Репозитарій ОНУ імені І.І.Мечникова

Перегляд за Автор "Reut, Viktor V."

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A wave field of a semi-strip under a nonstationary load
(2019) Reut, Viktor V.; Vaisfeld, Natalia D.; Zhuravlova, Zinaida Yu.; Реут, Віктор Всеволодович; Вайсфельд, Наталя Данилiвна; Журавльова, Зінаїда Юріївна; Вайсфельд, Наталья Даниловна; Журавлева, Зинаида Юрьевна
The plane problems of elasticity for a semi-strip in a static statement were investigated by many authors. However many unresolved issues remain especially for a dynamic statement of the problem. As for the static statements, for example, the problem for a symmetrically loaded semi-strip fixed by its short edge was reduced to the Fredholm integral equation of the first kind in. The static problem for an elastic semi-strip loaded by its short edge in three configurations was solved in. The solving of the dynamic problems is usually done with the help of Laplace’s transformation. However, the inversion of this transformation is enough complicated, so some authors use a numerical inversion or an asymptotic analysis of the derived solution in the transformation’s domain. The Laplace’s transform was used for the stress state evaluation of an elastic half-strip under a nonstationary load applied to its boundary and the solution is expanded into a Fourier series in. Dynamic stress in an infinite elastic strip, containing two circular cylindrical cavities, of equal radii, were explored under the assumption of plane strain in. In the Laplace’s transform domain, boundary conditions at the plane surfaces and those at the circular cavity were satisfied with the Fourier transformation and the Schmidt method respectively. The application of an asymptotic method for the investigation of the non-stationary stress-deformable state under the impact at the semi-strip’s edge was studied in. The analysis of the solution of the approximate asymptotic equations derived by the symbolic Lurie method and the exact solution in the Fourier-Laplace’s transform domain was conducted there.
An Arbitrary Oriented Crack in the Box Shell
(Birkhlluser Verlag Basel / Switzerland, 2000) Migdalski, V. I.; Reut, Viktor V.; Реут, Віктор Всеволодович
Stresses are considered in the box shell formed by two semi-infinite plates joined at right angles. The plates are similar but their thicknesses are different. The crack is an arbitrarily oriented and goes to the shell’s tip. The edges of the crack are loaded in a plane of box shell’s plate. It has been known that numerical methods of solving of stress state problems in the box shell weakened by a crack coming out on the tip possess bad convergence through the necessity of taking into account real singularities near the crack. The problem is solved on the assumption that the plates have small thickness with respect to the length of crack and this makes possible the consideration of problem in an asymptotical formulation, (see Popov, Reut[4]).
Box-like Shells with Longitudinal Cracks
(2009) Hryshyn, Volodymyr O.; Reut, Viktor V.; Reut, Olena V.; Гришин, Володимир Олексійович; Гришин, Владимир Алексеевич; Реут, Елена Викторовна; Реут, Олена Вiкторiвна; Реут, Віктор Всеволодович
The problem of how to determine the stress state of an infinite boxlike shell of rectangular profile is solved. Two cracks are located on opposite sides of the shell and parallel to its edges. On applying a Fourier transform, the problem can be reduced to a system of two integral equations with respect to jumps at the corner of rotation and normal displacements of the crack edges. The system of integral equations is solved by the method of orthogonal polynomials. Dependence of the stress intensity factor on the length of cracks and the geometrical dimensions of the cross-sections of the shell is demonstrated.
Definition of boundary values of thickness of chrome Coverings of piston rings
(Odessa I.I. Mechnikov National University, 1994) Sokolov, A. D.; Reut, Viktor V.; Shukhat, A. A.; Mil'man, A. L.; Реут, Віктор Всеволодович
An approach to the definition of adhesion and cohesion stresses that appear in a piston ring after chroming and its mounting on the piston, its performance in a motor, and corresponding conditions of the critical thicknesses of the covering on the basis of a representation of the ring as a two-layer beam is described.
