shell ring. It is considered that the length of the clamp is so great that the mutual influence of its ends can be neglected; the clamp is modeled as semi-infinite shell. This model allows the different initial and boundary value problems to be formulated, depending on the boundary conditions and clamp mounting methods on a conductor.2019-12-15T00:00:00+05:00Copyright (c) 2019 Danilin A.N., Zhavoronok S.I., Rabinsky L.N.https://ered.pstu.ru/index.php/mechanics/article/view/549Creation and verification of computational models for analysis of the mechanical behaviour of jet engines composite components under high-velocity impact: main problems and basic recommendations2020-01-28T14:42:42+05:00O A Kudryavtsev-M V Zhikharev-N A Olivenko-Currently, modern CAE programs like ANSYS, LS-DYNA, ABAQUS, Simcenter 3D etc. are widely used to develop each engineering product. CAE reduces development costs and speeds up product launches. Computer modelling allows eliminating unsuccessful design options at early design stages and minimising or eliminating critical design changes at the prototype testing stage. Computer simulations are especially needed for the development of high-performance perfection designs like jet engines. The use of composites in the engines requires the availability of appropriate design tools to assess the mechanical behaviour of structural elements made of such materials under operational loads and in an emergency. Predictive modelling of the deformation and fracture of the composite fan blades and fan case subjected to dynamic loading cause considerable interest of engineers. As in the case of simulation of shock loading of metals, a model of a composite material must be verified. However, the problem is that the fibrous composite material itself is already a structure and can be modelled in various ways: without considering the layered structure (homogeneous approach) taking the mesostructure into account (at the ply-level or at the yarn-level) taking the microstructure into account (at the filament level). The requirements for the initial data, the number of parameters determined during the verification process, the complexity of creating geometric models will differ in each case. This paper briefly describes the main approaches to the numerical simulation of composite elements under high-velocity impact loading. The main advantages and disadvantages of these approaches are also considered. On the example of the meso-scale approach, the main parameters of the computational models that affect the results of calculations are shown. Based on the obtained data, the main recommendations were formulated on the validation of meso-scale models of composites.2019-12-15T00:00:00+05:00Copyright (c) 2019 Kudryavtsev O.A., Zhikharev M.V., Olivenko N.A.https://ered.pstu.ru/index.php/mechanics/article/view/550Numerical study of the influence of gaps between tiles and backing type on overall high-velocity impact performance of a ceramic-faced protective structure2020-01-28T14:42:42+05:00O A Kudryavtsev-S B Sapozhnikov-M V Zhikharev-The intelligent design of lightweight, protective systems requires the use of numerical simulations widely to weed unsuccessful tests and minimise the number of expensive experiments. At the same time, it is necessary to have verified numerical models of all materials that are used in a protective structure to obtain adequate numerical simulation results. In this research, the impact performance of the ceramic-faced mosaic panel against the impactor with a complicated structure was studied using numerical simulations in thу commercially available package LS-DYNA. Backing types being considered were Aluminium AA 5083 and Dyneema® HB80 UD composite. A new mesoscale model of 99.5% alumina based on the bonded particle method was calibrated and verified through the comparison with the known experimental data. Further, designs with different configurations of mosaic ceramic layers having hex tiles were studied and compared. The results indicated that even small lateral gaps between ceramic tiles decreased the overall panel performance regardless of both the impact site and a backing type. At the same time, the presence of gaps reduces damages of the ceramic layer and can change the impactor trajectory that can be used in multi-layered structures with distant layers. Thus, it is necessary to find a balance between survivability and mass efficiency for each protective structure.2019-12-15T00:00:00+05:00Copyright (c) 2019 Kudryavtsev O.A., Sapozhnikov S.B., Zhikharev M.V.https://ered.pstu.ru/index.php/mechanics/article/view/551Analysis of models for porosity evolution in reservoir during steam injection2020-01-28T14:42:42+05:00A A Kostina-M S Zhelnin-O A Plekhov-Depletion of traditional hydrocarbon reserves leads to the development of extracting methods for heavy crude oil and bitumen characterized by extremely high viscosity. The most effective technology is the steam-assisted gravity drainage. The aim of this method is to decrease oil viscosity by