Кафедра "Математичне моделювання та інтелектуальні обчислення в інженерії"

Постійне посилання колекціїhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/1366

Офіційний сайт кафедри http://web.kpi.kharkov.ua/dpm

Від 2022 року кафедра має назву "Математичне моделювання та інтелектуальні обчислення в інженерії", первісна назва – "Динаміка та міцність машин".

Iсторія кафедри починається в 1930 році, коли в нашому університеті, що називався тоді Харківський механіко-машинобудівний інститут, була створена спеціальність "Динаміка і міцність машин".

Засновниками спеціальності були видатні вчені: академіки Йоффе Абрам Федорович, Обреїмов Іван Васильович, Синельников Кирило Дмитрович, професор Бабаков Іван Михайлович. В різні роки кафедрою завідували: член-корреспондент АН УРСР Майзель Вениамин Михайлович (1936-1941); академік АН УРСР Філіппов Анатолій Петрович (1948-1960), професор, доктор технічних наук, лауреат Державної премії України Богомолов Сергій Іванович (1960-1991); професор, доктор технічних наук, академік АН вищої школи України Львов Геннадій Іванович (1992-2020). Від 2020 року і по теперішній час завідувач кафедри – лауреат премії Президента України для молодих вчених за видатні досягнення, доцент, кандидат технічних наук Водка Олексій Олександрович.

Кафедра входить до складу Навчально-наукового інституту комп'ютерного моделювання, прикладної фізики та математики Національного технічного університету "Харківський політехнічний інститут". Наукова школа з динаміки і міцності машин, створена в нашому університеті, широко відома у світі.

У складі науково-педагогічного колективу кафедри працюють; 2 доктора технічних наук, 7 кандидатів технічних наук, 1 доктор філософії; 2 співробітника мають звання професора, 5 – доцента.

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Application of computational intelligence methods for the heterogeneous material stress state evaluation
(Національний університет "Одеська політехніка", 2022) Babudzhan, Ruslan A.; Vodka, Oleksii O.; Shapovalova, Mariia I.
The use of surrogate models provides great advantages in working with computer-aided design and 3D modeling systems, which opens up new opportunities for designing complex systems. They also allow us to significantly rationalize the use of computing power in automated systems, for which response time and low energy consumption are critical. This work is devoted to the creation of a surrogate model for approximating the finite element solution of the problem of dispersion–strengthened composite plane sample deformation. An algorithm for constructing a parametric two–dimensional model of a composite is proposed. The calculation model is created using the ANSYS Mechanical computer-aided design and analysis program using the APDL scripting model builder. The parameters of the stress-strain state of the material microstructure are processed using a convolutional neural network. A neural network based on the U–Net architecture of the encoder-decoder type has been created to predict the distribution of equivalent stresses in the material according to the sample geometry and load values. A direct sequence of layers is taken from the specified architecture. To increase the speed and stability of training, the type of part of the convolutional layers has been changed. The architecture of the network consists of serially connected blocks, each of which combines layers such as convolution, normalization, activation, subsampling, and a latent space that connects the encoder and decoder and adds load data. To combine the load vector, such a neural network architecture as a concatenator is created, which additionally includes the Dense, Reshape and Concatenate layers. The model loss function is defined as the root mean square error over all points of the source matrix, which calculates the difference between the actual value of the target variable and the value generated by the surrogate model. Optimization of the loss function is performed using the first–order gradient local optimization method ADAM. The study of the model learning process is illustrated by plots of loss functions and additional metrics. There is a tendency for the indicators to coincide between the training and validation sets, which indicates the generalizing capability of the model. Analyzing the output of the model and the value of the metrics, a conclusion is made about the sufficient quality of the model. However, the values of the network weights after training are still not optimal in terms of minimizing the loss function. And also, to accurately reproduce the solution of the finite element method (FEM), the proposed model is quite simple and requires clarification. The speed comparison of obtaining results by the FEM and using the architecture of the neural network is proposed. The surrogate model is significantly ahead of the FEM and is used to speed up calculations and determine the overall quality of the approximation of problems of mechanics of this type.
