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Development Trefftz Method for Problems of Nonhomogeneous Media 非均质介质问题的特雷弗兹法发展
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602534
D. B. Volkov-Bogorodskiy
{"title":"Development Trefftz Method for Problems of Nonhomogeneous Media","authors":"D. B. Volkov-Bogorodskiy","doi":"10.1134/s1995080224602534","DOIUrl":"https://doi.org/10.1134/s1995080224602534","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A new scheme for solving problems in the mechanics of structurally nonhomogeneous media is proposed. This scheme is based on dividing of the initial domain into system of subdomain-blocks similar to finite elements and on approximation of the solution in each block by a systems of functions that exactly satisfy the equation and do not assume unlike the finite element method continuity at the block boundaries. This scheme is based on the Papkovich–Neuber analytical representation through the auxiliary potentials, which makes it possible to construct the complete approximation systems in nonhomogeneous media that analytically satisfy the initial equations and contact conditions on the boundaries of inhomogeneities. Also this scheme is based on the generalization of a direct Trefftz method in the system of subdomain-blocks, which approximates the solution in discontinuous energy space. It is shown that generalized Trefftz method has the ability simultaneously with minimizing of the energy functional to stitch together all the necessary quantities at the block boundaries. They are displacements, surface forces and for gradient elasticity models also derivatives and cohesion moments. This ability is achieved solely due to the analytical representation of the used functions. This analytical representation opens up the possibility of construction of finite element approximations for complex nonhomogeneous media on unstructured meshes and inconsistent shape functions, that analytically accurately reproduce the stress state at the vicinity of inclusions and can be considered as a new technology of finite element approximations.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"33 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217034","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}
引用次数: 0
Stationary Modes of Compressible Fluid Flow in a Thermodynamically Consistent Coupled Model 热力学一致耦合模型中可压缩流体流动的静态模式
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602492
N. N. Nazarenko, A. G. Knyazeva
{"title":"Stationary Modes of Compressible Fluid Flow in a Thermodynamically Consistent Coupled Model","authors":"N. N. Nazarenko, A. G. Knyazeva","doi":"10.1134/s1995080224602492","DOIUrl":"https://doi.org/10.1134/s1995080224602492","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Processes of fluid flow in porous media are encountered in various spheres of human activity. The structure of porous media is extremely diverse, and the gases, liquids, mixtures, suspensions, suspensions, etc. moving in them are significantly different in terms of transport and rheological properties. The models used by different authors to describe fluid flows in porous media are also different. In this paper, classical models of filtration theory are supplemented with thermodynamically consistent constitutive relations that take into account the phenomenon of barodiffusion and an example of a coupled two-dimensional model that takes into account the pressure change associated with the redistribution of impurities due to different transport phenomena is presented. Different flow regimes in a flat layer with asymmetric inlet and outlet are demonstrated.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"297 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217036","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}
引用次数: 0
Numerical Analysis of Gas Well Test Results in Naturally Fractured Reservoirs 天然裂缝储层气井测试结果的数值分析
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602352
M. N. Shamsiev, V. R. Gadil’shina
{"title":"Numerical Analysis of Gas Well Test Results in Naturally Fractured Reservoirs","authors":"M. N. Shamsiev, V. R. Gadil’shina","doi":"10.1134/s1995080224602352","DOIUrl":"https://doi.org/10.1134/s1995080224602352","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, a mathematical model of real gas filtration to a vertical well in naturally fractured reservoir is constructed. The curves of bottomhole pressure and pressure derivative depending on the filtration parameters of the reservoir are analyzed. A method for well test analysis is proposed based on solving an ill-posed inverse problem.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"08 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217095","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}
引用次数: 0
Oscillations of Nanofilms in a Fluid 流体中纳米薄膜的振荡
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602212
M. A. Ilgamov