Elastic crack-tip stress field in a semi-strip
(2018) Reut, Viktor V.; Vaisfeld, Natalia D.; Zhuravlova, Zinaida Yu.; Вайсфельд, Наталя Данилiвна; Вайсфельд, Наталья Даниловна; Журавлева, Зинаида Юрьевна; Журавльова, Зінаїда Юріївна; Реут, Віктор Всеволодович
In this article the plain elasticity problem for a semi-strip with a transverse crack is investigated in different cases of boundary conditions at the semi-strip’s end. Unlike many works dedicated to this subject, the fixed singularities in the singular integral equation’s kernel are considered. The integral transformations’ method is applied by a generalized scheme to reduce the initial problem to a one-dimensional problem. The one-dimensional problem is formulated as a vector boundary value problem which is solved with the help of matrix differential calculations and Green’s matrix apparatus. The problem is reduced to solve the system of three singular integral equations. Depending on the conditions given on the short edge of the semistrip, the obtained singular integral equation can have one or two fixed singularities. A special method is applied to solve this equation in regard to the singularities existence. Hence, the system of the singular integral equations (SSIE) is solved with the help of the generalized method. The stress intensity factors (SIF) are investigated for different lengths of crack. The novelty of this work is the application of a new approach allowing the consideration of fixed singularities in the problem of a transverse crack in the elastic semi-strip. The comparison of the accuracy of numerical results during the use of different approaches to solve the SSIE is calculated.
Forced Vibrations of a Boxed Shell of Square Cross-Section
(Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2009) Vorobel, Viacheslav M.; Popov, H. Ya.; Reut, Viktor V.; Реут, Віктор Всеволодович
We construct the solution of the problem on the steady-state vibrations of a finite boxed shell of square cross-section with symmetry conditions at the shell ends.We present the dispersion curves, find the natural frequencies, and study the stress distribution in the shell.We obtain a simple formula for the approximate analysis of the shell in the case of low-frequency vibrations on the basis of the expansion of the solution in two small parameters and on the Lagrange interpolation formula.
Forced Vibrations of the Infinite Shell of the Square Cross Section
(2009) Vorobel, Viacheslav M.; Reut, Viktor V.; Реут, Віктор Всеволодович
The problem about steady-state forced vibrations of an infinite shell of the square cross section is investigated. The dispersion curves are given, the resonance frequencies are found. The stress distribution in a construction is investigated. In case of low-frequency vibrations the engineering formula for approximate calculation of the construction is offered. The graph of dependence of a relative accuracy on frequency is given.
Investigation of idealized virus capsid model with the dynamic elasticity apparatus
(2017) Zhuravlova, Zinaida Yu.; Nerukh, Dmitry; Reut, Viktor V.; Vaisfeld, Natalia D.; Вайсфельд, Наталья Даниловна; Вайсфельд, Наталя Данилiвна; Журавльова, Зінаїда Юріївна; Журавлева, Зинаида Юрьевна; Реут, Виктор Всеволодович; Реут, Віктор Всеволодович
The three-dimensional dynamic theory of elasticity is applied to investigate the mechanical properties of virus capsid. The idealized model of the virus is based on the 3D boundary-value problem of mathematical physics formulated in spherical coordinate system for the steady-state oscillation process. The virus is modeled as a hollow elastic sphere filled by acoustic medium and is located in different acoustic medium. The stated boundary-value problem is solved with the help of the integral transform method and method of the discontinuous solutions. As a result, the exact solution of the problem is obtained. The numerical calculations of the virus elastic characteristics are carried out.
Investigation of the stress state of the elastic semi-strip with a transverse crack
(2018) Reut, Viktor V.; Vaisfeld, Natalia D.; Zhuravlova, Zinaida Yu.; Вайсфельд, Наталя Данилiвна; Вайсфельд, Наталья Даниловна; Журавльова, Зінаїда Юріївна; Журавлева, Зинаида Юрьевна; Реут, Віктор Всеволодович
The stress state of the semi-strip with a transverse crack is investigated. The mechanical load is applied to the semi-strip’s short edge. The initial problem is reduced to the one-dimensional vector boundaryvalue problem with the help of the semi-infinite Fourier transformation applied by the generalized scheme. The vector boundary-value problem is solved with the help of the matrix differential calculation apparatus and Green’s matrix-function apparatus. The solving of the problem is reduced to the solving of the system of three singular integral equations (SSIE). First singular equation contains two fixed singularities, so the special method is used for the SSIE’s solving. Stresss intensity factors (SIF) are calculated for the different crack’s length
Investigation of the stress state of the elastic semi-strip with a transverse crack
(2019) Reut, Viktor V.; Vaisfeld, Natalia D.; Zhuravlova, Zinaida Yu.; Вайсфельд, Наталья Даниловна; Вайсфельд, Наталя Данилiвна; Журавлева, Зинаида Юрьевна; Журавльова, Зінаїда Юріївна; Реут, Віктор Всеволодович
The stress state of the semi-strip with a transverse crack is investigated. The mechanical load is applied to the semi-strip’s short edge. The initial problem is reduced to the one-dimensional vector boundary-value problem with the help of the semi-infinite Fourier transformation applied by the generalized scheme. The vector boundary-value problem is solved with the help of the matrix differential calculation apparatus and Green’s matrix-function apparatus. The solving of the problem is reduced to the solving of the system of three singular integral equations (SSIE). First singular equation contains two fixed singularities, so the special method is used for the SSIE’s solving. Stress intensity factors (SIF) are calculated for the different crack’s length.
