Stress-deformed state of a three-layer structure taking into account the hypothesis of cubic displacement pattern over the thickness of a filler
Objective. In most cases, when determining the stress-deformed state of three-layer structures, it is assumed that bearing layers obey the Kirchhoff-Love hypothesis, while a filler obey the Neit (vanderNeit), or “broken line”, hypothesis. But in many cases, the results of our research show that this...
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| Format: | Article |
| Language: | Russian |
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Dagestan State Technical University
2021-07-01
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| Series: | Вестник Дагестанского государственного технического университета: Технические науки |
| Subjects: | |
| Online Access: | https://vestnik.dgtu.ru/jour/article/view/942 |
| _version_ | 1797702357673312256 |
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| author | O. M. Ustarkhanov Kh. M. Muselemov Kh. M. Gapparov |
| author_facet | O. M. Ustarkhanov Kh. M. Muselemov Kh. M. Gapparov |
| author_sort | O. M. Ustarkhanov |
| collection | DOAJ |
| description | Objective. In most cases, when determining the stress-deformed state of three-layer structures, it is assumed that bearing layers obey the Kirchhoff-Love hypothesis, while a filler obey the Neit (vanderNeit), or “broken line”, hypothesis. But in many cases, the results of our research show that this is not always accurate. Methods. It is proposed to solve the three-dimensional problem of determining the stress-deformed state of a three-layer structure using cubic functions of the law of aggregate deformation distribution along the normal line, obtained on the basis of the law of deformation compatibility at “filler – bearing layer” boundaries and the construction of boundary conditions in joint zones. Results. Equilibrium equations of a three-layer beam obtained on the basis of this hypothesis are shown in Table 1. The given partial differential equations are of the 12th order and we transformed them into homogeneous equations of the 1st order to simplify the solution. This solution is implemented using the mathematical modelling software package Mаple 5.4. Conclusion. The work of the filler in the direction of OX axis has a certain value, which affects the overall stress state of the three-layer structure (in existing hypotheses, it is zero). |
| first_indexed | 2024-03-12T04:49:54Z |
| format | Article |
| id | doaj.art-601604b1aa5742ca8c835b85f466a23d |
| institution | Directory Open Access Journal |
| issn | 2073-6185 2542-095X |
| language | Russian |
| last_indexed | 2024-03-12T04:49:54Z |
| publishDate | 2021-07-01 |
| publisher | Dagestan State Technical University |
| record_format | Article |
| series | Вестник Дагестанского государственного технического университета: Технические науки |
| spelling | doaj.art-601604b1aa5742ca8c835b85f466a23d2023-09-03T09:26:27ZrusDagestan State Technical UniversityВестник Дагестанского государственного технического университета: Технические науки2073-61852542-095X2021-07-0148212413210.21822/2073-6185-2021-48-2-124-132642Stress-deformed state of a three-layer structure taking into account the hypothesis of cubic displacement pattern over the thickness of a fillerO. M. Ustarkhanov0Kh. M. Muselemov1Kh. M. Gapparov2Дагестанский государственный технический университетДагестанский государственный технический университетДагестанский государственный технический университетObjective. In most cases, when determining the stress-deformed state of three-layer structures, it is assumed that bearing layers obey the Kirchhoff-Love hypothesis, while a filler obey the Neit (vanderNeit), or “broken line”, hypothesis. But in many cases, the results of our research show that this is not always accurate. Methods. It is proposed to solve the three-dimensional problem of determining the stress-deformed state of a three-layer structure using cubic functions of the law of aggregate deformation distribution along the normal line, obtained on the basis of the law of deformation compatibility at “filler – bearing layer” boundaries and the construction of boundary conditions in joint zones. Results. Equilibrium equations of a three-layer beam obtained on the basis of this hypothesis are shown in Table 1. The given partial differential equations are of the 12th order and we transformed them into homogeneous equations of the 1st order to simplify the solution. This solution is implemented using the mathematical modelling software package Mаple 5.4. Conclusion. The work of the filler in the direction of OX axis has a certain value, which affects the overall stress state of the three-layer structure (in existing hypotheses, it is zero).https://vestnik.dgtu.ru/jour/article/view/942трёхслойная конструкциянесущий слойзаполнительгипотезанапряжённо-деформированное состояниеуравнения равновесия |
| spellingShingle | O. M. Ustarkhanov Kh. M. Muselemov Kh. M. Gapparov Stress-deformed state of a three-layer structure taking into account the hypothesis of cubic displacement pattern over the thickness of a filler Вестник Дагестанского государственного технического университета: Технические науки трёхслойная конструкция несущий слой заполнитель гипотеза напряжённо-деформированное состояние уравнения равновесия |
| title | Stress-deformed state of a three-layer structure taking into account the hypothesis of cubic displacement pattern over the thickness of a filler |
| title_full | Stress-deformed state of a three-layer structure taking into account the hypothesis of cubic displacement pattern over the thickness of a filler |
| title_fullStr | Stress-deformed state of a three-layer structure taking into account the hypothesis of cubic displacement pattern over the thickness of a filler |
| title_full_unstemmed | Stress-deformed state of a three-layer structure taking into account the hypothesis of cubic displacement pattern over the thickness of a filler |
| title_short | Stress-deformed state of a three-layer structure taking into account the hypothesis of cubic displacement pattern over the thickness of a filler |
| title_sort | stress deformed state of a three layer structure taking into account the hypothesis of cubic displacement pattern over the thickness of a filler |
| topic | трёхслойная конструкция несущий слой заполнитель гипотеза напряжённо-деформированное состояние уравнения равновесия |
| url | https://vestnik.dgtu.ru/jour/article/view/942 |
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