Defense of the dissertation of Mukhametov Yeldos for the degree of Doctor of Philosophy (PhD) in the specialty «6D070500 - Mathematical and Computer Modeling»
L.N. Gumilyov Eurasian National University, a dissertation defense for the degree of Doctor of Philosophy (PhD) by Mukhametov Yeldos on the topic «Modeling of the dynamics of three-dimensional shells» in the specialty «6D070500 - Mathematical and Computer Modeling».
The dissertation was carried out at the Department of «Mathematical and computer modeling» of L.N. Gumilyov Eurasian National University.
The language of defense is kazakh
Official reviewers:
Ramazanov Murat Ibraevich - doctor of Physical and Mathematical Sciences, Professor, Honored Professor of the Department of Mathematical Analysis and Differential Equations, Karaganda University named after E.A. Buketov (Karaganda, Republic of Kazakhstan);
Mukhambetzhanov Saltanbek Talapedenovich - doctor of Physical and Mathematical Sciences, Chief Researcher, "Institute of Mechanics and Mechanical Engineering named after Academician U.A. Dzholdasbekov" of the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan (Almaty, Republic of Kazakhstan).
Temporary members of the Dissertation Council:
Rysbayuly Bolatbek - doctor of Physical and Mathematical Sciences, Professor of the Department of Computing and Data Science, Astana IT University (Astana, Republic of Kazakhstan);
Gabbassov Mars Bekkalievich - Candidate of Physical and Mathematical Sciences, Leading Researcher, Institute of Mechanics and Mechanical Engineering named after Academician U.A. Dzholdasbekov" of the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Almaty, Republic of Kazakhstan);
Ashirbayev Nurgali Kudiyarovich - doctor of Physical and Mathematical Sciences, Professor, Professor of the Department of Mathematics, South Kazakhstan University named after M. Auezov (Shymkent, Republic of Kazakhstan).
Scientific consultants:
Bukenov Makhat - candidate of physical and mathematical sciences, associate professor of the department of Mathematical and computer modeling of the L.N. Gumilyov Eurasian National University (Astana, Republic of Kazakhstan);
Fatyanov Aleksey - сhief Researcher, doctor of Physical and Mathematical Sciences, Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences (Novosibirsk, Russian Federation).
The defense will take place on December 20, 2024, at 04:00 PM in the Dissertation Council for the training direction «8D061 - Information and communication technologies» in the specialty «6D070500 - Mathematical and Computer Modeling» of L.N. Gumilyov Eurasian National University. The defense meeting is planned to be held offline and online.
Link: http://surl.li/hvsvhz
Address: Astana, st. Kazhymukan, 13, auditorium No. 205.
Abstract (English): The relevance The intensive development of mechanical engineering, aircraft and rocket engineering and other branches of modern technology has made it relevant to solve new theoretical and applied problems, which include the study of high-speed deformation of materials and structures made from them. The mathematical complexity of multidimensional problems of mechanics of a deformable solid, studied by methods of mathematical physics, is explained by many reasons and, in particular, by the presence of a wide range of objectively existing mechanical and rheological properties of a continuous medium, such as heterogeneity, anisotropy, nonlinearity, viscosity, plasticity, etc. An effective solution to many problems of wave dynamics has become possible thanks to the results achieved in the field of computer technology and numerical methods, which has made it possible to predict with high accuracy the stress-strain state of fairly complex mechanical systems to determine their load-bearing capacity and the nature of probable damage under conditions of fast-moving external loads (force, thermal, acoustic). The study of the dynamics and stability of three-dimensional shells of revolution, as well as shell systems, due to their applied importance, is one of the most pressing and important problems in shell theory. Obtaining a picture of the distribution of stresses, as well as the displacements of any node in time in shell systems under different types of loading is a rather complex task. Therefore, the problems of obtaining a picture of stress isolines, as well as graphs of transient processes, stability of shell systems are an open question. In this regard, the relevance of the research topic lies in the need to obtain solutions to three-dimensional problems of shell dynamics using numerical methods with subsequent assessment of the convergence and stability of approximate methods. The aim of the study is to construct a mathematical model and a conservative difference scheme for determining the dynamic and kinematic characteristics of multilayer plates, shells, and shell structures. The objects of research in this work are multilayer plates under impact interaction with a deformable stamp in one-dimensional and two-dimensional settings, as well as Timoshenko-type shells under axisymmetric loading in three-dimensional and two-dimensional settings. In accordance with the stated goal of the dissertation, the following research tasks were set: - construction of a mathematical model of the collision of a cylindrical indenter with a multilayer plate and its justification at the difference level; - construction of a mathematical model of the collision of a deformable stamp with a multilayer plate and its study at the difference level; - formulation of boundary value problems of elastic wave propagation in shell systems and their solution using a difference scheme; - analysis of stability and convergence of the applied numerical methods. Research methods. The methods for solving the set problems are numerical methods (grid-characteristic methods, finite difference methods), methods for assessing the stability and convergence of approximate solutions, and methods of elasticity theory. Scientific novelty of the research. Novelty of the work: mathematical models of the impact of an indenter on a multilayer plate, the dynamics of composite shells, completely conservative difference schemes are constructed and their numerical algorithm is indicated. The main provisions submitted for defense: - was constructed for the numerical study of an axisymmetric collision of a cylindrical indenter with a multilayer medium containing layers with different mechanical properties, free cavities and rigid inclusions. - Numerical modeling was performed taking into account the associated processes of deformation and thermal conductivity, which made it possible to describe the distribution of temperatures, stresses and velocities in multilayer media