IV Всесоюзная конференция «Смешанные задачи механики деформируемого тела» (Одесса, 26—28 сентября 1989 г.)
(1990) Попов, Геннадий Яковлевич; Онищук, О. В.; Реут, Виктор Всеволодович; Реут, Віктор Всеволодович; Reut, Viktor V.
Тематика конференции тесно связана с вопросами обеспечения надежности и долговечности машиностроительных конструкций, расчета фундаментов зданий, шахт, крупных гидротехнических сооружений, аэродромных и дорожных покрытий, задачами вибросейсморазведки, теории разрушения, созданием новых прогрессивных технологий и другими вопросами современной техники. Разрабатываемые математические методы исследования указанных проблем могут быть также использованы и в других отраслях науки и народного хозяйства в целом.
Modelling of virus vibration with 3-d dynamic elasticity theory
(2017) Zhuravlova, Zinaida Yu.; Kozachkov, D.; Pliusnov, D.; Radzivil, V.; Reut, Viktor V.; Shpynarov, O.; Tarasova, Elvira; Nerukh, Dmitry; Vaisfeld, Natalia D.; Вайсфельд, Наталя Данилiвна; Вайсфельд, Наталья Даниловна; Журавльова, Зінаїда Юріївна; Журавлева, Зинаида Юрьевна; Реут, Віктор Всеволодович
Elastic properties of virus shells (capsids) are important as they protect the virus genome and play important role in virus internalization (the process of virus entering the cell). These properties can also be measured experimentally by direct deformation of the capsid with a microscope's tip. A 3-D mathematical model of a virus under an external non-stationary load is proposed in this paper. The apparatus of the boundary value problems of mathematical physics was used during modeling. The stated initial boundary value problem of elasticity was solved with the help of the integral transformation method and the method of discontinuous solutions. As a result, the analytical solution of the problem was obtained in Laplace transformation domain. The numerical calculations of the virus elastic characteristics were illustrated for the case of a steady-state oscillation.
Problem of a randomly oriented crack in a box-shaped shell
(Kluwer Academic / Plenum Publishers, 1998) Migdalski, V. I.; Reut, Viktor V.; Реут, Віктор Всеволодович
This paper deals with the stress state of a box-shaped shell formed by two semi-infinite plates joined at a right angle. The plates are homogeneous but have different thicknesses. The shell is weakened by a finite rectilinear crack of unit length which reaches one edge of the shell. The orientation of the crack and the load on its edges are arbitrarily chosen. The problem is solved with the assumption that the thickness of the plates is small compared to the length of the crack, which allows an asymptotic formulation of the problem. The problem is reduced to a special type of Riemannian vector problem in which the stress-intensity factor allows matrix factorization in accordance with Khrapkov's scheme. The asymptotes of the resulting solution and the stress-intensity factor are examined in relation to the thickness of the shell and the angle formed by the crack and the edge of the shell.
The axisymmetric contact interaction of an infinite elastic plate with an absolutely rigid inclusion
(Odessa I.I. Mechnikov National University, 2015) Vaisfeld, Natalia D.; Popov, H. Ya.; Reut, Viktor V.; Вайсфельд, Наталья Даниловна; Вайсфельд, Наталя Данилiвна; Реут, Віктор Всеволодович
In the proposed paper, the analytical solution of the problem on an axisymmetric stress-strength state of an infinite elastic layer (a plate) with an absolutely rigid inclusion, coupled with this plate, is solved. The upper plate plane side is under the axisymmetric compressive load. The bottom side of the plate could be in different conditions with the absolutely rigid base: it can be the conditions of a smooth contact or the conditions of a full adhesion. The integral Weber-type transformation is applied to the axisymmetric Lamé equations for the displacements and stress field construction. It leads to a one-dimensional vector inhomogeneous boundary problem. With the help of this problem solution, after satisfying a boundary condition, the initial problem is reduced by solving an integral singular equation on the finite interval. The equation is solved approximately by the orthogonal polynomial method with the previous extraction of the solution’s singularities on the interval ends.