Application of machine learning methods for predicting the mechanical behavior of dispersion-strengthened composite material
(ФОП Паляниця В. А., 2022) Babudzhan, Ruslan A.; Vodka, Oleksii O.; Shapovalova, Mariia I.
The work is devoted for creating a model for approximating the solution by the finite element method of the problem of plane deformation of a dispersion-strengthened composite material. An algorithm for constructing a parametric 2-D composite model is proposed. The processing of the parameters of the microstructure material stress-strain state occurs using a convolutional neural network. A surrogate model is used for calculations speed up and determine the overall approximations quality of such type mechanics problems.
Application of nonlinear models for a well-defined description of the dynamics of rotors in magnetic bearings
(Scientific Route, Estonia, 2016) Martynenko, Gennadii
A research report has been submitted. It deals with implementing a method for a mathematical description of the nonlinear dynamics of rotors in magnetic bearings of different types (passive and active). The method is based on Lagrange-Maxwell differential equations in a form similar to that of Routh equations in mechanics. The mathematical models account for such nonlinearities as the nonlinear dependencies of magnetic forces on gaps in passive and active magnetic bearings and on currents in the windings of electromagnets; nonlinearities related to the inductances in coils; the geometric link between the electromagnets in one AMB and the link between all AMBs in one rotor, which results in relatedness of processes in orthogonal directions, and other factors. The suggested approach made it possible to detect and investigate different phenomena in nonlinear rotor dynamics. The method adequacy has been confirmed experimentally on a laboratory setup, which is a prototype of a complete combined magnetic-electromagnetic suspension in small-size rotor machinery. Different variants of linearizing the equations of motion have been considered. They provide for both linearization of restoring magnetic or electromagnetic forces in passive and active magnetic bearings, and exclusion of nonlinear motion equation terms. Calculation results for several linearization variants have been obtained. An appraisal of results identified the drawbacks of linearized mathematical models and allowed drawing a conclusion on the necessity of applying nonlinear models for a well-defined description of the dynamics of rotor systems with magnetic bearings.
The calculation of effective elastic constants in a composite with 3d orthogonal nonwoven fibers
(Томский государственный университет, 2015) Darya zadeh, S.; Lvov, G. I.
The paper is devoted to the research of the effective characteristics of 3D orthogonal nonwoven fibers composites. The results were received via ANSYS software package. In this research a volume element of fibers in cubic unit cell is considered. The effective elastic properties of fiber reinforced composite have been defined by the numerical stress analysis of the unit cell.
Development of a web-application for creating notes and schedules
(Національний технічний університет "Харківський політехнічний інститут", 2018) Chechel, V. M.; Vodka, O. O.
Estimation of residual strength of pipeline's elbow with volumetric corrosion defect, which is developing
(Державний університет "Одеська політехніка", 2017) Larin, O. O.; Potopalska, K. E.
Pipelines are used as one of the most practical and low cost methods for transmission of different liquid petroleum products and gases. Damage on the pipeline is capable to appear during operation due to the accumulation of fatigue and arising of corrosion. The Aim is estimation the residual strength of pipeline's elbow with volumetric surface defect development of which is modeled in time. Deformed state assessment of damaged elbow of pipelines was held in the framework of computer modeling by using finite-element method (FEM). Corrosion damage modeled explicitly as volumetric defect on the outside of the knee pipeline. Based on the results of the study the assessment of the residual strength of pipeline with increasing surface defects in operation from 10 to 45 years has been obtained. Besides, the areas in which there is localization of maximum equivalent stresses and respectively plastic deformation depending on the size of damage were defined. By obtained results may be noted that after 37 years of operation the pipelines with the corresponding defect on surface cannot withstand the maximum load.
