Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences

The Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences is the periodical scientific edition published by Samara State Technical University since 1996.

For a long time the journal was an edition where the new scientific results of Russian scientific schools had been published. Now the journal is focused on both Russian and foreign scientists, working in the priority research areas of Samara State Technical University because the main purpose of the journal is an open dissemination of scientific knowledge among Russian and foreign scientists.

Since 2011 the journal is a quarterly printed edition (four issues a year); issue size — 200 p.; language of articles — Russian, English. The journal is published in printed and electronic version.

The editorial board takes and estimates the manuscripts irrespective of race, gender, nationality, heritage, citizenship, occupation, employment, residence, political, philosophic, religious and any other views of the author.

The contributed article should be a completed scientific research. It shouldn't have been published, or be in process of publication in other editions.

The manuscript should contain novel scientific results in the priority research areas of Samara State Technical University, including “Differential Equations and Mathematical Physics”, “Mechanics of Solids”, “Mathematical Modeling, Numerical Methods and Software Systems”.

The journal is published at the expense of publisher. All materials are publishing free of charge, the author's fee is not provided. All materials of the electronic version are freely available.

The target audience of the journal are the scientists working in the following areas:

  • “Differential Equations and Mathematical Physics”,
  • “Deformable Solid Body Mechanics”,
  • “Mathematical Modeling, Numerical Methods and Software Systems”.

The journal is included in the Russian Science Citation Index database on the Web of Science platform. The journal is included in VINITI abstracts databases. The issue details are publishing in ULRICH’S Periodical Directory. The journal articles are indexed in Scholar.Google.com, zbMATH, СyberLeninka.ru, Math-Net.ru. The journal is integrated in CrossRef and FundRef search systems.

Current Issue

Vol 27, No 3 (2023)

Differential Equations and Mathematical Physics

Stability and convergence of the locally one-dimensional scheme A. A. Samarskii, approximating the multidimensional integro-differential equation of convection-diffusion with inhomogeneous boundary conditions of the first kind
Beshtokova Z.V.
Abstract

The first initial-boundary value problem for a multidimensional (in space variables) integro-differential equation of convection-diffusion is studied. For an approximate solution of the problem a locally one-dimensional scheme by A. A. Samarskii with order of approximation O(h2+τ) is proposed. The study of the uniqueness and stability of the solution is carried out using the method of energy inequalities. A priori estimates for the solution of a locally one-dimensional difference scheme are obtained, which imply the uniqueness of the solution, the continuous and uniform dependence of the solution on the input data, and the convergence of the solution of the scheme to the solution of the original differential problem at a rate equal to the order of approximation of the difference scheme. For a two-dimensional problem, a numerical solution algorithm is constructed, numerical calculations of test cases are carried out, illustrating the theoretical results obtained in the study.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(3):407-426
pages 407-426 views
Description of the spectrum of one fourth-order operator matrix
Rasulov T.K., Latipov H.M.
Abstract

An operator matrix A of fourth-order is considered. This operator corresponds to the Hamiltonian of a system with non conserved number and at most four particles on a lattice. It is shown that the operator matrix A is unitarily equivalent to the diagonal matrix, the diagonal elements of which are operator matrices of fourth-order. The location of the essential spectrum of the operator A is described, that is, two-particle, three-particle and four-particle branches of the essential spectrum of the operator A are singled out. It is established that the essential spectrum of the operator matrix A consists of the union of closed intervals whose number is not over 14. A Fredholm determinant is constructed such that its set of zeros and the discrete spectrum of the operator matrix A coincide, moreover, it was shown that the number of simple eigenvalues of the operator matrix A lying outside the essential spectrum does not exceed 16.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(3):427-445
pages 427-445 views
On the solvability of a class of nonlinear two-dimensional integral equations Hammerstein–Nemytskii type on the plane
Khachatryan K.A., Petrosyan H.S.
Abstract

We consider a class of nonlinear integral equations with a stochastic and symmetric kernel on the whole line. With certain particular representations of the kernel and nonlinearity, equations of the above character arise in many branches of mathematical natural science. In particular, such equations occur in the theory p-adic strings, in the kinetic theory of gases, in mathematical biology and in the theory of radiative transfer. Constructive existence theorems are proved for non-negative non-trivial and bounded solutions under various restrictions on the function describing the nonlinearity in the equation. Under additional restrictions on the kernel and on the nonlinearity, a uniqueness theorem is also proved in a certain class of bounded and non-negative functions that have a finite limit in ±∞. Specific applied examples of the kernel and non-linearity are given that satisfy all the restrictions of the proven statements.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(3):446-461
pages 446-461 views

Mechanics of Solids

Elastic compound plane with an interfacial absolutely rigid thin inclusion partially detached form the matrix subject to slippage at the ends
Hakobyan V.N., Amirjanyan H.A., Dashtoyan L.L., Sahakyan A.V.
Abstract