The stress state of the continuous rectangular plate
(2012) Rogovskiy, Stanislav T.; Reut, Viktor V.; Роговський, Станіслав Т.; Реут, Віктор Всеволодович; Роговский, Станислав Т.
The problems on the continuous plates with the intermediate bearers are often necessary at the calculations of the building structures and constructions’ elements in the mechanical engineering. As it was shown in [1, 2], the problems on the calculations of the plate shells and the folded-plate constructions are reduced to such problems also. The works of many native and foreign scientists are devoted to the calculation of the plates’ stress state. The review of these works one can find in [3-5]. In the proposed article with the help of the integral transformation method [6], and the method of the three moments [7] the influence function is constructed. That allows to consider the more intricate problems on the stress state of the folded-plate constructions. The calculations of the characteristic values (the reactions and the bending moments on the bearers) are shown.
Бесконечно длинная коробчатая оболочка, подкрепленная двумя скрещивающимися жесткими включениями
(2002) Воробель, Вячеслав Михайлович; Реут, Виктор Всеволодович; Реут, Віктор Всеволодович; Reut, Viktor V.
Розглянута коробчаста оболонка, що підкріплена двома прямолінійними абсолютно жорсткими включениями, яю розташоваш на протилежних гранях оболонки: одне - паралельно, інше - перпендикулярно ребрам оболонки. Використовується асимптотичний підхід , який враховує тільки згин пластин, що складають оболонку. За допомогою інтегрального перетворення Фур’є задача зведена до системи двох інтегральних рйвнянь з неперервними ядрами, розв’язок якої шукаеться в классі функцій з неінтегровними особливостями.
Бесконечно длинная коробчатая оболочка, подкрепленная тонким абсолютно жестким включением, параллельным её ребрам
(2000) Воробель, Вячеслав Михайлович; Реут, Виктор Всеволодович; Реут, Віктор Всеволодович; Reut, Viktor V.
Розглядаеться задача про напружено-деформований стан нескінченно довгої коробчастої оболонки прямокутного nepepiзy з тонкостінним прямолінійним абсолютно жорстким включениям, паралельним ребрам оболонки. Використовуеться асимптотичний підхід [1, 2, 12], який дозволяє враховувати тільки згин пластин, які складають оболонку, при дії на оболонку навантаження, перпендикулярного її серединної поверхні. Побудовано графіки залежності осідання включения від зведеної довжини включения.
Введение в численные методы алгебры : Учебное пособие для студентов высших учебных заведений, обучающихся по специальности "Прикладная математика"
(Одеський національний університет імені І. І. Мечникова, 2015) Вербицкий, Виктор Васильевич; Реут, Виктор Всеволодович; Вербіцький, Віктор Васильович; Реут, Віктор Всеволодович; Verbitskyi, Viktor V.; Reut, Viktor V.
В учебном пособии излагаются основные численные методы решения линейных и нелинейных систем уравнений, полной и частичной проблем собственных значений, линейной задачи наименьших квадратов. Для студентов высших учебных заведений, обучающихся по специальности "Прикладная математика".
Введення в чисельнi методи аналiзу i диференцiальних рiвнянь
(Одеський національний університет імені І. І. Мечникова, 2018) Вербiцький, Віктор Васильович; Реут, Віктор Всеволодович; Reut, Viktor V.
У навчальному посiбнику розглядаються питання апроксимацiї функцiї iнтерполяцiйними многочленами та сплайнами. На основi iнтерполянтiв виводяться формули чисельного диференцiювання та iнтегрування. Вивчаються однокроковi i багатокроковi методи розв’язання початкових задач для звичайних диференцiальних рiвнянь. Викладаються чисельнi методи вирiшення крайових задач. Для студентiв вищих навчальних закладiв, що навчаються за спецiальнiстю "Прикладна математика".
Вторая основная задача для бесконечного упругого клина
(2012) Вайсфельд, Наталья Даниловна; Попов, Геннадий Яковлевич; Реут, Виктор Всеволодович; Вайсфельд, Наталя Данилiвна; Попов, Геннадій Якович; Реут, Віктор Всеволодович; Vaisfeld, Natalia D.; Popov, H. Ya.; Reut, Viktor V.
Рассмотрена вторая основная задача для бесконечного упругого клина. Применение интегрального преобразования Меллина приводит к векторной краевой задаче в пространстве трансформант, которая решается методом матричного дифференциального исчисления. Установлен порядок особенности напряжений в острие клина и проведено его сравнение с порядком особенности напряжений, полученных по методу Вильямса. Установлен критерий применимости последнего в случае неоднородных дифференциальных уравнений.

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