Torsional and Transversal Stiffness of Orthotropic Sandwich Panels
In the present work, an analytical equation describing the plate torsion test taking into account the transverse shear stiffness in sandwich plates is derived and numerically validated. Transverse shear becomes an important component if the analyzed plate or shell is thick with respect to the in-pla...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Materials |
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| Online Access: | https://www.mdpi.com/1996-1944/13/21/5016 |
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| author | Tomasz Garbowski Tomasz Gajewski Jakub Krzysztof Grabski |
| author_facet | Tomasz Garbowski Tomasz Gajewski Jakub Krzysztof Grabski |
| author_sort | Tomasz Garbowski |
| collection | DOAJ |
| description | In the present work, an analytical equation describing the plate torsion test taking into account the transverse shear stiffness in sandwich plates is derived and numerically validated. Transverse shear becomes an important component if the analyzed plate or shell is thick with respect to the in-plane dimensions and/or its core has significantly lower stiffness than the outer faces. The popular example of such a sandwich plate is a corrugated cardboard, widely used in the packaging industry. The flat layers of a corrugated board are usually made of thicker (stronger) material than that used for the corrugated layer, the role of which is rather to keep the outer layers at a certain distance, to ensure high bending stiffness of the plate. However, the soft core of such a plate usually has a low transverse shear stiffness, which is often not considered in the plate analysis. Such simplification may lead to significant calculation errors. The paper presents the generalization of the Reissner’s analytical formula, which describes the torsional stiffness of the plate sample including two transverse shear stiffnesses. The paper also presents the implementation of the numerical model of the plate torsion test including the transverse shear stiffnesses. Both approaches are compared with each other on a wide range of material parameters and different aspect ratios of the specimen. It has been proved that both analytical and numerical formulations lead to an identical result. Finally, the performance of presented formulations is compared with other numerical models using commercial implementation of various Reissner–Mindlin shell elements and other analytical formulas from the literature. The comparison shows good agreement of presented theory and numerical implementation with other existing approaches. |
| first_indexed | 2024-03-10T15:02:33Z |
| format | Article |
| id | doaj.art-e402834289da4ab590175e911703bf60 |
| institution | Directory Open Access Journal |
| issn | 1996-1944 |
| language | English |
| last_indexed | 2024-03-10T15:02:33Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
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| series | Materials |
| spelling | doaj.art-e402834289da4ab590175e911703bf602023-11-20T20:04:27ZengMDPI AGMaterials1996-19442020-11-011321501610.3390/ma13215016Torsional and Transversal Stiffness of Orthotropic Sandwich PanelsTomasz Garbowski0Tomasz Gajewski1Jakub Krzysztof Grabski2Institute of Structural Analysis, Poznan University of Technology, Piotrowo Street 5, 60-965 Poznań, PolandInstitute of Structural Analysis, Poznan University of Technology, Piotrowo Street 5, 60-965 Poznań, PolandInstitute of Applied Mechanics, Poznan University of Technology, Jana Pawła II Street 24, 60-965 Poznań, PolandIn the present work, an analytical equation describing the plate torsion test taking into account the transverse shear stiffness in sandwich plates is derived and numerically validated. Transverse shear becomes an important component if the analyzed plate or shell is thick with respect to the in-plane dimensions and/or its core has significantly lower stiffness than the outer faces. The popular example of such a sandwich plate is a corrugated cardboard, widely used in the packaging industry. The flat layers of a corrugated board are usually made of thicker (stronger) material than that used for the corrugated layer, the role of which is rather to keep the outer layers at a certain distance, to ensure high bending stiffness of the plate. However, the soft core of such a plate usually has a low transverse shear stiffness, which is often not considered in the plate analysis. Such simplification may lead to significant calculation errors. The paper presents the generalization of the Reissner’s analytical formula, which describes the torsional stiffness of the plate sample including two transverse shear stiffnesses. The paper also presents the implementation of the numerical model of the plate torsion test including the transverse shear stiffnesses. Both approaches are compared with each other on a wide range of material parameters and different aspect ratios of the specimen. It has been proved that both analytical and numerical formulations lead to an identical result. Finally, the performance of presented formulations is compared with other numerical models using commercial implementation of various Reissner–Mindlin shell elements and other analytical formulas from the literature. The comparison shows good agreement of presented theory and numerical implementation with other existing approaches.https://www.mdpi.com/1996-1944/13/21/5016transverse shear stiffnessplate torsion testcorrugated cardboardsandwich platefinite element methodshell element |
| spellingShingle | Tomasz Garbowski Tomasz Gajewski Jakub Krzysztof Grabski Torsional and Transversal Stiffness of Orthotropic Sandwich Panels Materials transverse shear stiffness plate torsion test corrugated cardboard sandwich plate finite element method shell element |
| title | Torsional and Transversal Stiffness of Orthotropic Sandwich Panels |
| title_full | Torsional and Transversal Stiffness of Orthotropic Sandwich Panels |
| title_fullStr | Torsional and Transversal Stiffness of Orthotropic Sandwich Panels |
| title_full_unstemmed | Torsional and Transversal Stiffness of Orthotropic Sandwich Panels |
| title_short | Torsional and Transversal Stiffness of Orthotropic Sandwich Panels |
| title_sort | torsional and transversal stiffness of orthotropic sandwich panels |
| topic | transverse shear stiffness plate torsion test corrugated cardboard sandwich plate finite element method shell element |
| url | https://www.mdpi.com/1996-1944/13/21/5016 |
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