PNRPU Mechanics Bulletin最新文献

{"title":"Vibrations of a strip with delamination in the framework of the one-parameter Aifantis model of gradient elasticity theory","authors":"A. Vatulyan, O. V. Yavruyan","doi":"10.15593/perm.mech/2022.3.08","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.3.08","url":null,"abstract":"The problems on in-plane and anti-planar steady-state vibrations of an isotropic elastic strip with delamination at the lower boundary has been investigated. The goal of the study is to analyze the stress-strain state in the crack tips areas and to construct a crack opening function being the main mechanical characteristics in the crack theory problems. The problems under study have been solved in the framework of the nonclassical gradient elasticity theory (GET) on the basis of the one-parameter model proposed by Aifantis. The boundary integral equations (BIE) are obtained with respect to crack opening functions or their derivatives. The analysis of BIEs is carried out, regular and irregular parts are distinguished, the obtained BIEs with singular (e.g., with hypersingular, with cubic singularity) integrals are solved via collocation methods, approximating Chebyshev polynomials, quadrature formulas for singular integrals. For the in-plane problem solution, the simplified Ru-Aifantis method has been applied. The Ru-Aifantis method allows to divide the initial boundary value problem into two sub-problems - the classical linear elasticity theory (LTE) problem and the simplified boundary value problem for finding the gradient solution which includes the solution found via the classical theory. For each of the problems, semi-analytical expressions for the functions of crack opening have been constructed, and the analysis of the stress-strain state in the area of crack tips has been carried out. The problems have also been solved in the case of a crack with small relative length, the analysis of BIE depending on small parameters ratio has been carried out, and explicit expressions for the crack opening functions have been obtained. Numerical calculations have been performed; the applicability conditions for the asymptotic method are determined, and a comparative analysis of the results obtained on the basis of GET and LTE models, depending on the values of the gradient parameter and the delamination length, is realized.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":"77 5-6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41294318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"EVALUATION OF THE DYNAMICS OF ELASTIC PLATE AND LIQUID SECTION DYNAMIC ABSORBER","authors":"","doi":"10.15593/perm.mech/2022.3.06","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.3.06","url":null,"abstract":"","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43759937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Features of diffusion-controlled processes of regulated volumetric synthesis from powder mixtures Ti-Al-Fe-Fe2O3","authors":"","doi":"10.15593/perm.mech/2022.3.13","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.3.13","url":null,"abstract":"Experimentally and theoretically analyzed processes occurring in mixtures of powders Ti-Al-Fe-Fe2O3 during reactive sintering (sintering from chemically interacting components) under controlled heating. As one of the components wastes of steel billets were used. This makes the study relevant. The heating rate was varied. Possible physical and chemical stages, their sequence and the assumed phase composition of the synthesis products were analyzed. Although reactive sintering has attracted considerable interest for the production of composite materials, the regularities established for binary systems cannot be purely transferred to sintering powders of more than two kinds. It is shown that the multistage process results in the formation of sets of nonequilibrium phases of variable composition based on α-titanium solid solution. The structures obtained from powder compositions «Ti+Al+Fe» and «Ti+Al+metal chips» do not differ much from each other, despite the presence of an appreciable share of oxides in the latter. The examples of particular problem solutions which correspond to the possible variants of diffusion interaction in a heterogeneous system are presented. Analytical solutions are obtained in the quasi-stationary approximation. The diffusive nature of changes in the position of interfaces is the same for constant and variable diffusion coefficients. The shape of the refractory reagent particle has little effect on the dynamics of the process. An example of calculating the stresses and strains in a conditional reaction cell when the phases are separated by moving boundaries is given. In the quasi-static approximation, the time for the mechanical part of the problem is a parameter. It is shown that the driving forces of diffusion transfer may be related to local stresses, which, in turn, may be related to changes in composition.