Maksymiuk O. Numerical study of the shape change of spatial bodies using the semi-analytical method of finite elements

Українська версія

Thesis for the degree of Doctor of Philosophy (PhD)

State registration number

0824U003201

Thesis Registration Form

0824U003201.pdf

Applicant for

Specialization

  • 131 - Прикладна механіка

05-09-2024

Specialized Academic Board

ДФ 27.131

Kyiv National University of Construction and Architecture

Essay

Dissertation for the Doctor of Philosophy degree in specialty 131 "Applied Mechanics". - Kyiv National University of Construction and Architecture, Kyiv, 2024. Among spatial structures widely used in various fields of technology, prismatic bodies occupy a significant place, the geometric and physical-mechanical characteristics of which are variable in all three directions. Within the framework of this work, three-dimensional objects of an arbitrary, not necessarily single-link, cross-section with some restrictions on the nature of the geometry change will be considered with some restrictions on the nature of the geometry change along the coordinates, namely, the object can be represented as a result movements of cross-section points along some spatial pieces. -Smooth curves. The bodies can also have cutouts and holes, the contours of which are parallel to the coordinate surfaces. Such spatial bodies will be called curvilinear prismatic bodies, and in the presence of inhomogeneity of physical and mechanical properties of the material - curvilinear heterogeneous bodies. A large number of spatial structures are represented by prismatic bodies, the geometric and physical-mechanical characteristics of which are variable in all three directions. Objects of the selected class are used as natural structures, nodes and details in construction and various branches of mechanical engineering. For example, they include the foundations of industrial and civil buildings, elements of ceilings and coatings, arched dams, brackets, cutters, teeth of helical wheels, etc. Deformation of the considered structures occurs under the influence of force and temperature factors, and, due to the presence of significant temperature differences, a change in the physical and mechanical characteristics of the material is possible. At the current level of technical and technological development, plastic deformations are allowed in individual structural elements. For a number of parts in the process of operation and manufacture, the development of plastic deformations is accompanied by a significant change in the original shape. This is typical for the processes of processing metals by pressure, for example, in the manufacture of stamp heels, stretching of stripes. Further improvement of constructive solutions for the development of responsible nodes and technological processes largely depends on the completeness and reliability of information about the peculiarities of the change in the picture of the stress-strain state during the loading process. In this regard, the development of research methods for a selected class of objects is an urgent problem. The need to study the nature of the stress-strain state of curvilinear heterogeneous prismatic bodies leads to the solution of complex spatial problems of thermoelasticity and thermoplasticity both at small and large plastic deformations. The introduction shows the relevance of the intended research direction, analyzes literary sources, sets the goal of the work, reveals its scientific novelty and practical value. The first chapter is devoted to obtaining the solving equations of the semi-analytical method of finite elements for the study of inhomogeneous curvilinear prismatic bodies. The main relations of the spatial problem of the theory of elasticity in the rectangular Cartesian coordinate system, the theory of plastic flow for an isotropic material that strengthens under the condition of Mises yield and the theory of strengthening are given. All ratios take into account the dependence of material properties on temperature. A new non-homogeneous curvilinear prismatic finite element is proposed, the stiffness matrix of which is obtained according to the technique of the moment scheme of finite elements. The developed approach is a common solution of geometrically nonlinear problems, and the decisive equations are reduced to a form similar to that obtained earlier for a geometrically linear problem. The second chapter describes the algorithms for solving systems of linear and nonlinear equations, the semi-analytical method of finite elements, stress corrections when plasticity and creep deformations occur. Much attention is paid to the question of the effectiveness of the block iteration method for solving problems of elastic-plastic deformation of prismatic bodies with variable parameters along the decomposition coordinate. The scheme of the computational process and the structure of the complex of programs implementing it are described. In the third section, a numerical study of the convergence of solutions obtained taking into account the developed approach is performed. A wide range of test tasks for bodies with smoothly and abruptly changing physical and geometric characteristics in elastic and elastic-plasti

Read more

Research papers

1. Bazhenov V.A., Maksimyuk Yu.V., Horbach M.V., Martyniuk I.Yu., Maksimyuk О.V. Convergence of the finite element method and the semi-analytical finite element method for prismatic bodies with variable physical and geometric parameters. Strength of Materials and Theory of Structures: Scientific-&-Technical collected articles – Kyiv: KNUCA, 2021. – Issue 106. – P. 92-104. https://doi.org/10.32347/2410-2547.2021.106.92-104

2. Vorona Y.V., Maksimyuk Yu.V., Martyniuk I.Yu., Maksimyuk О.V. Reliability of results obtained by semi-analytical finite element method for prismatic bodies with variable physical and geometric parameters. Strength of Materials and Theory of Structures: Scientific-&-Technical collected articles – Kyiv: KNUCA, 2021. – Issue 107. – P. 184-192. https://doi.org/10.32347/2410-2547.2021.107.184-192

3. Maksimyuk Yu.V., Chuprina Yu.A., Kozak O.V., Martyniuk I.Yu., Maksimyuk О.V. Investigation of the influence of flange thickness on the nature of the development of zones of plasticity in casing detail. Strength of Materials and Theory of Structures: Scientific-&-Technical collected articles – Kyiv: KNUCA, 2022. – Issue. 108. – P. 97-106. https://doi.org/10.32347/2410-2547.2022.108.97-106

4. Maksimyuk Yu.V., Kuzminets M.P., Martyniuk I.Yu., Maksimyuk О.V. Research of the stressed and deformed state of a metal strip in the broaching process. Strength of Materials and Theory of Structures: Scientific-&-Technical collected articles – Kyiv: KNUCA. – Issue 109. – P. 229-238. https://doi.org/10.32347/2410-2547.2022.109.229-238

