Contact problem for functionally graded orthotropic strip
Within the framework of plane elasticity, the equilibrium problem for an inhomogeneous orthotropic elastic strip under the action of a stamp with a smooth base is investigated. Based on the Fourier transform, a canonical system of differential equations with variable coefficients with respect to tra...
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| Format: | Article |
| Language: | English |
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Saratov State University
2022-11-01
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| Series: | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
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| Online Access: | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2022/11/479-493-vatulyan-plotnikov.pdf |
| _version_ | 1797986436704632832 |
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| author | Vatulyan, Alexander Ovanesovitsch Plotnikov, Dmitry K. |
| author_facet | Vatulyan, Alexander Ovanesovitsch Plotnikov, Dmitry K. |
| author_sort | Vatulyan, Alexander Ovanesovitsch |
| collection | DOAJ |
| description | Within the framework of plane elasticity, the equilibrium problem for an inhomogeneous orthotropic elastic strip under the action of a stamp with a smooth base is investigated. Based on the Fourier transform, a canonical system of differential equations with variable coefficients with respect to transformants of the displacement vector and stress tensor components is constructed. A connection between the vertical displacement and the normal boundary stress is constructed, with which an integral equation of the first kind with a difference kernel is formulated. Using the shooting method, the kernel symbol for the integral equation of the contact problem is constructed numerically. Based on the Vishik – Lyusternik method, an asymptotic analysis of the kernel symbol for large values of the transformation parameter is carried out. A computational scheme for solving an integral equation with an unknown contact area is~constructed. The solution of the contact problem for different laws of strip inhomogeneity is presented. |
| first_indexed | 2024-04-11T07:33:47Z |
| format | Article |
| id | doaj.art-248084bd0d5f4ba2be423c0d0f4275c2 |
| institution | Directory Open Access Journal |
| issn | 1816-9791 2541-9005 |
| language | English |
| last_indexed | 2024-04-11T07:33:47Z |
| publishDate | 2022-11-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
| spelling | doaj.art-248084bd0d5f4ba2be423c0d0f4275c22022-12-22T04:36:48ZengSaratov State UniversityИзвестия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика1816-97912541-90052022-11-0122447949310.18500/1816-9791-2022-22-4-479-493Contact problem for functionally graded orthotropic stripVatulyan, Alexander Ovanesovitsch0Plotnikov, Dmitry K.1South Federal University, 105/42 Bolshaya Sadovaya St., Rostov-on-Don 344006, RussiaSouthern Mathematical Institute, Vladikavkaz Scientific Center of the Russian Academy of Sciences, 53 Vatutina St., Vladikavkaz 362025, RussiaWithin the framework of plane elasticity, the equilibrium problem for an inhomogeneous orthotropic elastic strip under the action of a stamp with a smooth base is investigated. Based on the Fourier transform, a canonical system of differential equations with variable coefficients with respect to transformants of the displacement vector and stress tensor components is constructed. A connection between the vertical displacement and the normal boundary stress is constructed, with which an integral equation of the first kind with a difference kernel is formulated. Using the shooting method, the kernel symbol for the integral equation of the contact problem is constructed numerically. Based on the Vishik – Lyusternik method, an asymptotic analysis of the kernel symbol for large values of the transformation parameter is carried out. A computational scheme for solving an integral equation with an unknown contact area is~constructed. The solution of the contact problem for different laws of strip inhomogeneity is presented.https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2022/11/479-493-vatulyan-plotnikov.pdfcontact problemfunctionally graded striporthotropic materialasymptotic analysisboundary element method |
| spellingShingle | Vatulyan, Alexander Ovanesovitsch Plotnikov, Dmitry K. Contact problem for functionally graded orthotropic strip Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика contact problem functionally graded strip orthotropic material asymptotic analysis boundary element method |
| title | Contact problem for functionally graded orthotropic strip |
| title_full | Contact problem for functionally graded orthotropic strip |
| title_fullStr | Contact problem for functionally graded orthotropic strip |
| title_full_unstemmed | Contact problem for functionally graded orthotropic strip |
| title_short | Contact problem for functionally graded orthotropic strip |
| title_sort | contact problem for functionally graded orthotropic strip |
| topic | contact problem functionally graded strip orthotropic material asymptotic analysis boundary element method |
| url | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2022/11/479-493-vatulyan-plotnikov.pdf |
| work_keys_str_mv | AT vatulyanalexanderovanesovitsch contactproblemforfunctionallygradedorthotropicstrip AT plotnikovdmitryk contactproblemforfunctionallygradedorthotropicstrip |