Information Technology in the Modeling of Dry Gas Seal for Centrifugal Compressors
(2020) Rozova, Lyudmila; Martynenko, Gennadii
The developed specialized software package for computer modeling of dry gas seals for the rotors of centrifugal compressors is presented. This software package implements the mathematical model that describes improved methodology for seals modeling and solving under steady-state compressor operating conditions. It allows to make a model of working gap between the seal rings, which changes under the influence of gas pressure and temperature. This improved computer modeling can provide the reliable operation of dry gas seals. The developed software package has been tested on real constructions of dry gas seals with different types of groves. The results of test solutions were compared with available in literature and experimental studies.
The interrelated modelling method of the nonlinear dynamics of rigid rotors in passive and active magnetic bearings
(ЧП "Технологический Центр", 2016) Martynenko, Gennadii
A method is suggested for building mathematical models of dynamics of rotors in magnetic bearings of different types (passive and active). It is based on Lagrange-Maxwell differential equations in a form identical to that of Routh equations in mechanics. The expressions for magnetic energy and forces in active magnetic bearings with account for control laws for introducing them into the mathematical models have been found by adapting the analytical method of analysing magnetic circuits. This method is based on building equivalent circuits and using the loop flux method to account for dissipation fluxes and magnetic resistances of AMB magnetic circuit sections and ensure noncriticality of the mathematical model to emergence of "zero" gaps and currents. Besides, the mathematical models account for such nonlinearities as nonlinear dependence of magnetic forces on gaps in passive and active magnetic bearings and on currents in the coils of electromagnets, nonlinearities linked to coil inductance, a geometric link between electromagnets in one AMB and links between all AMB in one rotor, which results, among other factors, in connectedness of processes in orthogonal directions. The method’s validity has been confirmed experimentally by a laboratory setup being a prototype of a complete combined magnetic-electromagnetic suspension in small-size rotor machinery. The suggested approach has helped detect in the system and investigate different nonlinear rotor dynamics phenomena such as super- and subharmonic vibrations with determination of resonance modes.
Kontaktwechselwirkung einer Rohrleitung mit der Reparaturbandage aus einem Kompositwerkstoff
(Springer, 2014) Beschetnikov, Dmitriy A.; Lvov, Gennadiy I.; Naumenko, Konstantin; Sukiasov, Vladimir G.; Altenbach, Holm
In der vorliegenden Arbeit wird die Kontaktaufgabe über die Wechselwirkung einer langen Zylinderschale mit einer koaxialen zylindrischen Bandage aus einem Verbundwerkstoff untersucht. Der Verbundwerkstoff wird als ein homogenes orthotropes Material mit bekannten effektiven elastischen Eigenschaften modelliert. Basierend auf der klassischen Schalentheorie werden die Grundgleichungen für die Kontaktaufgabe sowie allgemeine Lösungen für die Durchbiegungen und Schnittgrößen formuliert. Die unbekannten Integrationskonstanten sowie die Kontaktfläche werden numerisch mit Hilfe des Programmpakets Maple ermittelt. Drei charakteristische Längen der Bandage, bei denen der Übergang von einemKontaktschema der Wechselwirkung zu einem anderen erfolgt, wurden ermittelt. Es wurde festgestellt, dass die Änderung des Innendrucks nicht zum Übergang von einem Kontaktschema zu einem anderen führt. Der Charakter der Kontaktwechselwirkung wird durch geometrische Parameter derVerbindung und elastische Materialeigenschaften der Schale und der Bandage bestimmt.