5. Maksimyuk Yu.V., Kozak O.V., Martyniuk I.Yu., Maksimyuk О.V. Numerical analysis of the stressed-deformed state of a tubular element under thermal loading. Strength of Materials and Theory of Structures: Scientific-&-Technical collected articles – Kyiv: KNUCA, 2023. – Issue 110. – P. 199-206 https://doi.org/10.32347/2410-2547.2023.110.199-206

6. Maksimyuk Yu.V., Andriievskyi V.P., Martyniuk I.Yu., Maksimyuk О.V. Analysis of structures with arbitrary kinematic boundary conditions by the semi-analytical finite element method. Strength of Materials and Theory of Structures: Scientific-&-Technical collected articles – Kyiv: KNUCA, 2023. – Issue 111. – P. 140-146. https://doi.org/10.32347/2410-2547.2023.111.140-146

7. Максим’юк Ю., Козак А., Максим’юк О. Розв’язувальні співвідношення моментної схеми скінчених елементів в задачах термов’язкопружнопластичного деформування. Будівельні конструкції теорія і практика – 2019. – Вип. 4. – С. 10–20. https://doi.org/10.32347/2522-4182.4.2019.10-20

8. Гуляр О., Максим’юк Ю., Козак А., Максим’юк О. Універсальний призматичний скінчений елемент загального типу для фізично і геометрично нелінійних задач деформування призматичних. Будівельні конструкції теорія і практика – 2020. – Вип. 6. – С. 72–84. https://doi.org/10.32347/2522-4182.6.2020.72-84

9. Максим’юк Ю., Гончаренко М, Мартинюк І., Максим’юк О. Алгоритм розв’язання системи лінійних та нелінійних рівнянь напіваналітичним методом скінчених елементів для криволінійних неоднорідних призматичних тіл. Будівельні конструкції теорія і практика – 2020. – Вип. 7. – С. 101–108. https://doi.org/10.32347/2522-4182.7.2020.101-108

10. Максим’юк Ю., Козак А., Мартинюк І., Максим’юк О. Особливості виведення формул для обчислення вузлових реакцій і коефіцієнтів матриці жорсткості скінченого елемента з усередненими механічними і геометричними параметрами. Будівельні конструкції теорія і практика. – 2021. – Вип. 8. – С. 97–108. https://doi.org/10.32347/2522-4182.8.2021.97-108

11. Баженов В.А., Максим’юк Ю.В., Мартинюк І.Ю., Максим’юк О.В. Напіваналітичний метод скінченних елементів в просторових задачах деформування, руйнування та формозмінення тіл складної структури – Київ: Вид-во “Каравела”, 2021. – 280с. ISBN 978-966-8019-59-3

12. Максим’юк Ю.В., Мартинюк І.Ю., Максим’юк О.В. Напіваналітичний метод скінчених елементів в лінійних і нелінійних задачах деформування, руйнування та формозмінення просторових тіл з урахуванням неканонічності форми та складної структури. ІІІ Науково-практична конференція «Будівлі та споруди спеціального призначення: сучасні матеріали та конструкції» – К.: КНУБА., 25-25.09.2021 – 73-74с.

13. Максим’юк Ю., Мартинюк І., Максим’юк О. Моментна схема скінчених елементів в геометрично та фізично нелінійних задачах деформування вісесиметричних тіл обертання з урахуванням континуального руйнування. ІV Науково-практична конференція «Будівлі та споруди спеціального призначення: сучасні матеріали та конструкції» кафедра ЗБК, КНУБА, 26 квітня 2023.

14. Maksimyuk Yu.V., Martyniuk I.Yu., Maksimyuk О.V. Research of convergence, reliability and efficiency of the results obtained using the given finite elements. Materiály XX Mezinárodní vĕdecko - praktická konference «Věda a technologie: krok do budoucnosti», Volume 4 : Praha. 2023. Pp. 91-94. Publishing House «Education and Science» -96 s. ISSN 1561-6940 (online).

15. Maksimyuk Yu.V., Martyniuk I.Yu., Maksimyuk О.V. The effectiveness of the algorithm for solving nonlinear equations in isotropic load. Scientific progress: innovations, achievements and prospects. Proceedings of the 6th International scientific and practical conference. MDPC Publishing. Munich, Germany. 2023. Pp. 117-120.

16. Maksimyuk Yu.V., Martyniuk I.Yu., Maksimyuk О.V. Study of the influence of taking into account geometric nonlinearity on the value of the resource of a christmas tree joint under creep conditions. Modern research in science and education. Proceedings of the 2nd International scientific and practical conference. BoScience Publisher. Chicago, USA. 2023. Pp. 148-150.

Read more

Similar theses

0824U002987

Yurii Zaichyk

TECHNOLOGICAL METHODS FOR PROVIDING QUALITY CHARACTERISTICS OF THE PRODUCTS FROM THE MATERIALS PRONE TO CRACK OCCURRENCE DURING THE FINAL MACHINING OPERATIONS

0824U002429

Denys Molochkov

Improvement of the metal layer formation process in 3D printing based on arc welding

0824U002369

Yaroslav Shved

Strength and deformability of a rectangular welded truss under force and temperature effects

0824U002368

Nazarii Bykiv

Increasing the deformability of structural elements under cyclic loads by using shape memory alloys

0824U002078

Vadym Prykhodko

Technological maintenance of stainless-steel surface roughness with short pulse laser radiation