Кафедра "Прикладна математика"
Постійне посилання зібрання
Офіційний сайт кафедри http://web.kpi.kharkov.ua/apm
Від 1981 року кафедра має назву "Прикладна математика", первісна назва – кафедра теоретичної й математичної фізики.
Кафедра теоретичної й математичної фізики була заснована в 1947 році. Організатором і першим завідувачем цієї кафедри був відомий вчений-математик, фахівець із конструктивної теорії функцій, член-кореспондент Української Академії наук Наум Ілліч Ахієзер. У 1970 році кафедра цілком чітко взяла курс на дослідження прикладних питань математики, і ще тоді припускалося перейменування кафедри в кафедру "Прикладна математика".
Кафедра входить до складу Навчально-наукового інституту комп'ютерного моделювання, прикладної фізики та математики Національного технічного університету "Харківський політехнічний інститут".
У складі науково-педагогічного колективу кафедри працюють: 1 доктор технічних наук, 1 доктор фізико-математичних наук, 5 кандидатів технічних наук, 4 кандидата фізико-математичних наук; 2 співробітника мають звання професора, 8 – доцента, 1 – старшого наукового співробітника.
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Перегляд Кафедра "Прикладна математика" за Автор "Burlayenko, V. N."
Результатів на сторінці
Налаштування сортування
Документ Analysis of structural performance of aluminium sandwich plates with foam-filled hexagonal cores(2007) Sadowski, Tomasz; Burlayenko, V. N.Документ Creep damage anisotropy of thinwalled elements structures(IPPT PAN, Poland, 2004) Morachkovsky, O. K.; Burlayenko, V. N.The paper is devoted to the development and theoretical justification of an anisotropy creep damage material model. For the description of initial anisotropy and damage-induced anisotropy the second-order damage tensor has been used. The numerical method of anisotropy creep damage lifetime prediction in thin-walled elements of structures was elaborated on the basis of the proposed model and FE scheme. The results of anisotropy creep damage analysis in models of plates were discussed.Документ FE modeling of delamination growth in interlaminar fracture specimens(Politechnika Lubelska, 2008) Burlayenko, V. N.; Sadowski, TomaszInterlaminar fracture specimens like Double Cantilever Beam (DCB), End Notched Flexural (ENF), Single Leg Bending (SLB) etc. are widely used for studying the interlaminar toughness of composite laminates. The aim of this paper is to analysis delamination specimens within the framework of a meso-level damage modeling of composite laminates. In this case interlaminar interface is assumed as a damageable homogeneous layer between adjacent layers of the specimen bulk material. The degradation of the interlaminar connection can be taken into account by means either of an appropriate damage initiation criterion and damage evolution law or using fracture mechanics approach. Onset and growth of the delamination pre-existing crack in the fracture specimens are simulated by using both modeling possibility within commercial finite element code ABAQUSᵀᴹ. Comparisons between numerical predictions of used different finite element models as well as available experimental data have been performed.Документ FE modeling of dynamics of impact damaged sandwich plates with intermittent CONTACT in detached fragments(Wydawnictwo-Drukarnia Liber Duo s.c., 2010) Burlayenko, V. N.; Sadowski, TomaszДокумент FE-analysis of dynamic creep-damage in thin-walled structures(Springer-Verlag, 2002) Morachkovsky, Oleg; Breslavsky, Dmitry; Burlayenko, V. N.The models for description of creep-damage behaviour in materials and thin shallow shells and plates deforming in conditions of joint action of static and fast cyclic load are given. The properties of the proposed material model were established by comparison of experimental and numerical data. The method for numerical simulation by in-house code of a dynamic creep and long-term strength of shallow shells and plates is created on the basis of the FEM. New laws of dynamic creep influence on stress-strain state, shaping and fracture of thin-walled elements of structures had been established by numerical calculations. With the purpose of verification of the created method of dynamic creep numerical simulation of rectangular plates made of an aluminium alloy were carried in order to verify the method of calculation.Документ Finite element modelling and simulations of sandwich beam dynamics considering crack growth and contact(ARSA Druk i Reklama, Lodz, Poland, 2019) Burlayenko, V. N.