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44305418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The method of fictitious discrete models in calculations of composite bodies","authors":"A. Matveev","doi":"10.15593/perm.mech/2022.1.05","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.1.05","url":null,"abstract":"As is known, the calculation of the static strength of elastic composite bodies (CB) is reduced to finding the maximum equivalent stresses for these bodies. The finite element method (FEM) is widely used for the analysis of the stress state of CB. The basic discrete models (BM), which take into account the inhomogeneous structure of bodies in the framework of a micro-approach, have a high dimension. To reduce the dimension of discrete models, multigrid finite elements (MgFE) are effectively used. However, there are BM CB (for example, BM bodies with a micro-homogeneous structure), which have such a high dimension that the implementation of FEM for such BM using MgFE, due to limited computer resources, is difficult. To solve this problem, it is proposed to use fictitious discrete models whose dimensions are less than the dimension of the BM CB. In this paper, we propose a method of fictitious discrete models (MFDM) for calculating the strength of elastic bodies with an inhomogeneous, micro-homogeneous regular structure. The proposed method is implemented using FEM with the use of MgFE and adjusted strength conditions that take into account the error of approximate solutions. The method is based on the position that the solutions that meet the BM CB differ little from the exact ones. The calculation of CB according to MFDM is reduced to the construction and calculation of the strength of fictitious discrete models (FM), which have the following properties. The FM reflects: the shape, characteristic dimensions, attachment, loading and type of the inhomogeneous structure of the CB, and the distribution of elastic modulus corresponding to the BM CB. The FM dimension is less than the BM dimension of the CB. The sequence consisting of FM converges to BM, i.e. the limiting FM coincides with BM. The convergence of such a sequence ensures uniform convergence of the maximum equivalent voltages of the FM to the maximum equivalent voltage of the BM. Two types of FM are considered. The first type of FM consists of scaled discrete models, the second type consists of FM with variable characteristic dimensions. Calculations show that the implementation of FEM for FM using MgFE leads to a large saving of computer resources, which allows the use of MFDM for bodies with a micro-homogeneous regular structure. The calculation of the strength of CB according to MFDM requires times less computer memory than a similar calculation using BM CB, and does not contain a procedure for grinding BM. The use of adjusted strength conditions allows us to use approximate solutions with a large error in the calculations of CB for strength, which leads to an increase in the efficiency of MFDM. The given example of calculating the strength of a beam with an inhomogeneous regular fibrous structure according to MFDM shows its high efficiency.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43054159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite element calculation of an elliptical cylinder in a geometrically nonlinear formulation using the vector form of the interpolation procedure","authors":"Ю.В. Клочков, А.Ш. Джабраилов, Т.Р. Ищанов, С.С. Марченко, А.С. Андреев, М.Ю. Клочков, Yu. V. Klochkov, M. Klochkov, A. Dzhabrailov, T. R. Ishchanov, S. S. Marchenko, A. S. Andreev","doi":"10.15593/perm.mech/2022.1.06","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.1.06","url":null,"abstract":"The article describes the developed algorithm for calculating the strength parameters of a thin shell in the form of an elliptical cylinder, taking into account shear deformations in a geometrically nonlinear setting. The numerical finite element method (FEM) was used as a research tool. An algorithm for the formation of the stiffness matrix and the column of nodal forces at the loading step was developed using two versions of the interpolation procedure. In the first version, the standard for FEM interpolation of individual components of the step vector of displacement and the components of the step vector of the angles of rotation of the normal was implemented through the nodal values of the corresponding components. In the second version, the developed vector form of the interpolation procedure was used, in which the interpolation expression was written directly for the step vector and the step vector of the normal rotation angles. As a result of the implementation of the vector form of the interpolation procedure, alternative standard interpolation expressions containing the parameters of the used curvilinear coordinate system were obtained. The element of discretization of the elliptical cylinder was a four-node fragment of the middle surface with nodal variable parameters in the form of components of the step vector of displacement, their first derivatives, as well as the component of the step vector of the angles of rotation of the normal. On the example of calculating an elliptical cylinder in a geometrically nonlinear formulation, loaded in the middle of the span with a concentrated force, a comparative analysis of two variants of the interpolation procedure was carried out. It was shown that when calculating elliptical cylinders in a curvilinear coordinate system in a geometrically nonlinear formulation, it is necessary to apply the developed vector form of the interpolation procedure. The use of the standard FEM form of interpolation of the unknown unknowns made it possible to obtain correct results only in the case of a circular cylinder.