This article discusses the stress state of an elastic composite plane with a crack of finite length on the joining line of the half-planes. An absolutely rigid thin inclusion of the same length is indented into one of the edges of an interfacial crack under the action of a concentrated force. It is assumed that for the contacting side of the inclusion, there is adhesion to the matrix in its middle part, and slippage occurs along the edges, which is described by the law of dry friction. The problem is mathematically formulated as a system of singular integral equations. The behavior of the unknown functions in the vicinity of the ends of the inclusion-crack and at the separation points of the adhesion and slip zones is studied. The governing system of integral equations is solved by the method of mechanical quadratures. The laws of distribution of contact stresses, as well as the lengths of the adhesion and slip zones, depending on the coefficient of friction, Poisson's ratios and the ratio of Young's moduli of the materials of half-planes, as well as the inclination angle of the external force, are found.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(3):462-475
pages 462-475 views
The influence of surface plastic hardening on the geometric parameters of circular stress concentrators in plates
Glebov V.E.
Abstract

A methodology for studying the influence of strengthening treatment on the shape of stress concentrators in the form of through circular holes in plates after surface-plastic deformation has been developed.
Two model problems have been considered:
– determination of the geometric configuration of a circular stress concentrator cut in a rectangular plate subjected to prior surface-plastic deformation;
– determination of the geometric configuration of a circular stress concentrator in a circular cylindrical plate whose surface has undergone surface-plastic deformation.
Phenomenological methods for restoring residual stress fields and plastic deformations in plates after the strengthening procedure are presented. Boundary problems of reconstructing the stress-strain state are reduced to well-posed fictitious thermoelasticity problems. The adequacy of the proposed approaches has been illustrated through computational modeling for a rectangular plate made of EP742 alloy and a circular cylindrical plate made of EI698 alloy.
Profiles of the generatrix of the stress concentrators in plates have been obtained. In the case of prior surface-plastic deformation of the upper surface of a square hinged-supported plate with a thickness of 10 mm, the maximum displacement of the generatrix relative to the initial configuration was approximately 4 μm. It has been shown that with a decrease in plate thickness, the maximum displacement of the formation decreases. In the case of surface strengthening of the circular stress concentrator in the cylindrical plate, the maximum displacement of the stress concentrator formation was approximately 1.4 μm for plates supported by hinges and with rigid fixation of the side surface. It has been demonstrated that with a decrease in the radius of the hole, the displacement of the formation increases.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(3):476-490
pages 476-490 views
Numerical solution of the problem of stress-strain state of a surface-hardened prismatic V-notched specimen in elastic and elastoplastic formulations
Radchenko V.P., Shishkin D.M., Saushkin M.N.
Abstract

A method has been developed for solving the problem of calculating the stress-strain state in a surface-hardened prismatic V-notched specimen at different values of the opening angle in both elastic and elastoplastic formulations. The method is based on finite element modeling and the known initial stress-strain state for a smooth hardened specimen. A detailed study was conducted on the influence of the notch opening angle and its depth on the level and distribution of residual stresses from the stress concentrator bottom throughout the thickness of the hardened layer for both formulations of the problem. Based on the calculation data, the feasibility of investigating the problem in the elastoplastic formulation was justified when the notch is located completely or partially in the hardened layer, as the magnitudes of residual stresses in the elastic formulation are physically unrealizable, since their values exceed the material's yield strength several times.
In this case, the error between solutions in the elastic and elastoplastic formulations for residual stresses reaches 100–200 % in the root-mean-square norm, and reaches several hundred percent in the uniform estimate (Chebyshev norm). If the depth of the stress concentrator exceeds the thickness of the hardened layer by more than 1.5 times, the elastic and elastoplastic solutions yield similar results.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(3):491-508
pages 491-508 views
Parametric analysis of the stress-strain and continuity fields at the crack tip under creep regime taking into account the processes of damage accumulation using UMAT
Chapliy D.V., Stepanova L.V., Belova O.N.
Abstract

The subject of this study is the analysis of the stress-strain and continuity fields in the proximal nearness of the crack tip, which is in creep regime conditions with due regard for the accumulation of damage. The aim of the work is to conduct computer finite element modeling of uniaxial stretching of a two-dimensional plate with a central crack under creep conditions and to analyze the continuity field around the crack tip. The Bailey–Norton power law of creep is used in numerical modeling. The simulation was performed in the software multifunctional complex SIMULIA Abaqus. The analysis of the circumferential apportionment of stresses, creep deformations and continuity in the direct of the crack tip is carried out.
The power law of creep with the help of the user procedure UMAT (User Material) of the SIMULIA Abaqus package was supplemented by the kinetic equation of damage accumulation of Kachanov–Rabotnov in a related formulation. The UMAT subroutine has many advantages in predicting material damage and allows you to work with materials that are not in the Abaqus materials library. The UMAT subroutine is called at all points of the material calculation and updates the stresses and state variables depending on the solution to their values at the end of the increment. After that, the updated elements of the Jacobi matrix are calculated.
Stress, strain and continuity distributions under creep conditions are gained, considering the damage accumulation of over time. Angular distributions of continuity, stresses and deformations are constructed using the Matplotlib library over time at various distances from the crack tip. The obtained angular distributions of the stress and strain tensor components are compared when modeling without taking into account damage and when taking into account damage accumulation. It is shown that the presence of damage leads to large values of creep deformations and lower stresses.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(3):509-529
pages 509-529 views