Документ Finite-element free vibration and buckling analyses of sandwich plates with honeycomb and foam cores(National Technical University "Kharkov Polytechnic Institute", 2007) Sadowski, Tomasz; Burlayenko, V. N.The free vibration and linear buckling analyses of the sandwich flat panels has been considered. The commercial finite element ABAQUS software was used to calculate natural frequencies and bearing capacities of sandwich plates with honeycomb and foam cores. These problems were analysed to assess the role of the core on the natural frequencies and critical loads of sandwich plates. The calculated for sandwich plates results were compared with those for solid plates having the same weight. According to the comparative results the structural performance of the sandwich plates are discussed.Документ Free vibrations and static analysis of functionally graded sandwich plates with three-dimensional finite elements(2020) Burlayenko, V. N.; Sadowski, TomaszA three-dimensional modelling of free vibrations and static response of functionally graded material (FGM) sandwich plates is presented. Natural frequencies and associated mode shapes as well as displacements and stresses are determined by using the finite element method within the ABAQUSTM code. The three-dimensional (3-D) brick graded finite element is programmed and incorporated into the code via the user-defined material subroutine UMAT. The results of modal and static analyses are demonstrated for square metal-ceramic functionally graded simply supported plates with a power-law through-the-thickness variation of the volume fraction of the ceramic constituent. The through-the-thickness distribution of effective material properties at a point are defined based on the Mori-Tanaka scheme. First, exact values of displacements, stresses and natural frequencies available for FGM sandwich plates in the literature are used to verify the performance and estimate the accuracy of the developed 3-D graded finite element. Then, parametric studies are carried out for the frequency analysis by varying the volume fraction profile and value of the ceramic volume fraction.Документ Influence of Dynamic Loading on Fracture Behaviour of DCB Sandwich Specimen(2019) Burlayenko, V. N.; Sadowski, Tomasz; Pietras, D.Numerical simulations of dynamic fracture behaviour of a double cantilever sandwich beam subjected to uneven bending moments in plane conditions are carried out using the dynamic finite element analyses with the ABAQUSTM code. The strain energy release rate was evaluated by means of the finite element model developed within the two-dimensional (2-D) linear elastodynamic theory. This demonstrates the capability and the reliability of the finite element modelling as an extremely useful numerical tool for solving dynamic fracture mechanics problems. Also, the dynamic behaviour of fracture parameters and interface crack progression is discussed.Документ Influence of geometry, elasticity properties and boundary conditions on the Mode I purity in sandwich composites(2020) Burlayenko, V. N.; Pietras, D.; Sadowski, TomaszThe present work addresses the problem of skin/core debonding in sandwich materials. The main goal is to carry out parametric analyses for studying the influence of various materials, geometrical parameters and boundary conditions of sandwich fracture specimens such as a Single Cantilever Beam and a Double Cantilever Beam on the skin/core opening (KI ) and shearing (KII ) modes. The analyses have been performed by means of fracture mechanics tools implemented into the commercial finite element code ABAQUS™. A two-dimensional model of the fracture specimens has been developed with plane strain finite elements. The dependence of the stress intensity factors in the sandwich specimens on the skin thickness, ratio between the Young’s moduli of the skin and core materials and boundary conditions imposed on the specimens has been examined under quasi-static loading by using the interaction integral method.Документ Linear and non-linear dynamic analyses of sandwich panels with face sheet-tocore debonding(2020) Burlayenko, V. N.; Sadowski, TomaszА survey of recent developments in the dynamic analysis of sandwich panels with face sheet-to-core debonding is presented. The finite element method within the ABAQUSTM code is utilized. The emphasis is directed to the procedures used to elaborate linear and non-linear models and to predict dynamic response of the sandwich panels. Recently developed models are presented, which can be applied for structural health monitoring algorithms of real-scale sandwich panels. First, various popular theories of intact sandwich panels are briefly mentioned and a model is proposed to effectively analyse the modal dynamics of debonded and damaged (due to impact) sandwich panels. The influence of debonding size, form and location, and number of such damage on the modal characteristics of sandwich panels are shown. For nonlinear analysis, models based on implicit and explicit time integration schemes are presented and dynamic response gained with those models are discussed. Finally, questions related to debonding progression at the face sheet-core interface when dynamic loading continues with time are briefly highlighted.