Longitudinal and Transverse Bending on the Cylindrical Shape of a Sandwich Plate Reinforced with Absolutely Rigid Bodies in the Front Sections
A geometrically nonlinear problem of longitudinal and transverse bending on the cylindrical shape of a sandwich plate with transversally soft core reinforced in the front sections by absolutely rigid bodies intended to ensure the transfer of load to the carrier layers when they interact with other s...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2017-06-01
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| Series: | Учёные записки Казанского университета. Серия Физико-математические науки |
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| Online Access: | https://kpfu.ru/longitudinal-and-transverse-bending-on-the_309760.html |
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| author | I.B. Badriev M.V. Makarov V.N. Paimushin |
| author_facet | I.B. Badriev M.V. Makarov V.N. Paimushin |
| author_sort | I.B. Badriev |
| collection | DOAJ |
| description | A geometrically nonlinear problem of longitudinal and transverse bending on the cylindrical shape of a sandwich plate with transversally soft core reinforced in the front sections by absolutely rigid bodies intended to ensure the transfer of load to the carrier layers when they interact with other structural elements has been considered. The equations of the refined geometrically nonlinear theory, which allow one to describe the process of their precritical deformation and to reveal all possible buckling forms of the carrier layers (in-phase, antiphase, mixed bending and mixed bending-shear, and also arbitrary, including all of the above) have been used. These equations have been derived by introducing the contact forces of the interaction of the outer layers with the filler, as well as those of the outer layers and the filler with the reinforcing bodies at all points of the surfaces of their conjugation, as unknown parameters. A numerical method for solving the formulated problem has been developed. The method has been constructed by preliminary reduction of the problem to a system of integro-algebraic equations solved with the help of the finite-sum method. A method has been developed for studying the precritical geometrically nonlinear behavior of the plate as a result of its front compression through a reinforcing body. The results of the numerical experiments have been presented and analyzed. |
| first_indexed | 2024-04-11T06:57:15Z |
| format | Article |
| id | doaj.art-dd62f99988ed4dabb2176521a1ee2ee6 |
| institution | Directory Open Access Journal |
| issn | 2541-7746 2500-2198 |
| language | English |
| last_indexed | 2024-04-11T06:57:15Z |
| publishDate | 2017-06-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета. Серия Физико-математические науки |
| spelling | doaj.art-dd62f99988ed4dabb2176521a1ee2ee62022-12-22T04:38:59ZengKazan Federal UniversityУчёные записки Казанского университета. Серия Физико-математические науки2541-77462500-21982017-06-011592174190Longitudinal and Transverse Bending on the Cylindrical Shape of a Sandwich Plate Reinforced with Absolutely Rigid Bodies in the Front SectionsI.B. Badriev0M.V. Makarov1V.N. Paimushin2Kazan Federal University, Kazan, 420008 RussiaKazan Federal University, Kazan, 420008 RussiaTupolev Kazan National Research Technical University, Kazan, 420111 RussiaA geometrically nonlinear problem of longitudinal and transverse bending on the cylindrical shape of a sandwich plate with transversally soft core reinforced in the front sections by absolutely rigid bodies intended to ensure the transfer of load to the carrier layers when they interact with other structural elements has been considered. The equations of the refined geometrically nonlinear theory, which allow one to describe the process of their precritical deformation and to reveal all possible buckling forms of the carrier layers (in-phase, antiphase, mixed bending and mixed bending-shear, and also arbitrary, including all of the above) have been used. These equations have been derived by introducing the contact forces of the interaction of the outer layers with the filler, as well as those of the outer layers and the filler with the reinforcing bodies at all points of the surfaces of their conjugation, as unknown parameters. A numerical method for solving the formulated problem has been developed. The method has been constructed by preliminary reduction of the problem to a system of integro-algebraic equations solved with the help of the finite-sum method. A method has been developed for studying the precritical geometrically nonlinear behavior of the plate as a result of its front compression through a reinforcing body. The results of the numerical experiments have been presented and analyzed.https://kpfu.ru/longitudinal-and-transverse-bending-on-the_309760.htmlsandwich platetransversely soft corecontour reinforcing bodymiddle plate bendingrefined model of corecontact stressesintegro-algebraic equationsfinite sums methodgeometrically nonlinear deformationprecritical behavior |
| spellingShingle | I.B. Badriev M.V. Makarov V.N. Paimushin Longitudinal and Transverse Bending on the Cylindrical Shape of a Sandwich Plate Reinforced with Absolutely Rigid Bodies in the Front Sections Учёные записки Казанского университета. Серия Физико-математические науки sandwich plate transversely soft core contour reinforcing body middle plate bending refined model of core contact stresses integro-algebraic equations finite sums method geometrically nonlinear deformation precritical behavior |
| title | Longitudinal and Transverse Bending on the Cylindrical Shape of a Sandwich Plate Reinforced with Absolutely Rigid Bodies in the Front Sections |
| title_full | Longitudinal and Transverse Bending on the Cylindrical Shape of a Sandwich Plate Reinforced with Absolutely Rigid Bodies in the Front Sections |
| title_fullStr | Longitudinal and Transverse Bending on the Cylindrical Shape of a Sandwich Plate Reinforced with Absolutely Rigid Bodies in the Front Sections |
| title_full_unstemmed | Longitudinal and Transverse Bending on the Cylindrical Shape of a Sandwich Plate Reinforced with Absolutely Rigid Bodies in the Front Sections |
| title_short | Longitudinal and Transverse Bending on the Cylindrical Shape of a Sandwich Plate Reinforced with Absolutely Rigid Bodies in the Front Sections |
| title_sort | longitudinal and transverse bending on the cylindrical shape of a sandwich plate reinforced with absolutely rigid bodies in the front sections |
| topic | sandwich plate transversely soft core contour reinforcing body middle plate bending refined model of core contact stresses integro-algebraic equations finite sums method geometrically nonlinear deformation precritical behavior |
| url | https://kpfu.ru/longitudinal-and-transverse-bending-on-the_309760.html |
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