injection of hot steam into the reservoir. Increase of temperature, pore pressure and change of stress-strain state during this process significantly affect porosity which is the key storage parameter of the reservoir. This work is devoted to the analysis of models for porosity evolution during the steam-assisted gravity drainage process. The authors have developed an original model to describe steam-assisted gravity drainage which includes the mass balance equation for a three-phase flow, the energy balance equation involving latent heat due to vaporization/condensation of water/steam and Darcy’s law for fluid filtration. Numerical implementation of the proposed equations was based on the pressure-saturation algorithm. The results have shown a substantial qualitative and quantitative disagreement between the considered models. Coupling of porosity with volumetric strain leads to the rise of its magnitude. Models relating porosity to pore pressure show simultaneous existence of high-porous (near the injection well) and low-porous (near the production well) areas. In case when porosity is dependent on effective stress a circular area of a compacted soil is formed. Therefore, to obtain a correct estimation of the oil production rate in an arbitrary reservoir it is necessary to define the prevailing mechanism of porosity evolution (volumetric strain, pore pressure or effective stress).2019-12-15T00:00:00+05:00Copyright (c) 2019 Kostina A.A., Zhelnin M.S., Plekhov O.A.https://ered.pstu.ru/index.php/mechanics/article/view/552Numerical modeling of nonlinear dynamic and static compression of the metal mesh2020-01-28T14:42:43+05:00A V Kochetkov-I A Modin-N V Leontev-I A Turigina-E Y Poverennov-Simulation of elastoplastic compression of a symmetric fragment of a bundle of woven steel grids was carried out. The simulation was carried out under static and dynamic loading modes in ANSYS and ANSYS LS-DYNA computing systems. A porous mesh package is formed by overlaying the layers on top of each other while maintaining the directions of wires. Such a packet has a quasiperiodic structure; therefore, a certain symmetric fragment can be distinguished. The compression was carried out by a pair of absolutely rigid plates moving symmetrically towards each other. In the calculations, a multilinear plasticity model with isotropic hardening was used. The diagram of static deformation of the material was used which was obtained experimentally. The calculations were carried out according to the algorithm of a perfect symmetric contact of bodies without friction and with friction. The dynamic loading of a fragment of the mesh packet was carried out at a constant speed. The characteristics of the pulse and the loading rate correspond to those observed in previous experimental studies. The dynamic strain diagram was assumed to be similar to a static one with an increased yield strength. Calculations showed that in all loading modes there is a high level of internal stresses, and complex inhomogeneous stress-strain state. We investigated two factors that could cause differences in the behavior of the curves of deformation of a porous medium - the finite length of the acting pulse and the differences in the dynamic and static compression diagrams of the initial mesh material. The main influence on the dynamic behavior of a fragment of a porous packet of a steel mesh is exerted by the dynamic properties of the wire material. The strain curves of the porous fragment qualitatively change in accordance with the behavior observed in static and dynamic experiments. The final duration of the loading pulse and the friction between the wires for this type of mesh do not have a significant effect. The numerical dependences of the relative area of the normal and lateral through sections of the symmetric fragment of the grid packet on the compression deformation are obtained.2019-12-15T00:00:00+05:00Copyright (c) 2019 Kochetkov A.V., Modin I.A., Leontev N.V., Turigina I.A., Poverennov E.Y.https://ered.pstu.ru/index.php/mechanics/article/view/553Determination of the critical velocity of the fluid flowing in a single-walled carbon nanotubes embedded in a polymer matrix2020-01-28T14:42:43+05:00D S Lolov-Sv V Lilkova-Markova-Since 90’s carbonic nanotubes are broadly used in nanophysics, nanobiology and nanomechanics in nanofluidic devices, nanocontainers for gas storage and nanopipes conveying fluid. They have a perfect hollow cylindrical geometry and superior mechanical strength. The flowing fluid can be water, oil, dynamic flow of methane, ethane and ethylene molecules. The problem of the fluid-structure interaction could be considered in the case of nanoscale. However, the experiments at the nanoscale are difficult and expensive. That is why the continuum elastic models have been used to study the fluid-structure interaction. The carbon nanotubes are considered with Euler- and Timoshenko-beam models. In this paper the dynamic stability of a single-walled carbon nanotube is investigated on the basis of the Euler-beam