Документ Nonlinear fracture dynamics of double cantilever beam sandwich specimens(Sapienza University of Rome, 2019) Burlayenko, V. N.; Sadowski, Tomasz; Dimitrova, SvetlanaA virtual testing of double cantilever beam interlaminar fracture toughness sandwich specimens under different types of dynamic loads and loading rates is considered. The nonlinear dynamic response of those sandwich specimens being fractured during the test is numerically examined using the two-dimensional finite element model within the ABAQUSTM code. The interaction integral method is exploited to extract the dynamic stress intensity factor. Cohesive elements allocated along the face/core interface are used to simulate the dynamic fracturing of the specimens.Документ A numerical analysis of near tip fields in a bending moment-loaded double cantilever sandwich beam fracture specimen(НТУ "ХПІ", 2018) Burlayenko, V. N.; Sadowski, Tomasz; Pietras, DanielThe paper presents an interfacial crack problem adopted for studying fracture toughness and debonding tolerance of sandwich composite materials. A specific example of the fracture sandwich specimens such as a double cantilever sandwich beam subjected to uneven bending moments (DCB-UBM) is considered. A finite element modelling of this test method is carried out using the ABAQUS™ code. Atwo-dimensional (2-D) model has been developed to highlight the distribution of stress and displacement fields and to calculate the energy release rate (ERR) and the phase angle at the interface crack between two dissimilar orthotropic materials. The J − integral approach built-in ABAQUS code and the crack surface displacement method programmed as an add-on subroutine within the Matlab® environment are used for computing those fracture parameters. The influence of different moment ratios on the near crack tip stress state, the ERR, and phase angle fracture parameters is estimated.Документ Numerical modal analysis of sandwich plates partially damaged due to impacts(Національний технічний університет "Харківський політехнічний інститут", 2010) Burlayenko, V. N.; Sadowski, TomaszDynamic responses of sandwich composite plates containing impactinduced damage are studied. A finite element formulation of the problem is developed by using the high-order sandwich plate theory. The finite element code ABAQUS is used to create a finite element model of the sandwich plate accounting for geometrical imperfections, stiffness changes and intermediate contact of detached plate parts caused by impact damage and to fulfil the free and forced vibration analyses.Документ Numerical modeling of dynamics of sandwich plates with partially damaged facesheet-to-core interface(Apostrophe, 2011) Burlayenko, V. N.; Sadowski, Tomasz; Nazarenko, S. A.A finite element (FE) model has been developed for analysis of the dynamic response of sandwich plates with partially damaged facesheet-to-core interface. The effect of intermittent dynamic contact between the fragments detached at the damaged interface is taken into account in the vibrating sandwich plate. The general mathematical statement of such non-linear elastodynamic problem for a cracked body is first formulated. Numerical results for the transient and steadystate dynamic responses of a foam-cored sandwich plate damaged by debonding are obtained by using the ABAQUS code. The influence of the strongly nonlinear local contact behavior on dynamics of the sandwich plate is examined.Документ Thermal shock analysis of a functionally graded plate using finite element method(Цифрова друкарня, 2016) Burlayenko, V. N.; Bhaskar, AtulДокумент Three-dimensional free vibration analysis of thermally loaded fgm sandwich plates(2020) Burlayenko, V. N.; Sadowski, Tomasz; Dimitrova, SvetlanaUsing the finite element code ABAQUS and the user-defined material utilities UMAT and UMATHT, a solid brick graded finite element is developed for three-dimensional (3D) modeling of free vibrations of thermally loaded functionally gradient material (FGM) sandwich plates. The mechanical and thermal material properties of the FGM sandwich plates are assumed to vary gradually in the thickness direction, according to a power-law fraction distribution. Benchmark problems are firstly considered to assess the performance and accuracy of the proposed 3D graded finite element. Comparisons with the reference solutions revealed high efficiency and good capabilities of the developed element for the 3D simulations of thermomechanical and vibration responses of FGM sandwich plates. Some parametric studies are carried out for the frequency analysis by varying the volume fraction profile and the temperature distribution across the plate thickness.