Linear dynamic properties in curved laminated glasses
(Національний технічний університет "Харківський політехнічний інститут", 2021) Sukhanova, Olha Ihorivna; Larin, Oleksiy Oleksandrovych
The study presents the results of linear dynamics of laminated glass panels with different curvatures. This is an actual task in the field of mechanical engineering, aviation, shipbuilding, energy, architecture, etc. Such composites are durable, easy to care for and have a wide range of design options. The aim of the work is to study the influence of the curvature parameter on the frequencies and modes of composites. The paper considers the linear characteristics for laminated glass with polyvinyl butyral interlayer. The article considers behavior of the triplex and the propagation of elastic waves in the linear state. The paper performs calculations using the finite element method in the framework of modal analysis in a three-dimensional formulation in the framework of a physical linear-elastic formulation. The study uses hexagonal finite element with 8 nodes with 3 degrees of freedom in each. This work model laminated glass with a curvature parameter ranging from 0 mm to 250 mm. The composite consisted of three layers: two glass layers thickness of each was 3 mm, and a polyvinyl butyral interlayer with 0.38 mm thickness. The size of the plates was 500×500 mm. As a boundary condition, the laminate was fixed on two opposite sides. The article performs mesh size convergence analysis. The results of natural frequencies in accordance with the curvature parameter are derived. The graphs of natural vibration modes are also shown, that give a clear view about the state of composites.
The Method of Singular Integral Equation in Problems of Liquid Oscillations in Coaxial Shells
(2019) Usatova, O.; Strelnikova, E.; Rozova, Lyudmila; Naumenko, Y.
The paper deals with problems of free vibrations of an ideal incompressible fluid in coaxial shells of revolution. It is assumed that the motion of the fluid is irrotational that allows us to introduce a velocity potential. In these suppositions the potential is satisfied to the Laplace equation. Boundary conditions are formulated on wetted surfaces of the shells and on a free liquid surface. The non-penetration conditions are applied to the wetted surfaces. On the free surface we consider dynamical and kinematical boundary conditions. The dynamical condition consists in equality of the liquid pressure on the free surface to the atmospheric one. The kinematic condition requires that total time derivative of the free surface elevation will be equal to zero at any instant. Regarding the potential of velocities, a boundary value problem is formulated that is further reduced to an eigenvalue problem. To solve the boundary value problem for the Laplace equation, boundary element methods are used in a direct formulation.
Modernization of an experimental installation and a procedure for investigating the anisotropic viscoelastic properties of composite materials at elevated temperatures
(Інститут проблем машинобудування ім. А. М. Підгорного НАН України, 2018) Martynenko, V. G.; Ulianov, Yu. N.
The paper describes the process of modernizing the existing installation designed for performing long-term tests of steel and aluminum cylindrical specimens for high-temperature creep. The modernization allowed conducting experimental studies of the anisotropic strength and viscoelastic characteristics of planar composite specimens at elevated temperatures. In order to reach the objective set, a scheme for reconstructing the specimen holders in the experimental installation was proposed, as well as the method of fixing them in the installation. The developed, designed and built automatic temperature control block for the electric furnace allowed maintaining elevated temperature with a sufficiently small error during its long use and controlling the heating temperature in a given range, which was necessary for studying the mechanical properties of composite specimens, as well as regulating the heating temperature in a given range. Conducting the experimental study of the instantaneous and long-term mechanical properties demonstrated the effectiveness of the improvements made for the experimental installation, as applied to the realization of such experiments.
Nade mnou hora Ještěd
(Майдан, 2017) Kopecká, Věra
Вірші нової збірки відомої поетки Віри Копецької, автора більше 20 книг, переклав з чеської мови українською та російською Сергій Шелковий, теж автор багатьох книг поезії та перекладів. Книга В. Копецької «Наді мною гора Йештед» склалася водночас і цільною — поєднаною виразною авторською інтонацією, і багатовек- торною — такою, яка лунає на багатьох людських регістрах і покладена на музику трьох неповторних слов’янських мов.
A New Numerical Method for Calculation of Micro- Stress on Unidirectionally Reinforced Plates with Circular Hole In Case of Extension to a Principal Direction
(ORIC Publications, 2014) Darya zadeh, S.; Lvov, G. I.; Daryazadeh, P.
The aim of the present study was to compute the stress concentration in reinforced composite plate with circular hole with respect to the volume ratio of the component materials in composite. The contour of the circular hole and its dependency on the structure of plates were calculated in order to study the behaviors of macro and micro-stresses. The boundary conditions at a large distance from the hole are pressure, uniformly distributed on the plate. Also this problem is analyzed with the finite element method by package ANSYS. The results demonstrated the macro and micro stress and behavior of the orthotropic plate with a circular hole calculated for two different structures.
