Abstract
This research introduces an innovative mixed finite element methodology for analysing functionally graded plates (FGP). The new method employs an isoparametric formulation in the natural (ξ, η) plane and integrates an exponential material gradient and a constant Poisson ratio for the FGP, providing a new perspective on FGP analysis. The effectiveness of this new method is demonstrated by employing numerical modelling in a representative example involving an FGP under tension. Results are comprehensively compared with numerical and analytical solutions found in the existing literature to establish validity and accuracy. The findings reveal that the proposed methodology exhibits superior computational efficiency and accuracy in evaluating the tension behaviour of FGP, with a particular focus on the impact of a reduced number of degrees of freedom. The outcomes of this study contribute to advancing the analysis and design of FGP for various applications.
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References
Akavci, S. S., & Tanrikulu, A. H. (2015). Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories. Composites. Part B, Engineering, 83, 203–215. https://doi.org/10.1016/j.compositesb.2015.08.043
Akbaş, ŞD. (2015). Free vibration and bending of functionally graded beams resting on elastic foundation. Research on Engineering Structures and Materials. https://doi.org/10.17515/resm2015.03st0107
Aldousari, S. M. (2017). Bending analysis of different material distributions of functionally graded beam. Applied Physics A, 123, 296. https://doi.org/10.1007/s00339-017-0854-0
Ameur, M., Tounsi, A., Mechab, I., & El Bedia, A. A. (2011). A new trigonometric shear deformation theory for bending analysis of functionally graded plates resting on elastic foundations. KSCE Journal of Civil Engineering, 15, 1405–1414. https://doi.org/10.1007/s12205-011-1361-z
Bellifa, H., Benrahou, K. H., Hadji, L., Houari, M. S. A., & Tounsi, A. (2016). Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38, 265–275. https://doi.org/10.1007/s40430-015-0354-0
Benmalek, H., Bouziane, S., & Bouzerd, H. (2021). Mixed finite element for the analysis of FGM beams. International Review of Mechanical Engineering (IREME), 15, 36–43. https://doi.org/10.15866/ireme.v15i1.19680
Benmalek, H., Bouziane, S., Bouzerd, H., & Remmani, S. A. (2023). Mixed finite element for crack analysis in functionally graded material. International Journal of Sustainable Construction Engineering and Technology, 14, 227–237.
Benmalek, H., Bouziane, S., Bouzerd, H., & Suleiman, H. (2024). Innovative mixed finite element method for bending analysis of functionally graded beams: Modelling, validation, and applications. Engineering Research Express. https://doi.org/10.1088/2631-8695/ad1f16
Bousahla, A. A., Houari, M. S. A., Tounsi, A., & Adda Bedia, E. A. (2013). A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates. International Journal of Computational Methods, 1, 1350082. https://doi.org/10.1142/S0219876213500825
Bouzerd, H. (1992). Mixed finite element for coherent or cracked interface. Thesis, Lyon 1.
Bouziane, S., Bouzerd, H., & Guenfoud, M. (2009). Mixed finite element for modelling interfaces. European Journal of Computational Mechanics, 18, 155–175. https://doi.org/10.3166/ejcm.18.155-175
Brischetto, S., & Carrera, E. (2010). Advanced mixed theories for bending analysis of functionally graded plates. Computers and Structures, 88, 1474–1483. https://doi.org/10.1016/j.compstruc.2008.04.004
Derouiche, S., Bouziane, S., & Bouzerd, H. (2021). mixed finite element computation of energy release rate in anisotropic materials based on virtual crack closure-integral method. Frattura Ed Integrita Strutturale, 15, 359–372. https://doi.org/10.3221/IGF-ESIS.57.26
Erdogan, F., & Wu, B. H. (1997). The surface crack problem for a plate with functionally graded properties. Journal of Applied Mechanics, 64, 449–456. https://doi.org/10.1115/1.2788914
Kaveh, A,. & Ebrahimi, E. (2012). Graph-theoretical force method of finite element models with triangular and rectangular elements.
Kaveh, A., & Bondarabady, H. R. (2002). A hybrid method for finite element ordering. Computers and Structures, 80, 219–225. https://doi.org/10.1016/S0045-7949(02)00018-4
Kaveh, A., & Koohestani, K. (2008). An efficient graph-theoretical force method for three-dimensional finite element analysis. Communications in Numerical Methods in Engineering, 24, 1533–1551. https://doi.org/10.1002/cnm.1051
Kim, J. H., & Paulino, G. H. (2002). Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials. Journal of Applied Mechanics, 69, 502–514. https://doi.org/10.1115/1.1467094
Kirlangiç, O., & Akbaş, ŞD. (2020). Comparison study between layered and functionally graded composite beams for static deflection and stress analyses. Journal of Computational Applied Mechanics, 51, 294–301.