model and with the employment of the Generalized Differential Quadrature Method. The tube under investigation is assumed hinged at its both ends and is embedded in a polymer matrix. To study the influence of the surrounding elastic medium (for example, a polymer) on the stability of the pipe, an elastic base of Pasternak is introduced. A differential equation is presented that describes the transverse vibrations of a nanotube embedded in a polymer matrix. Dimensionless parameters are introduced. The scheme of Chebycheva-Gauss-Lobato is used for sampling. The coefficients are calculated using Lagrange interpolation functions. A system of homogeneous equations is written in the matrix form. The obtained numerical results are for flowing fluids with different densities. In order to study the effect of the surrounding elastic medium (such as polymer) on the stability of the pipe the Pasternak elastic foundation is introduced. The critical velocities of each type of fluid are determined for different stiffnesses of this matrix. A decrease in the critical speed with the increasing mass ratio has been established.2019-12-15T00:00:00+05:00Copyright (c) 2019 Lolov D.S., Lilkova-Markova S.V.https://ered.pstu.ru/index.php/mechanics/article/view/554Elastoplastic deformation of a rotating hollow cylinder with a rigid casing2020-01-28T14:42:43+05:00A N Prokudin-S V Firsov-A rotating hollow cylinder with fixed ends is considered, the inner surface of which is free of stresses, and the outer one is fixed from radial movements. It is assumed that the cylinder is made of an ideal isotropic elastoplastic material, and the deformations in it are small and represent the sum of elastic and plastic deformations. Stresses are associated with elastic deformations by Hooke's law. Plastic deformations are determined using the Tresca - Saint-Venant condition and the plastic flow rule associated with it. The cylinder rotation speed first monotonically increases to a maximum value, and then decreases to zero. By using the elastic solution, the dependence is found for the critical rotation speed at which the plastic flow begins. It is established that, depending on the thickness of the cylinder and the Poisson's ratio, plastic flow can begin, either on the inner or on the outer surface of the cylinder. In addition, 3 plastic regions appear in the cylinder at the loading stage, and 4 plastic regions appear at the unloading stage. These regions correspond to two faces and two edges of the Treska prism. For each plastic region, an exact analytical solution of the determining system of equations is found. The system of conditions at the boundaries between the regions providing continuity of the obtained solutions throughout the cylinder is given. Two cases are considered, i.e. the case with a plastic flow which starts first on the inner, and then on the outer surface of the cylinder. Analytical expressions are obtained for rotational speeds at which new regions appear. The relationship between the nucleation rates of the secondary and primary plastic flow is established. The value of the maximum rotation speed sufficient for a complete transition of the cylinder to the state of the secondary plastic flow was also found. It has been revealed that the adding of a rigid casing can significantly increase the resource of an exploited part.2019-12-15T00:00:00+05:00Copyright (c) 2019 Prokudin A.N., Firsov S.V.https://ered.pstu.ru/index.php/mechanics/article/view/555Boundary value problems for systems of inhomogeneous polyharmonic equations with applications in the theory of thin shells and plates2020-01-28T14:42:44+05:00E A Mikishanina-A number of problems in the theory of elasticity, the theory of heterogeneous media, the theory of thin shells and plates is reduced to solving boundary value problems for systems of inhomogeneous polyharmonic equations. The paper proposes a numerical algorithm for solving systems of polyharmonic equations of the form in single-connected and multi-connected areas with a piecewise smooth contour with specified boundary conditions. Two cases are considered when the function is a known polyharmonic function and when the function is also the desired polyharmonic function. The boundary conditions can have the form similar to Dirichlet conditions, Neiman conditions, and can have a mixed form when on one part of the boundary conditions of the Dirichlet type are given, and on the other - hand, the conditions of the Neiman type. On the basis of multiple applications of the Laplace operator and the boundary element method, which is based on the green integral identity, the given system is reduced to a system of integral identities. After approximating the boundary by an inscribed n-gon and discretizing the system of integral identities, the latter is reduced to a system of linear algebraic equations, which is conveniently represented as a system of matrix equations. The existence and uniqueness of the solution follows from the existence of a unique solution of a system of linear algebraic