A new numerical method for determination of effective elastic constants in a composite with 3D orthogonal nonwoven fibers
(НТУ "ХПИ", 2015) Darya zadeh, S.; Lvov, G. I.
A new numerical method for determination of effective elastic constants in a composite with cross-ply fibers
(НТУ "ХПИ", 2014) Darya zadeh, S.; Lvov, G. I.; Kiahosseini, Seyed Rahim
In this paper a composite material with similar cross-ply fibers is considered. Assuming orthotropic structure, theory of elasticity is used for investigating the stress concentration. The effective characteristicsof this composite are studied numerically by using ANSYS software. In this research a volume element of fibers in square array in the coordinate x, y, z and the generalized stress state is considered. In order to investigate the numerical finite element modeling, the modeling of a quarter unit cell is considered. For determining the elasticity coefficients, stress analysis is performed for considered volume with noting to boundary conditions. Effective elasticity and mechanical properties of composite which polymer epoxy is considered as its matrix, are determined theoretically and also by the proposed method in this paper with finite element method. Numerical experiments modeled four cases of uniaxial tension in the directions x, z and shear in the planes xy, yz. Finally, the variations of mechanical properties with respect to fiber-volume fraction are studied. Numerical results are compared with approximate estimates method proposed.
A New Numerical Procedure for Determination of Effective Elastic Constants in Unidirectional Composite Plates
(IAU, Arak Branch, 2016) Darya zadeh, S.; Lvov, G. I.; Tajdari, M.
In this paper a composite plate with similar unidirectional fibers is considered. Assuming orthotropic structure, theory of elasticity is used for investigating the stress concentration. Also, complex variable functions are utilized for solving the plane stress problems. Then the effective characteristics of this plate are studied numerically by using ANSYS software. In this research a volume element of fibers in square array is considered. In order to investigate the numerical finite element modeling, the modeling of a quarter unit cell is considered. For determining the elasticity coefficients, stress analysis is performed for considered volume with noting to boundary conditions. Effective elasticity and mechanical properties of composite which polymer epoxy is considered as its matrix, are determined theoretically and also by the proposed method in this paper with finite element method. Finally, the variations of mechanical properties with respect to fiber-volume fraction are studied.
Nonlinear Dynamics — 2013
(National Technical University "Kharkov Polytechnic Institute", 2013)
The book of Proceedings includes extended abstracts of presentations on the Fourth International conference on nonlinear dynamics.
Nonlinear Dynamics — 2016
(National Technical University "Kharkov Polytechnic Institute", 2016)
The book of Proceedings includes extended abstracts of presentations on 5th International Conference on Nonlinear Dynamics dedicated to 90th anniversary of Academician V. L. Rvachev.
Numerical and experimental investigation of heating processes in rubber-cord composite under cyclic deformation
(Одеський національний політехнічний університет, 2017) Larin, O. O.; Viazovychenko, Y. A.
Composite materials such as elastomers, are widely used in modern engineering. An essential feature of such materials is their viscoelasticity. It’s accompanied with the release of energy as a heat. The self-heating process leads to rising of temperature, which causes the mechanical properties changing. That significantly influences on the strength of designs, accelerates the aging and degradation processes and significantly reduces a design life. Aim deals with the identification of the regularities of thermal state of rubber-cord composites by numerical simulation using data which was obtained experimentally at different conditions of cyclic loading. Numerical modeling of heat-transfer problem was carried out using finite element method; the experimental studies were carried out by using of modern measuring complex INSTRON/E3000. The qualitative and quantitative regularities of hysteresis loops that were formed during cyclic deformation of rubber-cord composite depending on time were obtained during the research. As a result of the numerical simulation of convective heat transfer problem the temperature distribution pattern of the specimen were obtained. Heating curves were also obtained in dependence of temperature on strain amplitudes and the frequency of loading. Comparison of the results that were obtained in the experiment and in numerical simulation shows a good convergence.