Analysis of the Stress State for a Layer with Two Incut Cylindrical Supports
The stress state of a homogeneous isotropic layer under the action of a spatial static external load is studied. Two circular cylindrical supports are cut into the body of the layer parallel to its borders. The supports and body of the layer are rigidly coupled. The spatial problem theory of elastic...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
NAS of Ukraine, A. Pidhornyi Institute of Mechanical Engineering Problems
2023-03-01
|
| Series: | Journal of Mechanical Engineering |
| Subjects: |
| _version_ | 1797837509945720832 |
|---|---|
| author | Vitalii Yu. Miroshnikov Oleksandr B. Savin Mykhailo M. Hrebennikov Vladyslav F. Demenko |
| author_facet | Vitalii Yu. Miroshnikov Oleksandr B. Savin Mykhailo M. Hrebennikov Vladyslav F. Demenko |
| author_sort | Vitalii Yu. Miroshnikov |
| collection | DOAJ |
| description | The stress state of a homogeneous isotropic layer under the action of a spatial static external load is studied. Two circular cylindrical supports are cut into the body of the layer parallel to its borders. The supports and body of the layer are rigidly coupled. The spatial problem theory of elasticity is solved using the analytical-numerical generalized Fourier method. The layer is considered in the Cartesian coordinate system, the supports are considered in the local cylindrical coordinates. Stresses are set on the upper and lower surfaces of the layer. The supports are considered as cylindrical cavities in a layer with zero displacements set on their surfaces. Satisfying the boundary conditions on the upper and lower surfaces of the layer, as well as on the cylindrical surfaces of the cavities, a system of infinite integro-algebraic equations, which are further reduced to linear algebraic ones, is obtained. An infinite system is solved by the reduction method. In the numerical studies, the parameters of integration oscillatory functions are analyzed, problems at different distances between supports are solved. A unit load in the form of a rapidly decreasing function is applied to the upper boundary between the supports. For these cases, an analysis of the stress state was performed on the surfaces of the layer between the supports and on the cylindrical surfaces in contact with the supports. The numerical analysis showed that when the distance between the supports increases, the stresses σx on the lower and upper surfaces of the layer and the stresses τρφ on the surfaces of the cavities increase. The use of the analytical-numerical method made it possible to obtain a result with an accuracy of 10-4 for stress values from 0 to 1 at the order of the system of equations m=6. As the order of the system increases, the accuracy of fulfilling the boundary conditions will increase. The presented analytical-numerical solution can be used for high-precision determination of the stress-strain state of the presented problems type, as well a reference for problems based on numerical methods |
| first_indexed | 2024-04-09T15:26:58Z |
| format | Article |
| id | doaj.art-6bda41c39b004f8b911fc46afecd5564 |
| institution | Directory Open Access Journal |
| issn | 2709-2984 2709-2992 |
| language | English |
| last_indexed | 2024-04-09T15:26:58Z |
| publishDate | 2023-03-01 |
| publisher | NAS of Ukraine, A. Pidhornyi Institute of Mechanical Engineering Problems |
| record_format | Article |
| series | Journal of Mechanical Engineering |
| spelling | doaj.art-6bda41c39b004f8b911fc46afecd55642023-04-28T17:38:18ZengNAS of Ukraine, A. Pidhornyi Institute of Mechanical Engineering ProblemsJournal of Mechanical Engineering2709-29842709-29922023-03-01261152210.15407/pmach2023.01.015Analysis of the Stress State for a Layer with Two Incut Cylindrical SupportsVitalii Yu. Miroshnikov0https://orcid.org/0000-0002-9491-0181Oleksandr B. Savin1https://orcid.org/0000-0002-2664-0255Mykhailo M. Hrebennikov2https://orcid.org/0000-0001-7648-3027Vladyslav F. Demenko3https://orcid.org/0000-0002-9555-4596National Aerospace University Kharkiv Aviation InstituteNational Aerospace University Kharkiv Aviation InstituteNational Aerospace University Kharkiv Aviation InstituteNational Aerospace University Kharkiv Aviation InstituteThe stress state of a homogeneous isotropic layer under the action of a spatial static external load is studied. Two circular cylindrical supports are cut into the body of the layer parallel to its borders. The supports and body of the layer are rigidly coupled. The spatial problem theory of elasticity is solved using the analytical-numerical generalized Fourier method. The layer is considered in the Cartesian coordinate system, the supports are considered in the local cylindrical coordinates. Stresses are set on the upper and lower surfaces of the layer. The supports are considered as cylindrical cavities in a layer with zero displacements set on their surfaces. Satisfying the boundary conditions on the upper and lower surfaces of the layer, as well as on the cylindrical surfaces of the cavities, a system of infinite integro-algebraic equations, which are further reduced to linear algebraic ones, is obtained. An infinite system is solved by the reduction method. In the numerical studies, the parameters of integration oscillatory functions are analyzed, problems at different distances between supports are solved. A unit load in the form of a rapidly decreasing function is applied to the upper boundary between the supports. For these cases, an analysis of the stress state was performed on the surfaces of the layer between the supports and on the cylindrical surfaces in contact with the supports. The numerical analysis showed that when the distance between the supports increases, the stresses σx on the lower and upper surfaces of the layer and the stresses τρφ on the surfaces of the cavities increase. The use of the analytical-numerical method made it possible to obtain a result with an accuracy of 10-4 for stress values from 0 to 1 at the order of the system of equations m=6. As the order of the system increases, the accuracy of fulfilling the boundary conditions will increase. The presented analytical-numerical solution can be used for high-precision determination of the stress-strain state of the presented problems type, as well a reference for problems based on numerical methodscylindrical cavities in a layergeneralized fourier methodlamé equation |
| spellingShingle | Vitalii Yu. Miroshnikov Oleksandr B. Savin Mykhailo M. Hrebennikov Vladyslav F. Demenko Analysis of the Stress State for a Layer with Two Incut Cylindrical Supports Journal of Mechanical Engineering cylindrical cavities in a layer generalized fourier method lamé equation |
| title | Analysis of the Stress State for a Layer with Two Incut Cylindrical Supports |
| title_full | Analysis of the Stress State for a Layer with Two Incut Cylindrical Supports |
| title_fullStr | Analysis of the Stress State for a Layer with Two Incut Cylindrical Supports |
| title_full_unstemmed | Analysis of the Stress State for a Layer with Two Incut Cylindrical Supports |
| title_short | Analysis of the Stress State for a Layer with Two Incut Cylindrical Supports |
| title_sort | analysis of the stress state for a layer with two incut cylindrical supports |
| topic | cylindrical cavities in a layer generalized fourier method lamé equation |
| work_keys_str_mv | AT vitaliiyumiroshnikov analysisofthestressstateforalayerwithtwoincutcylindricalsupports AT oleksandrbsavin analysisofthestressstateforalayerwithtwoincutcylindricalsupports AT mykhailomhrebennikov analysisofthestressstateforalayerwithtwoincutcylindricalsupports AT vladyslavfdemenko analysisofthestressstateforalayerwithtwoincutcylindricalsupports |