equations. Special attention is paid to the application of the algorithm to the solution of problems on the bending of thin plates, and the bending load can be a known function, and can be an unknown polyharmonic function of an arbitrary order with given boundary conditions. The problem of bending a thin plate of elliptic shape with a known load on the surface is solved, as well as the problem of bending a thin square plate with an unknown load, which is the solution of a harmonic equation with given boundary conditions. The level lines are constructed and the forms of curved plates are given.2019-12-15T00:00:00+05:00Copyright (c) 2019 Mikishanina E.A.https://ered.pstu.ru/index.php/mechanics/article/view/556New analytical solutions for vibration problem of thick plates2020-01-28T14:42:44+05:00S O Papkov-Exact solutions for the vibrations and stability problems in the mechanics of solids are sufficiently rare. For rectangular thick plates, exact solutions in the form of trigonometric series were constructed only for the case when all or two opposite sides of the plate are simply-supported. The discussion about the possibility of constructing exact solutions continues to this day. As a rule, an approximate solution is constructed in the analytical form on the basis of a variational approach. It should be noted, that as frequency increases, the number of basic functions involved in the solution also has to be increased, consequently the solutions of such type are inefficient for describing a structural element within the framework of such methods as the Continuous Element method, the Spectral Element method and the Dynamic Stiffness method. In the present research, for the first time, the analytical solutions for the vibration problem of thick orthotropic plates are obtained. The modified trigonometric basis is used to construct the general solution for the free vibration problem of the plate in a series, permitting the derivation of an infinite system of linear algebraic equations. Cases of practically important boundary conditions of completely free sides and fully clamped sides are considered. It should be noted that the presented analytical solutions for FFFF and CCCC boundary allows to completely describe the structural element in the form of a plate by means of a dynamic stiffness matrix and their use for modeling more complex structures, also in the framework of methods such as Continuous Element method, Spectral Element method and Dynamic Stiffness method. The obtained results could also be applied in projecting constructions, in developing new devices and in the optimization of their parametersin projecting of constructions, in developing new devices and in the optimization of their parameters.2019-12-15T00:00:00+05:00Copyright (c) 2019 Papkov S.O.https://ered.pstu.ru/index.php/mechanics/article/view/557Experimental analysis of the effect of discrete aggregate on the bending stability of thin-walled cylindrical shells2020-01-28T14:42:44+05:00M V Petrov-The effect of a discrete aggregate on the bending stability of thin-walled cylindrical shells was studied. The samples for the study were made of aluminum alloy 3004 (temper H19). The samples were cantilevered; a vertical concentrated cross force was applied to its free end. Ten empty samples and ten samples 90% filled with iron powder were tested. The samples were loaded in stages by 10N, and when approaching the moment of buckling the samples were loaded by 1N or less. The force, deflection of the free end of the sample, and axial strain were recorded at each stage of loading. Displacement of the free end of the sample versus cross force diagrams is plotted. The buckling force was determined by the inflection point of the diagrams. The samples lost the stability in elasticity. The diagrams for the empty and filled samples for each series almost coincide until the loss of stability of the empty sample. This means that when the empty sample loses its stability, the buckle directed towards the center line is formed; and for the filled samples, the formation of buckles is prevented by the discrete material, therefore the critical force increased by 18.8%. The influence of discrete aggregate is considered on the basis of approximation [24] for tank trucks manufactured at the enterprise. The critical stress is calculated using the superposition principle, since the stability is lost in the elasticity. The critical stress for the filled tank is determined by the sum of the critical stress for an empty shell with the stresses created by the weight load and the hydrostatic pressure of the discrete filler. The calculation of critical stresses showed that for the pattern samples the influence of discrete filler is 8.3%, and for the full-sized tanks the influence of discrete filler on the value of the critical voltage is significant and amounts to 62%. We studied the effect of various discrete fillers on stability, such as river sand, iron and copper powders at different filling ratios of the samples. Due to an increase in