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48350363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ANALYSIS OF THE FORM AND EVOLUTION OF THE SOLID PHASE DURING DIRECTIONAL CRYSTALLIZATION OF NON-FERROUS METALS WITH ELECTROMAGNETIC INFLUENCE BY ULTRASONIC AND TEMPERATURE METHODS","authors":"G. Losev, A. Mamykin","doi":"10.15593/perm.mech/2022.4.15","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.4.15","url":null,"abstract":"The paper is devoted to the experimental study of new mechanisms of controlling the process of directional crystallization of non-ferrous metals. The focus of the study is on the development and testing of measuring techniques applicable both to laboratory modeling and to processes under real operating conditions. The mechanism of controlling the rate and homogeneity of crystallization of a metal melt by changing the phase angles between the supply currents of a traveling magnetic field induction stirrer is proposed. This makes it possible to generate vortex flows of various topologies in the liquid metal, in particular, to change the number of large-scale vortices or to suppress the large-scale flow. It is shown that the hydrodynamic flows have an impact on the crystallization front shape, which allows one to control the homogeneity of metal solidification by changing the characteristics of the power supply of the inductor. It is important to note that a change in the phase angles of the currents while maintaining the supply amplitude does not significantly affect the crystallization rate, which opens up wide possibilities for controlling processes by changing both the current strength and the phase angles. The temperature method for determining the position of the crystallization front was successfully applied and verified by ultrasonic velocimetry measurements. It has been found that, in the presence of developed flows in a liquid medium, thermocouple measurements provide good agreement (up to a few percent) of the measured position and geometric shape of the crystallization front with the ultrasonic measurement data. In the absence of liquid phase stirring, the difference between the thermocouple and ultrasonic measurements increases slightly. Nevertheless, even in this case, the thermocouple method can be used to correctly determine the position and velocity of the crystallization front.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42708105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical modeling of natural vibrations of coaxial shells partially filled with fluid, taking into account the effects on the free surface","authors":"","doi":"10.15593/perm.mech/2022.1.03","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.1.03","url":null,"abstract":"This work is devoted to the numerical analysis of vertical elastic coaxial cylindrical shells completely or partially filled with a quiescent compressible fluid with account for sloshing of its free surface. The problem is solved in the axisymmetric formulation using a semi-analytical version of the finite element method. The fluid medium is described by the wave equation, which together with the conditions prescribed at its boundaries is reduced to the weak form by the Bubnov - Galerkin method. A mathematical formulation of the dynamic problem for thin-walled structures is developed using the variational principle of virtual displacements and linear theory of thin shells based on Kirchhoff - Love hypotheses. The fluid pressure on the walls of the structure is calculated according to Bernoulli's equation. Sloshing modes caused by gravitational effects on free surface of liquid medium are excluded from the resulting system of equations through the use of the iteration dynamic condensation method. The numerical model has been verified by comparing it with the known data for the case of a single shell partially filled with fluid. The influence of the fluid level on the lowest natural frequencies of the system vibrations at different variants of kinematic boundary conditions for shells (rigid clamping at both edges, cantilever support) and different widths of the annular gap between them has been evaluated. It has been found that for the examined configurations, the level of the fluid in the annular channel has a stronger influence on the frequency spectrum compared to the level of fluid in the cavity of the inner shell due to the fact that vibration frequencies change in a wider range.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43759877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"DETERMINATION OF THE CONTACT AREA UNDER CYCLIC LOADING OF CONTACT PAIRS OF ISOTROPIC MATERIALS ON THE BASIS OF 3D SURFACE MICRORELIEF MODELLING","authors":"","doi":"10.15593/perm.mech/2022.4.14","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.4.14","url":null,"abstract":"The parameters of the surface microrelief are paramount in the problems of frictional interaction of parts, the flow of liquid and gas in channels, ensuring the required thermal conditions and the stress-strain state of the structure. The solution of the problem of ensuring the optimal thermal regime for a significant range of technical products often becomes decisive in the design of products operating under conditions of high-intensity heat flows. Transit heat fluxes flowing through the product, as well as heat fluxes from own heat sources, must be either accumulated or removed to the external space. In this case, the directions of the heat flux vectors are determined by the design features of the products, including through various contact connections. Obviously, a reliable determination of the parameters of the contact interaction of product parts is the basis for a reliable analysis of the