under impact and to take into account nonlinear effects in boundary conditions. - A theoretical analysis of the stability of the numerical scheme was carried out, on the basis of which the conditions for choosing time and space steps and the convergence of the numerical method were established. - Algorithms for the numerical solution of complex dynamic problems in deformable media were implemented, taking into account both the thermoviscoelastic behavior of materials and the features of the propagation of thermal waves, which represents an important contribution to the methods of computational mechanics. Reliability and validity of scientific provisions, conclusions and results. The reliability of the obtained results is substantiated by comparison of experimental data, and is also confirmed by publications in indexed international journals and in publications recommended by the Committee for Control in the Sphere of Education and Science of the Ministry of Education and Science of the Republic of Kazakhstan for publication of the main results of scientific activity, as well as in conference materials. Theoretical and practical significance. The application of the obtained results has an application in calculating the strength characteristics of shells. Approbation of research results. The main results of the dissertation work were reported and discussed: - at the international scientific conference “Theoretical and Applied Issues of Mathematics, Mechanics and Computer Science”, dedicated to the 70th anniversary of Doctor of Physical and Mathematical Sciences, Professor Murat Ibraevich Ramazanov (Karaganda, 2019); - at seminars of the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences during a scientific internship (Russia, Novosibirsk, 2019); - at seminars of the Department of Physical and Mathematical Sciences and Computer Science, JSC “ Shakarim University of Semey”; - at seminars of the Department of Mathematical and Computer Modeling, L.N. Gumilyov Eurasian National University; - at the seminars of the scientific center "Modification of the surface of materials" at the JSC " Shakarim University of Semey". Publications. The author published 5 works on the research topic, including 3 publications in scientific journals recommended by the Committee for Ensuring Control in the Sphere of Education and Science of the Ministry of Education and Science of the Republic of Kazakhstan for publishing the main results of scientific activity, 1 publication in scientific journals indexed by the Scopus database and 1 publication in the materials of domestic conferences. Articles in peer-reviewed scientific journals with a non-zero impact factor included in the Scopus , Web database of Science : 11) Bukenov MM, Adamov AA, Mukhametov YM Two-dimensional thermo-viscoelastic waves in layered media // Bulletin of the Karaganda University. Mathematics series. - 2019. - No. 2(94) (Scopus Q3 35%). Publications in editions included in the list of COCSON MES RK: 12) Bukenov M. M. , Mukhametov Y. M. , Ospanov Y .A. , Suleimenova S. Non - Axisymmetric equations of shell oscillations with attached masses // Bulletin of the Shakarim State University of Semey. - 2020. - No. 4 (92). - P. 116-125. 13) Bukenov MM, Mukhametov YM , Iskakova MT Impact of deformable stamp with a multilayered wall // Herald KazNPU named after Abay . Series "Physical and Mathematical Sciences". - 2020. - No. 4 (72). - P. 7-15. 14) Bukenov MM, Mukhametov YM Numerical solution of two-dimensional problems of thermoviscoelasticity // News of the National Academy of Sciences of the Republic of Kazakhstan. Physical-mathematical series. - 2021. - Vol. 1, Issue 335. - P. 60-64 . Abstracts and articles for reports at International and Republican conferences: 15) Bukenov M.M., Mukhametov E.M. Collision of a deformable stamp with a multilayer barrier // Proceedings of the International Scientific Conference "Theoretical and Applied Issues of Mathematics, Mechanics and Computer Science", dedicated to the 70th anniversary of Doctor of Physical and Mathematical Sciences, Professor Murat Ibraevich Ramazanov (Karaganda, 2019. - P. 127-128 ) . Structure and volume of the dissertation. The dissertation work consists of an introduction, 3 sections, a conclusion and a list of references. It is presented on 95 pages, contains 16 figures, a list of references from 58 titles and 2 appendices. The introduction includes an analysis and review of existing scientific works on the research topic, the relevance of the topic, the purpose of the dissertation, the object and objectives of the research, novelty, theoretical and practical significance, information about published works on the dissertation topic. The first section of the dissertation is devoted to the fundamentals of numerical solution of dynamic problems of deformation of layered media. The section presents the theoretical basis, including initial and boundary conditions, and also contains mathematical models for which the analysis of thermoviscoelastic waves in layered media is carried out. This section also includes the development of a grid-characteristic scheme and approaches to modeling complex contact problems using the corresponding equations of motion and heat conduction. The stability of the difference scheme and the convergence of the solution of the difference problem to the solution of the differential problem are proven. The second section of the dissertation presents a complete system of shell equations based on the hypotheses of S.P. Timoshenko [62, 63]. The use of a refined theory of shell dynamics, taking into account the rotational inertia and transverse shear of a normal element, is due to the fact that polymer and composite materials, widely used in modern technology, are characterized by weak resistance to shear deformations, which are not taken into account by the classical theory of shells, and within the framework of the approach under consideration take non-zero values. The third section presents the results of numerical experiments and their analysis. Specific cases of wave processes in layered media are considered, including wave reflection from boundaries and passage through layers with different mechanical and thermal properties. Using numerical methods, the actual behavior of materials under impact is predicted. Also in this section, the models are validated using available experimental data. The conclusion presents the main results obtained and their significance for the research area, an assessment of the completeness of the theoretical and numerical solution of the tasks set, as well as an assessment of the scientific level of the obtained results of the work.
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