powder density and filling volume, the value of the critical force increased. For the samples filled to 90% with the river sand had the critical force increase by 13.3%, while those filled with the iron powder had their critical force increase by 40.5%, the copper powder samples had an increase of the critical force by 43.1%.2019-12-15T00:00:00+05:00Copyright (c) 2019 Petrov M.V.https://ered.pstu.ru/index.php/mechanics/article/view/558Identification of crack-like defect and investigation of stress concentration in coated bar2020-01-28T14:42:44+05:00B V Sobol-A N Soloviev-E V Rashidova-P V Vasiliev-The first part of this work is devoted to the location of defects in a coated bar and the identification of their geometrical parameters. Using the methods of finite element modeling, ultrasonic non-destructive testing and machine learning technologies (artificial neural networks), the inverse problem of mechanics has been solved. A finite element model of ultrasonic wave propagation in a bar with a coating and an internal defect is constructed. Compared with previous works, the model used PML (Perfectly Matched Layer) structures, which suppress multiple reflections of the probe ultrasound pulse inside the bar and prevent signal noise. Based on the conducted numerical calculations of the finite element model, a data set was constructed. It contains the geometrical parameters of the defect and the corresponding amplitude-time characteristic of the ultrasonic signal. The architecture of a direct propagation neural network has been developed. The neural network was trained on the basis of previously processed data. As a result, on the basis of ultrasound data obtained from the outer surface of the bar, it is possible to restore the values of such defect parameters as depth, length and thickness. At the second stage, analytical-numerical technology for studying the stress intensity factor (SIF) at the crack tip is described using the example of the problem of a longitudinal internal crack of finite length located in an elastic strip reinforced with a thin flexible coating. The solution to this problem is based on the method of integral transformations, which made it possible to reduce it to a singular integral equation of the first kind with a Cauchy kernel, which is solved by the collocation method in the form of expansion in Chebyshev polynomials with a factor that explicitly takes into account a feature in the vicinity of the crack vertices. The latter allows you to directly find the SIF and evaluate the effect on it of various combinations of geometric and physical parameters of the problem.2019-12-15T00:00:00+05:00Copyright (c) 2019 Sobol B.V., Soloviev A.N., Rashidova E.V., Vasiliev P.V.https://ered.pstu.ru/index.php/mechanics/article/view/559Elastoplastic interaction of grains in polycrystalline materials2020-01-28T14:42:45+05:00A A Tashkinov-V E Shavshukov-A new method is developed for solving boundary value problems of elastoplastic deformation of polycrystalline materials based on the field-theoretical approach. The boundary value problem for inhomogeneous global strain fields in differential form is transformed into a system of integral equations for mesostrain tensors in grains. In this approach, strain at any point of any grain represented as a superposition of homogeneous macrostrain and contributions of interactions with strain in given grain and all another grains of polycrystalline body . It is shown that the effects of the interaction of strains in polycrystal grains can be described using tensors of the fourth rank. This tensor has 36 independent components. The interactions are additive in nature, that drastically simplifies the solution of some problems, for example, search for extreme microstructures of a polycrystal in which critical localized phenomena arise, such as nucleation of the first plastic slips occur. Constitutive equations of deformation type are used for whole body and separate grains. A model of elastoplastic deformation of single crystals of grains is constructed. The physical mechanisms of plastic deformation are shifts in slip systems of crystals. General expressions are obtained for calculating the secant modules of single crystals for any multiaxial deformation. To solve systems of integral equations for mesostrains in grains the perturbation theory upon intergrains interaction used. Nonlinear systems of equations for plastic strains are solved by the iteration method. The features of the elastoplastic interaction of grains are theoretically investigated. The intensity of the elastoplastic interaction depends on the deformed state of the grains. For two identical grains, the elastoplastic interaction of the pair is several times more intense than the elastic one. In this case, the effect of plastically deformed grain on elastically deformed grain is much higher than the inverse effect. An increase in the intensity of interaction with the development of plastic deformations leads to the effect of homogenization of mesodeformations. Computational