Mathematical Modeling, Numerical Methods and Software Complexes

Inhomogeneous Couette flows for a two-layer fluid
Burmasheva N.V., Larina E.A., Prosviryakov E.Y.
Abstract

The paper presents a new exact solution to the Navier–Stokes equations which describes a steady shearing isothermal flow of an incompressible two-layer fluid stratified in terms of density and/or viscosity, the vertical velocity of the fluid being zero. This exact solution belongs to the class of functions linear in terms of spatial coordinates, and it is an extension of the classical Couette flow in an extended horizontal layer to the case of non-one-dimensional non-uniform flows. The solution constructed for each layer is studied for the ability to describe the appearance of stagnation points in the velocity field and the generation of counterflows. It has been found that the flow of a two-layer fluid is stratified into two zones where the fluid flows in counter directions. It is also shown that the tangential stress tensor components can change their sign.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(3):530-543
pages 530-543 views
Transfer function identification by minimizing the adaptive vs. optimal filter state estimates mismatch
Semushin I.V.
Abstract

The article is concerned with a further development of the Active Principle of parametric system identification in the class of linear, time-invariant, completely observable models. As the identification target model, the optimal Kalman filter (OKF) is designated that is present, no more than conceptually, in the system’s discretely observed response to a training excitation of the white noise type. By modifying the physically given structure into the standard observable model in both the observed response and the Adaptive Kalman Filter (AKF), a so-called Generalized Residual (GR) is constructed equaling the mismatch between the adaptive and the optimal filter state estimates plus an AKF-independent noise component. By virtue of this modification, the GR mean square becomes a new model proximity criterion for these filters. Minimizing this criterion via conventional practical optimization methods produces exactly the same result (AKF = OKF) as would be obtained by minimizing the theoretical criterion being, unfortunately, inaccessible to any AKF numerical optimization methods. The article presents a detailed step-by-step procedure explaining the above solution in terms of a parameterized transfer function. For the sake of clarity and for stimulating real world applications of the approach, the article employs the transfer function model of a twisted-pair line in a typical xDSL system. The implementation challenges of theoretical provisions of the method are discussed. The issue of extending the proposed approach to the problems of identifying linear models for nonlinear systems is outlined in the directions for further research.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(3):544-572
pages 544-572 views
Wind direction stereo sensor for the wind turbine active yaw system
Solomin E.V., Martyanov A.S., Kovalyov A.A., Ryavkin G.N., Osintsev K.V., Bolkov Y.S., Antipin D.S.
Abstract

The traditional approach to the horizontal axis wind turbine yawing process leads to the appearance of a known differential yawing error due to the periodic deflection of the air flow by the rotating blades. To reduce its amplitude, usually recorded by a single weather vane located on the top of the nacelle.
This study proposes a new approach, namely the usage of a complex or “stereo” sensor in the form of two devices symmetrically located on both sides of the nacelle (similar to stereoscopic devices). To prove the effectiveness of the approach, several specific points near the nacelle were selected for subsequent modeling of air flows in ANSYS® CFX software using the k–ε turbulence model based on the Navier–Stokes differential equations. At each point, the average value of the orientation angle error was calculated under the following conditions: different wind speeds, tip speed ratios, and wind direction angles. As a result, two points most suitable for the placement of devices were identified. Also, the advantage of a stereo-panoramic device over a traditional one is clearly shown numerically by the example of a case study with nominal parameters. The Matlab/Simulink analysis showed an increase in wind turbine performance due to improved reliability of wind direction determination when properly positioned wind flow sensors are used.
This article does not give any idea of a sensor design, since any principle can be used to determine the correct wind direction. However, the authors are considering a new “stereo sensor”, which will be studied in more detail in the following articles.

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(3):573-592
pages 573-592 views

Short Communications

The study of the stress-strain state of an elastically supported compressed strip
Minaeva N.V., Gridnev S.Y., Skalko Y.I., Saphronov V.S., Alexandrova E.E.
Abstract

An analysis has been conducted on the continuous dependence of the function describing the behavior of the real structure on the characteristics of initial imperfections. A condition has been obtained, imposed on the parameter of external influence and the stiffness coefficient of the foundation, when that is violated, the shape of the cross-section of the strip will no longer be close to a rectangle, i.e. the strip loses shape stability. During the study, the parameters of external influences remained independent.
The first version of the article was published in Aktual'nye problemy prikladnoi matematiki, informatiki i mekhaniki [Current Problems of Applied Mathematics, Computational Science and Mechanics]. Voronezh, 2022. Pp. 1265–1269. (In Russian)

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2023;27(3):593-601
pages 593-601 views

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