Koutoati, K., Mohri, F., & Daya, E. M. (2019). Finite element approach of axial bending coupling on static and vibration behaviors of functionally graded material sandwich beams. Mechanics of Advanced Materials and Structures. https://doi.org/10.1080/15376494.2019.1685144
Kulkarni, K., Singh, B. N., & Maiti, D. K. (2015). Analytical solution for bending and buckling analysis of functionally graded plates using inverse trigonometric shear deformation theory. Composite Structures, 134, 147–157. https://doi.org/10.1016/j.compstruct.2015.08.060
Mantari, J. L., & Granados, E. V. (2015). A refined FSDT for the static analysis of functionally graded sandwich plates. Thin-Walled Structures, 90, 150–158. https://doi.org/10.1016/j.tws.2015.01.015
Martínez-Pañeda, E. (2019). On the finite element implementation of functionally graded materials. Materials, 12, 287. https://doi.org/10.3390/ma12020287
Mechab, I., Atmane, H. A., Tounsi, A., Belhadj, H. A., & Bedia, E. A. A. (2010). A two variable refined plate theory for the bending analysis of functionally graded plates. Acta Mechanica Sinica, 26, 941–949. https://doi.org/10.1007/s10409-010-0372-1
Minutolo, V., Ruocco, E., & Ciaramella, S. (2009). Isoparametric FEM vs. BEM for elastic functionally graded materials. CMES-Computer Modeling in Engineering and Sciences, 41, 27–48. https://doi.org/10.3970/cmes.2009.041.027
Nguyen, H. N., Hong, T. T., Vinh, P. V., & Thom, D. V. (2019). An efficient beam element based on quasi-3D theory for static bending analysis of functionally graded beams. Materials, 12, 2198. https://doi.org/10.3390/ma12132198
Orakdöğen, E., Küçükarslan, S., Sofiyev, A., & Omurtag, M. H. (2010). Finite element analysis of functionally graded plates for coupling effect of extension and bending. Meccanica, 45, 63–72. https://doi.org/10.1007/s11012-009-9225-z
Pandey, S., & Pradyumna, S. (2018). Analysis of functionally graded sandwich plates using a higher-order layerwise theory. Composites. Part B, Engineering, 153, 325–336. https://doi.org/10.1016/j.compositesb.2018.08.121
Rahmani, F., Kamgar, R., & Rahgozar, R. (2020). Finite element analysis of functionally graded beams using different beam theories. Civil Engineering Journal, 6, 2086–2102. https://doi.org/10.28991/cej-2020-03091604
Sami, D., Salah, B., & Hamoudi, B. (2021). Mixed finite element for kinking crack analysis in an orthotropic media. Procedia Structural Integrity, 33, 996–1006. https://doi.org/10.1016/j.prostr.2021.10.110
Thai, H. T., & Choi, D. H. (2013). A simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates. Composite Structures, 101, 332–340. https://doi.org/10.1016/j.compstruct.2013.02.019
Tran, T. T., Pham, Q. H., & Nguyen-Thoi, T. (2021). Static and free vibration analyses of functionally graded porous variable-thickness plates using an edge-based smoothed finite element method. Defence Technology. https://doi.org/10.1016/j.dt.2020.06.001
Van Long, N., Quoc, T. H., & Tu, T. M. (2016). Bending and free vibration analysis of functionally graded plates using new eight-unknown shear deformation theory by finite-element method. International Journal of Advanced Structural Engineering, 8, 391–399. https://doi.org/10.1007/s40091-016-0140-y
Xiang, S., & Kang, G. W. (2013). A nth-order shear deformation theory for the bending analysis on the functionally graded plates. European Journal of Mechanics A/Solids, 37, 336–343. https://doi.org/10.1016/j.euromechsol.2012.08.005
Zenkour, A. M. (2013a). A simple four-unknown refined theory for bending analysis of functionally graded plates. Applied Mathematical Modelling, 37, 9041–9051. https://doi.org/10.1016/j.apm.2013.04.022
Zenkour, A. M. (2013b). Bending analysis of functionally graded sandwich plates using a simple four-unknown shear and normal deformations theory. Journal of Sandwich Structures and Materials, 15, 629–656. https://doi.org/10.1177/1099636213498886
Zenkour, A. M., & Alghamdi, N. A. (2010). Bending analysis of functionally graded sandwich plates under the effect of mechanical and thermal loads. Mechanics of Advanced Materials and Structures, 17, 419–432. https://doi.org/10.1080/15376494.2010.483323
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1-Haroune Benmalek: Haroune Benmalek is the original writer of the research, bringing forth the foundational ideas and concepts. His dedication and expertise in the field have played a crucial role in shaping the research's direction and content. 2-Salah Bouziane: Salah Bouziane, as a supervisor, has played a crucial role in overseeing and guiding the research. His wealth of experience and knowledge in the field has been instrumental in ensuring the research adheres to high academic standards and contributes meaningfully to the body of knowledge. 3-Hamoudi Bouzerd: Hamoudi Bouzerd serves as a Co-supervisor, providing valuable guidance and insights throughout the research process. His expertise in the subject matter and dedication to academic excellence have played a pivotal role in shaping the research into a comprehensive and well-structured study. 4-Hisham Suleiman: Hisham Suleiman has significantly contributed to the research by providing corresponding and editing services. His meticulous attention to detail and commitment to ensuring the clarity and coherence of the manuscript have greatly enhanced the overall quality of the work. 5-Sid Ahmed Remmani: Sid Ahmed Remmani has contributed to the research by providing insightful revisions. His expertise and attention to detail have helped refine and strengthen the manuscript, ensuring that it meets the highest standards of scholarly excellence.
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Benmalek, H., Bouziane, S., Bouzerd, H. et al. Improved tensile analysis for functionally graded plates using an innovative mixed finite element method. Asian J Civ Eng (2024). https://doi.org/10.1007/s42107-024-01005-z
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DOI: https://doi.org/10.1007/s42107-024-01005-z