{"title":"Oscillations of Nanofilms in a Fluid","authors":"M. A. Ilgamov","doi":"10.1134/s1995080224602212","DOIUrl":"https://doi.org/10.1134/s1995080224602212","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Oscillations and waves in a nanofilm in contact with a gaseous medium are considered. It is assumed that the excitation frequencies are in the ultrasonic range. The simplest model is constructed, based on Timoshenko theory of plate bending and on the first approximation of the reaction from the gaseous medium. This takes into account the surface effect caused by the difference in elastic characteristics in the near-surface layer and in the main volume of the material. The derived relations within the Timoshenko model are simplified, which makes it possible to obtain visible results. The contribution of surface effects and reactions from the gaseous medium is assessed. Linear dynamics of a semi-infinite film is studied.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"15 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216915","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}
引用次数: 0
Effect of a Rigid Cone Inserted in a Tube on Resonant Gas Oscillations 插入管中的刚性锥体对共振气体振荡的影响
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602340
L. R. Shaidullin, S. A. Fadeev
{"title":"Effect of a Rigid Cone Inserted in a Tube on Resonant Gas Oscillations","authors":"L. R. Shaidullin, S. A. Fadeev","doi":"10.1134/s1995080224602340","DOIUrl":"https://doi.org/10.1134/s1995080224602340","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Resonant oscillations of gas in a tube with an end in the form of an inverted cone have been investigated. As the height of the inverted cone inserted into the tube increases, a decrease in the resonant frequency and amplitude of gas pressure oscillations is observed. The dispersion of the resonant frequency is due to the viscosity and thermal conductivity of the gas. It is found that tubes with an inverted cone-shaped end are less efficient resonators compared to uniform tubes with a flat closed end. The decrease in the amplitude of gas pressure oscillations is attributed to the increase in the near-wall losses due to the increase in the total sidewall extent.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"17 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216938","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}
引用次数: 0
Mathematical Modeling of Anisotropic Thermal Protection with a High Degree of Longitudinal Anisotropy 具有高度纵向各向异性的各向异性热保护数学模型
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s199508022460256x
V. F. Formalev, B. A. Garibyan
{"title":"Mathematical Modeling of Anisotropic Thermal Protection with a High Degree of Longitudinal Anisotropy","authors":"V. F. Formalev, B. A. Garibyan","doi":"10.1134/s199508022460256x","DOIUrl":"https://doi.org/10.1134/s199508022460256x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this work, based on a new analytical solution to the third initial-boundary value problem of thermal conductivity in an anisotropic strip, an effective method for thermal protection of high-speed aircraft is proposed by channeling heat flows from the central part of the strip to its periphery using an anisotropic material with a high degree of longitudinal anisotropy (longitudinal to transverse thermal conductivity coefficient ratio not less than twenty).</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"57 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216980","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}
引用次数: 0
The Asperities Density and Height Distribution Combined Effect on Rough Elastic Bodies Contact Characteristics 尖晶石密度和高度分布对粗糙弹性体接触特性的综合影响
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602595
I. G. Goryacheva, A. A. Yakovenko
{"title":"The Asperities Density and Height Distribution Combined Effect on Rough Elastic Bodies Contact Characteristics","authors":"I. G. Goryacheva, A. A. Yakovenko","doi":"10.1134/s1995080224602595","DOIUrl":"https://doi.org/10.1134/s1995080224602595","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The combined effect of the asperities density and their height distribution in contact of the rough rigid and smooth elastic half-spaces is investigated, taking into account the mutual influence of contact spots and statistical nature of the height distribution of asperities. The normal and exponential types of the height distribution of asperities with various densities and the dispersions of their height distribution are used in calculations of the contact characteristics at macroscale (the approach of contacting bodies and the relative contact area under given normal pressure) and the microscale (real contact pressure distributions). The obtained results are compared with ones calculated from the simplified models neglecting the mutual influence of individual contact spots. It is shown that neglecting the mutual influence of asperities in contact, which is made in many models of the discrete contact, can lead to significant errors in determining the contact characteristics on both the macro- and microscales. Based on the asymptotic analysis the analytical expressions for the approach of the contacting bodies and the relative contact area were derived and used for analysis of the microgeometry parameters effects on the rigid rough half-space penetration into the elastic half-space at high nominal pressures.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"4 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216982","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}