stress-strain and thermal state of a wide range of structures operating under conditions of high-intensity heat flows. The operational characteristics of the contacting parts of the structure are directly determined by the properties of the contact of the mating surfaces. When solving many problems of thermal, mechanical and electrical contact interaction, surface roughness is a major factor. The processes of friction and wear occur precisely on the actual contact area and depend not only on the properties of the material, but also on the intercontact pressure on this area, since the magnitude of the actual pressure determines the destruction of surface films and the appearance of adhesive bonds in the contact. In the presented work, the change in the actual contact area under cyclic loading of contact pairs of materials based on digital twins of contact surfaces in a wide range of compressive pressures is considered.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44530111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"INFLUENCE OF GEOMETRIC, KINEMATIC, GAS-DYNAMIC PARAMETERS ON ROTOR DYNAMIC STATE TAKING INTO ACCOUNT GAS DYNAMIC FLOW IN LABYRINTH SEALS CLEARANCES","authors":"V. Modorskii, I. Cherepanov, A. Babushkina","doi":"10.15593/perm.mech/2022.4.02","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.4.02","url":null,"abstract":"The present work details a new approach to the study of GTU rotor vibrations, based on the solution of a related dynamic problem for the «gas – dynamic flow – deformable structure» sys-tem. The modern tendency to increase an aggregates power with a simultaneous decrease stiffness results in new phenomenons that affected a rotor vibration state. The compressor rotor model with a labyrinth seal is considered. ANSYS software product is used. The calculations were carried out on a high-performance computer complex PNRPU. The performed calculations showed a qualitative and quantitative effect of a gas-dynamic gap on the rotor dynamics. A 2FSI calculations series was performed to study the influence of geometric, kinematic and gas-dynamic parameters on the rotor dynamic state. A pressure fluctuations spectral analysis in the gas-dynamic gap and displacements has been carried out. The obtained spectrograms pro-cessing it possible to plot amplitudes and frequencies dependences of resonant pressure oscil-lations over an initial pressure in the gas-dynamic gap. It was found that the initial pressure in a gas-dynamic gap has the greatest influence. A rotor and gas oscillations resonant frequency was found, which corresponds to a change in the shaft axis spatial position. The «gas – struc-ture» system resonant frequencies were obtained for models differing in mass and stiffness. A decrease in an elasticity modulus of the structure led to a decrease in the maximum pressure fluctuations amplitude, while a decrease in mass led to its increase. For the base model and the model with lower rigidity, the resonant pressure oscillations frequency depends on the initial pressure value according to a law close to linear, while for the model with a lower mass, the dependence has a pronounced non-linear character.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48516837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"INFLUENCE OF HIGH TEMPERATURE TREATMENT ON THE MECHANICAL CHARACTERISTICS OF CARBON-CARBON COMPOSITE MATERIALS WITHPYROCARBON MATRIX","authors":"","doi":"10.15593/perm.mech/2022.4.01","DOIUrl":"https://doi.org/10.15593/perm.mech/2022.4.01","url":null,"abstract":"Pyrolytic compaction of porous substrates is one of the methods for obtaining carbon-carbon composite materials. When using such materials at high temperatures, for example, as elements of heaters, it is necessary to take into account the effect of high temperatures on their mechanical characteristics. In this work, the influence of high-temperature treatment on me-chanical characteristics was studied and the mechanism of destruction of samples of the mate-rial \"Argolon GR\" produced by JSC \"Composite\" was considered. It is shown that with an in-crease in the processing temperature from 1800 to 2400 °C, the open porosity of the samples increases in proportion to the increase in the number and size of cracks in the samples. The compressive failure stress depends very weakly on temperature, however, the graph of the corresponding dependence clearly shows its slight decrease with an increase in the processing temperature from 2000 to 2400 °C, which corresponds to the accumulation of damage in the material matrix that reduces its strength. Attention is drawn to a significant increase in the ten-sile strength of the material after high-temperature treatment, which is not typical for carbon-carbon composite materials. The dependence of the breaking stress in tension with an increase in the processing temperature for material samples has a pronounced maximum at 2000 °C. The analysis of the change in impact strength, the roughness parameter of the fracture surface of the samples, and the breaking stress in tension showed that the dominant mechanism during fracture is the mechanism of strength increase associated with the violation of the compatibility condition of deformations in the components of the material, while the effect of thermal stress relaxation is very small.","PeriodicalId":38176,"journal":{"name":"PNRPU Mechanics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49117524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}