A FEM Free Vibration Analysis of Variable Stiffness Composite Plates through Hierarchical Modeling
Variable Angle Tow (VAT) laminates offer a promising alternative to classical straight-fiber composites in terms of design and performance. However, analyzing these structures can be more complex due to the introduction of new design variables. Carrera’s unified formulation (CUF) has been successful...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Materials |
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| Online Access: | https://www.mdpi.com/1996-1944/16/13/4643 |
| _version_ | 1797591389747281920 |
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| author | Gaetano Giunta Domenico Andrea Iannotta Marco Montemurro |
| author_facet | Gaetano Giunta Domenico Andrea Iannotta Marco Montemurro |
| author_sort | Gaetano Giunta |
| collection | DOAJ |
| description | Variable Angle Tow (VAT) laminates offer a promising alternative to classical straight-fiber composites in terms of design and performance. However, analyzing these structures can be more complex due to the introduction of new design variables. Carrera’s unified formulation (CUF) has been successful in previous works for buckling, vibrational, and stress analysis of VAT plates. Typically, one-dimensional (1D) and two-dimensional (2D) CUF models are used, with a linear law describing the fiber orientation variation in the main plane of the structure. The objective of this article is to expand the CUF 2D plate finite elements family to perform free vibration analysis of composite laminated plate structures with curvilinear fibers. The primary contribution is the application of Reissner’s mixed variational theorem (RMVT) to a CUF finite element model. The principle of virtual displacements (PVD) and RMVT are both used as variational statements for the study of monolayer and multilayer VAT plate dynamic behavior. The proposed approach is compared to Abaqus three-dimensional (3D) reference solutions, classical theories and literature results to investigate the effectiveness of the developed models. The results demonstrate that mixed theories provide the best approximation of the reference solution in all cases. |
| first_indexed | 2024-03-11T01:36:43Z |
| format | Article |
| id | doaj.art-ff188caf5e224aa9970fc2ad85ccdd4d |
| institution | Directory Open Access Journal |
| issn | 1996-1944 |
| language | English |
| last_indexed | 2024-03-11T01:36:43Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Materials |
| spelling | doaj.art-ff188caf5e224aa9970fc2ad85ccdd4d2023-11-18T16:57:45ZengMDPI AGMaterials1996-19442023-06-011613464310.3390/ma16134643A FEM Free Vibration Analysis of Variable Stiffness Composite Plates through Hierarchical ModelingGaetano Giunta0Domenico Andrea Iannotta1Marco Montemurro2Luxembourg Institute of Science and Technology, 5 Avenue des Hauts-Fourneaux, L-4362 Esch-sur-Alzette, LuxembourgLuxembourg Institute of Science and Technology, 5 Avenue des Hauts-Fourneaux, L-4362 Esch-sur-Alzette, LuxembourgArts et Métiers Institute of Technology, Université de Bordeaux, CNRS, INRA, Bordeaux INP, HESAM Université, I2M UMR 5295, F-33405 Talence, FranceVariable Angle Tow (VAT) laminates offer a promising alternative to classical straight-fiber composites in terms of design and performance. However, analyzing these structures can be more complex due to the introduction of new design variables. Carrera’s unified formulation (CUF) has been successful in previous works for buckling, vibrational, and stress analysis of VAT plates. Typically, one-dimensional (1D) and two-dimensional (2D) CUF models are used, with a linear law describing the fiber orientation variation in the main plane of the structure. The objective of this article is to expand the CUF 2D plate finite elements family to perform free vibration analysis of composite laminated plate structures with curvilinear fibers. The primary contribution is the application of Reissner’s mixed variational theorem (RMVT) to a CUF finite element model. The principle of virtual displacements (PVD) and RMVT are both used as variational statements for the study of monolayer and multilayer VAT plate dynamic behavior. The proposed approach is compared to Abaqus three-dimensional (3D) reference solutions, classical theories and literature results to investigate the effectiveness of the developed models. The results demonstrate that mixed theories provide the best approximation of the reference solution in all cases.https://www.mdpi.com/1996-1944/16/13/4643free vibration analysisfinite element methodvariable angle tow platesCarrera’s unified formulationReissner’s mixed variational theorem |
| spellingShingle | Gaetano Giunta Domenico Andrea Iannotta Marco Montemurro A FEM Free Vibration Analysis of Variable Stiffness Composite Plates through Hierarchical Modeling Materials free vibration analysis finite element method variable angle tow plates Carrera’s unified formulation Reissner’s mixed variational theorem |
| title | A FEM Free Vibration Analysis of Variable Stiffness Composite Plates through Hierarchical Modeling |
| title_full | A FEM Free Vibration Analysis of Variable Stiffness Composite Plates through Hierarchical Modeling |
| title_fullStr | A FEM Free Vibration Analysis of Variable Stiffness Composite Plates through Hierarchical Modeling |
| title_full_unstemmed | A FEM Free Vibration Analysis of Variable Stiffness Composite Plates through Hierarchical Modeling |
| title_short | A FEM Free Vibration Analysis of Variable Stiffness Composite Plates through Hierarchical Modeling |
| title_sort | fem free vibration analysis of variable stiffness composite plates through hierarchical modeling |
| topic | free vibration analysis finite element method variable angle tow plates Carrera’s unified formulation Reissner’s mixed variational theorem |
| url | https://www.mdpi.com/1996-1944/16/13/4643 |
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