experiments were performed using polycrystalline titanium as an example.2019-12-15T00:00:00+05:00Copyright (c) 2019 Tashkinov A.A., Shavshukov V.E.https://ered.pstu.ru/index.php/mechanics/article/view/560Non-stationary coupled axisymmetric thermoelasticity problem for a rigidly fixed round plate2020-01-28T14:42:45+05:00D A Shlyakhin-Zh M Dauletmuratova-A new closed solution is constructed for the axisymmetric dynamic problem of the classical (CTE) theory of thermoelasticity for a rigidly fixed circular isotropic plate in the case of a temperature change on its face surfaces (boundary conditions of the first kind). The mathematical formulation of the problem under consideration includes linear equations of thermal conductivity and equilibrium in a spatial setting, assuming that their inertial elastic characteristics can be neglected in the structures under study. In constructing a general solution of related non-self-conjugate equations, we use the mathematical apparatus of separation of variables in the form of finite integral transformations i.e. Hankel along the radial coordinate and biorthogonal transformation (FIT) with respect to the axial variable. At each stage of the investigation, a procedure is performed to reduce the boundary conditions to a form that allows the corresponding transformation to be applied. A particular feature of this solution is the application of a FIT based on a multicomponent relation of the eigenvector functions of two homogeneous boundary value problems. An important point in the procedure of the structural algorithm is the separation of the adjoint operator, without which it is impossible to solve non-self-adjoint linear problems of mathematical physics. This transformation is the most effective method for studying similar boundary value problems. The calculated design relationships make it possible to determine the stress-strain state and the character of the distribution of the temperature field in a rigidly fixed circular isotropic plate for an arbitrary external temperature effect with respect to time. Numerical analysis of the strength characteristics of the concrete structure shows that during the period of the unsteady load the maximum values of mechanical stresses are observed. Later, at a constant temperature regime, as a result of heating the entire plate, the displacements increase and the stresses fall.2019-12-15T00:00:00+05:00Copyright (c) 2019 Shlyakhin D.A., Dauletmuratova Z.M.https://ered.pstu.ru/index.php/mechanics/article/view/566In memoriam2020-02-05T14:44:45+05:00Механика Вестник ПНИПУ.pnrpu.mechanics@gmail.com<p class="a"><span style="letter-spacing: .1pt;">18 декабря 2019 года ушел из жизни прекрасный человек и замечательный ученый – профессор Рудольф Алексеевич Васин (род. 11 августа 1937 года). Вся его сознательная жизнь связана с Московским государственным университетом, выпускником которого он стал в 1959 году. После завершения аспирантуры с 1962 года Рудольф Алексеевич пришел в НИИ механики при МГУ, где и работал до своего последнего дня, пройдя путь от младшего да главного научного сотрудника и заведующего лабораторией, от кандидата до доктора физико-математических наук и профессора. Очень быстро Рудольф Алексеевич превратился в ведущего специалиста страны в области механики деформируемого твердого тела, особенно – в экспериментальной механике, где он обладал непререкаемым авторитетом. В связи с этим огромное время ему приходилось тратить на деятельность, отвлекающую от основной научной работы, – на оппонирование огромного числа докторских и кандидатских диссертаций, рецензирование статей в ведущих журналах (вначале – Советского Союза, позднее – России). И к этой работе Рудольф Алексеевич относился чрезвычайно ответственно, можно сказать – истово. Он всегда считал своим долгом «поднимать» молодых исследователей, особенно не имеющих административной поддержки в столичных городах. С большим удовольствием Рудольф Алексеевич приезжал в Пермь, где, по его мнению, сложилась серьезная школа механиков. Несмотря на свою занятость, он без малейших колебаний вошел в состав редколлегии вначале сборника ППИ, а позднее – журнала «Вестник ПНИПУ. Механика», где активно работал более 20 лет.</span></p> <p class="a"><span style="letter-spacing: .1pt;">Особенно следует отметить человеческие качества Рудольфа Алексеевича. В общении его всегда отличала какая-то внутренняя глубокая интеллигентность, деликатность. Будучи человеком чрезвычайно принципиальным (особенно – в вопросах науки и этики) и страстным, он умел так выстроить любой разговор, что даже его идейные противники относились к нему с глубоким уважением.</span></p> <p class="a"><span style="letter-spacing: .1pt;">Память о Рудольфе Алексеевиче навсегда останется с нами. Он всегда будет для нас примером Человека <br />и Ученого.</span></p> <p class="a" style="text-align: right;" align="right"> </p> <p class="a" style="text-align: right;" align="right">Редколлегия журнала «Вестник ПНИПУ. Механика»</p>2020-01-28T14:35:02+05:00Copyright (c) 2020 Вестник ПНИПУ. Механика