Boundary Conditions in 2D Numerical and 3D Exact Models for Cylindrical Bending Analysis of Functionally Graded Structures
The cylindrical bending condition for structural models is very common in the literature because it allows an incisive and simple verification of the proposed plate and shell models. In the present paper, 2D numerical approaches (the Generalized Differential Quadrature (GDQ) and the finite element (...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2016/2373862 |
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| author | F. Tornabene S. Brischetto N. Fantuzzi M. Bacciocchi |
| author_facet | F. Tornabene S. Brischetto N. Fantuzzi M. Bacciocchi |
| author_sort | F. Tornabene |
| collection | DOAJ |
| description | The cylindrical bending condition for structural models is very common in the literature because it allows an incisive and simple verification of the proposed plate and shell models. In the present paper, 2D numerical approaches (the Generalized Differential Quadrature (GDQ) and the finite element (FE) methods) are compared with an exact 3D shell solution in the case of free vibrations of functionally graded material (FGM) plates and shells. The first 18 vibration modes carried out through the 3D exact model are compared with the frequencies obtained via the 2D numerical models. All the 18 frequencies obtained via the 3D exact model are computed when the structures have simply supported boundary conditions for all the edges. If the same boundary conditions are used in the 2D numerical models, some modes are missed. Some of these missed modes can be obtained modifying the boundary conditions imposing free edges through the direction perpendicular to the direction of cylindrical bending. However, some modes cannot be calculated via the 2D numerical models even when the boundary conditions are modified because the cylindrical bending requirements cannot be imposed for numerical solutions in the curvilinear edges by definition. These features are investigated in the present paper for different geometries (plates, cylinders, and cylindrical shells), types of FGM law, lamination sequences, and thickness ratios. |
| format | Article |
| id | doaj-art-66381bcc87aa41bdb12513d9caa57fe4 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-66381bcc87aa41bdb12513d9caa57fe42025-08-20T03:34:17ZengWileyShock and Vibration1070-96221875-92032016-01-01201610.1155/2016/23738622373862Boundary Conditions in 2D Numerical and 3D Exact Models for Cylindrical Bending Analysis of Functionally Graded StructuresF. Tornabene0S. Brischetto1N. Fantuzzi2M. Bacciocchi3DICAM Department, University of Bologna, Bologna, ItalyDepartment of Mechanical and Aerospace Engineering, Politecnico di Torino, Torino, ItalyDICAM Department, University of Bologna, Bologna, ItalyDICAM Department, University of Bologna, Bologna, ItalyThe cylindrical bending condition for structural models is very common in the literature because it allows an incisive and simple verification of the proposed plate and shell models. In the present paper, 2D numerical approaches (the Generalized Differential Quadrature (GDQ) and the finite element (FE) methods) are compared with an exact 3D shell solution in the case of free vibrations of functionally graded material (FGM) plates and shells. The first 18 vibration modes carried out through the 3D exact model are compared with the frequencies obtained via the 2D numerical models. All the 18 frequencies obtained via the 3D exact model are computed when the structures have simply supported boundary conditions for all the edges. If the same boundary conditions are used in the 2D numerical models, some modes are missed. Some of these missed modes can be obtained modifying the boundary conditions imposing free edges through the direction perpendicular to the direction of cylindrical bending. However, some modes cannot be calculated via the 2D numerical models even when the boundary conditions are modified because the cylindrical bending requirements cannot be imposed for numerical solutions in the curvilinear edges by definition. These features are investigated in the present paper for different geometries (plates, cylinders, and cylindrical shells), types of FGM law, lamination sequences, and thickness ratios.http://dx.doi.org/10.1155/2016/2373862 |
| spellingShingle | F. Tornabene S. Brischetto N. Fantuzzi M. Bacciocchi Boundary Conditions in 2D Numerical and 3D Exact Models for Cylindrical Bending Analysis of Functionally Graded Structures Shock and Vibration |
| title | Boundary Conditions in 2D Numerical and 3D Exact Models for Cylindrical Bending Analysis of Functionally Graded Structures |
| title_full | Boundary Conditions in 2D Numerical and 3D Exact Models for Cylindrical Bending Analysis of Functionally Graded Structures |
| title_fullStr | Boundary Conditions in 2D Numerical and 3D Exact Models for Cylindrical Bending Analysis of Functionally Graded Structures |
| title_full_unstemmed | Boundary Conditions in 2D Numerical and 3D Exact Models for Cylindrical Bending Analysis of Functionally Graded Structures |
| title_short | Boundary Conditions in 2D Numerical and 3D Exact Models for Cylindrical Bending Analysis of Functionally Graded Structures |
| title_sort | boundary conditions in 2d numerical and 3d exact models for cylindrical bending analysis of functionally graded structures |
| url | http://dx.doi.org/10.1155/2016/2373862 |
| work_keys_str_mv | AT ftornabene boundaryconditionsin2dnumericaland3dexactmodelsforcylindricalbendinganalysisoffunctionallygradedstructures AT sbrischetto boundaryconditionsin2dnumericaland3dexactmodelsforcylindricalbendinganalysisoffunctionallygradedstructures AT nfantuzzi boundaryconditionsin2dnumericaland3dexactmodelsforcylindricalbendinganalysisoffunctionallygradedstructures AT mbacciocchi boundaryconditionsin2dnumericaland3dexactmodelsforcylindricalbendinganalysisoffunctionallygradedstructures |