引用次数: 0
One Problem for the Bessel Equation with a Spectral Parameter in the Boundary Condition 贝塞尔方程的一个问题，边界条件中有一个频谱参数
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s199508022460242x
N. Kapustin, A. Kholomeeva
{"title":"One Problem for the Bessel Equation with a Spectral Parameter in the Boundary Condition","authors":"N. Kapustin, A. Kholomeeva","doi":"10.1134/s199508022460242x","DOIUrl":"https://doi.org/10.1134/s199508022460242x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we consider the spectral problem for the\u0000semi-integer Bessel equation with a boundary condition containing\u0000the square of the spectral parameter and a complex physical\u0000parameter. The system of eigenfunctions of the problem and the\u0000characteristic equation for the eigenvalues are derived. The\u0000equation for multiple roots of the characteristic equation is\u0000derived. The results on the basis properties (Riesz basis) of the\u0000system of eigenfunctions at different values of the parameter are\u0000obtained. For each case a biorthogonally conjugate system is\u0000constructed. At the end of the paper there is an example for the\u0000order of Bessel functions equal to <span>(1/2)</span>.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"161 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216983","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}
引用次数: 0
Theory of Poisson’s Ratio for a Thermoelastic Micropolar Acentric Isotropic Solid 热弹性微极性同心各向同性固体的泊松比理论
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602480
E. V. Murashkin, Y. N. Radayev
{"title":"Theory of Poisson’s Ratio for a Thermoelastic Micropolar Acentric Isotropic Solid","authors":"E. V. Murashkin, Y. N. Radayev","doi":"10.1134/s1995080224602480","DOIUrl":"https://doi.org/10.1134/s1995080224602480","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The present paper deals with the triple weights pseudotensor formulation of multivariant thermoelasticity for acentric isotropic micropolar solids. The fundamental concepts of pseudoinvariant volume/area/arc elements of odd integer weights in three-dimensional spaces are discussed. The developed theory of acentric isotropic micropolar thermoelasticity is formulated in terms of contravariant pseudovector of spinor displacements having positive odd algebraic weight and covariant absolute vector of translational displacements. Three energetic forms (H), (E), and (A) of thermoelasticity potential are proposed. The latter is derived from the irreducible system of algebraic invarinats/pseudoinvariants being actually their linear span with coefficients thus allowing us to introduce the conventional thermoelasticity moduli (shear modulus of elasticity, Poisson’s ratio, characteristic nano/microlength, etc.). For others energetic forms thermoelasticity anisotropic micropolar (E) moduli are determined via (A) moduli and then (H) moduli are found in terms of (A) moduli. The triple weights formulation of multivariant constitutive equations for acentric isotropic thermoelastic solid are obtained and analyzed. A comparison of proposed multivariant constitutive equations elucidates the absolute invariance of Poisson’s ratio, i.e., it insensibility to mirror reflections and prohibition of assigning any algebraic weight to this constitutive scalar.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"20 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217029","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}
引用次数: 0
Dynamics of a Wheel with a Deformable Periphery 外围可变形车轮的动力学特性
IF 0.7
Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602510
V. G. Vil’ke, I. F. Kozhevnikov
{"title":"Dynamics of a Wheel with a Deformable Periphery","authors":"V. G. Vil’ke, I. F. Kozhevnikov","doi":"10.1134/s1995080224602510","DOIUrl":"https://doi.org/10.1134/s1995080224602510","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider a model of a wheel consisting of a disc and a continuous set of rods joined to the disc. The rods are replaced by a continuous set of masses at free ends, joined by springs and dampers (the longitudinal and transverse stiffness of the tread rods) to the wheel disc. The viscous friction acts at the contact points of the rods with the road. The equations of motion of the wheel in the vertical plane are obtained, taking into account the impact phenomena at the boundary points of the contact area. The shape of the deformed periphery, the contact area, the frequencies of rods vibrations in steady-state regime are found. The value of external forces power required to existence of a steady-state regime is determined when wheel translational motion speed and its angular velocity are constant. The wheel vibrations in the vertical plane about the equilibrium position of the loaded wheel are also studied.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"15 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217030","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}
引用次数: 0
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