Static bending analysis of functionally graded material sandwich plates using a finite element method
Email:
tuanmanhvkt123@gmail.com
Keywords:
Sandwich plates, functionally graded material, Q4 element, TSDT
Abstract
The functionally graded material (FGM) is increasingly widely applied in many engineering fields such as civil construction, aerospace, nuclear technology, and so on. Therefore, studying the mechanical behaviour of FGM sandwich structures is of interest to many domestic and foreign scientists. The main goal of this paper is to use the quadrilateral (Q4) element based on Shi’s third-order shear deformation plate theory (TSDT) for the static analysis of FGM sandwich plates. The proposed element with seven degrees of freedom (DOFs) per node is based on combining the Lagrange interpolations and the Hermit interpolations for establishing the governing equation of the FGM sandwich plate. This combination helps satisfy the zero-shear stress condition at the top and bottom surfaces of the plate. The accuracy and effectiveness of the proposed method are verified through comparative examples. Then, the effects of geometrical dimensions and material properties on the static response of FGM sandwich plates are studied in detailReferences
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[10]. A. Zenkour, A comprehensive analysis of functionally graded sandwich plates: Part 1–Deflection and stresses, International journal of solids and structures, 42 (2005) 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015
[11]. A.M. Zenkour, The effect of transverse shear and normal deformations on the thermomechanical bending of functionally graded sandwich plates, International Journal of Applied Mechanics, 1 (2009) 667-707. https://doi.org/10.1142/S1758825109000368
[12]. A.A. Daikh, A.M. Zenkour, Free vibration and buckling of porous power-law and sigmoid functionally graded sandwich plates using a simple higher-order shear deformation theory, Materials Research Express, 6 (2019) 115707. https://doi.org/10.1088/2053-1591/ab48a9
[13]. A.A. Daikh, A.M. Zenkour, Effect of porosity on the bending analysis of various functionally graded sandwich plates, Materials Research Express, 6 (2019) 065703. https://doi.org/10.1088/2053-1591/ab0971
[14]. H.-T. Thai, T.-K. Nguyen, T.P. Vo, J. Lee, Analysis of functionally graded sandwich plates using a new first-order shear deformation theory, European Journal of Mechanics-A/Solids, 45 (2014) 211-225. https://doi.org/10.1016/j.euromechsol.2013.12.008
[15]. Shi G, A new simple third-order shear deformation theory of plates, International Journal of Solids and Structures, 44 (2007) 4399-4417. https://doi.org/10.1016/j.ijsolstr.2006.11.031
[16]. T. H. Nguyen, T.T. Nguyen, T.T. Tran, Q. H. Pham, Research on the mechanical behaviour of functionally graded porous sandwich plates using a new C1 finite element procedure, Results in Engineering, 17 (2023) 100817. https://doi.org/10.1016/j.rineng.2022.100817
[17]. N. Vasiraja, P. Nagaraj, The effect of material gradient on the static and dynamic response of layered functionally graded material plate using finite element method, Bulletin of the Polish Academy of Sciences: Technical Sciences, 67 (2019) 827-838. https://doi.org/10.24425/bpasts.2019.130191
[2]. M. Asghari, M. Ahmadian, M. Kahrobaiyan, M. Rahaeifard, On the size-dependent behavior of functionally graded micro-beams, Materials & Design (1980-2015), 31 (2010) 2324-2329. https://doi.org/10.1016/j.matdes.2009.12.006
[3]. L.C. Trinh, T.P. Vo, A.I. Osofero, J. Lee, Fundamental frequency analysis of functionally graded sandwich beams based on the state space approach, Composite Structures, 156 (2016) 263-275. https://doi.org/10.1016/j.compstruct.2015.11.010
[4]. J. Reddy, Analysis of functionally graded plates, International Journal for numerical methods in engineering, 47 (2000) 663-684. https://doi.org/10.12989/anr.2021.11.1.055
[5]. Luat DT, Van Thom D, Thanh TT, Van Minh P, Van Ke T, Van Vinh P, Mechanical analysis of bi-functionally graded sandwich nanobeams, Advances in nano research, 11 (2021) 55-71. https://doi.org/10.12989/anr.2021.11.1.055
[6]. V.-H. Nguyen, T.-K. Nguyen, H.-T. Thai, T.P. Vo, A new inverse trigonometric shear deformation theory for isotropic and functionally graded sandwich plates, Composites Part B: Engineering, 66 (2014) 233-246. https://doi.org/10.1016/j.compositesb.2014.05.012
[7]. F. Tornabene, Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution, Computer Methods in Applied Mechanics and Engineering, 198 (2009) 2911-2935. https://doi.org/10.1016/j.cma.2009.04.011
[8]. J. L. Mantari, Refined and generalized hybrid type quasi-3d shear deformation theory for the bending analysis of functionally graded shells, Composites Part B: Engineering, 83 (2015) 142–152. https://doi.org/10.1016/j.compositesb.2015.08.048
[9]. J. Torabi, Y. Kiani, M. R. Eslami, Linear thermal buckling analysis of truncated hybrid FGM conical shells, Composites Part B: Engineering, 50 (2013) 265–272. https://doi.org/10.1016/j.compositesb.2013.02.025
[10]. A. Zenkour, A comprehensive analysis of functionally graded sandwich plates: Part 1–Deflection and stresses, International journal of solids and structures, 42 (2005) 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015
[11]. A.M. Zenkour, The effect of transverse shear and normal deformations on the thermomechanical bending of functionally graded sandwich plates, International Journal of Applied Mechanics, 1 (2009) 667-707. https://doi.org/10.1142/S1758825109000368
[12]. A.A. Daikh, A.M. Zenkour, Free vibration and buckling of porous power-law and sigmoid functionally graded sandwich plates using a simple higher-order shear deformation theory, Materials Research Express, 6 (2019) 115707. https://doi.org/10.1088/2053-1591/ab48a9
[13]. A.A. Daikh, A.M. Zenkour, Effect of porosity on the bending analysis of various functionally graded sandwich plates, Materials Research Express, 6 (2019) 065703. https://doi.org/10.1088/2053-1591/ab0971
[14]. H.-T. Thai, T.-K. Nguyen, T.P. Vo, J. Lee, Analysis of functionally graded sandwich plates using a new first-order shear deformation theory, European Journal of Mechanics-A/Solids, 45 (2014) 211-225. https://doi.org/10.1016/j.euromechsol.2013.12.008
[15]. Shi G, A new simple third-order shear deformation theory of plates, International Journal of Solids and Structures, 44 (2007) 4399-4417. https://doi.org/10.1016/j.ijsolstr.2006.11.031
[16]. T. H. Nguyen, T.T. Nguyen, T.T. Tran, Q. H. Pham, Research on the mechanical behaviour of functionally graded porous sandwich plates using a new C1 finite element procedure, Results in Engineering, 17 (2023) 100817. https://doi.org/10.1016/j.rineng.2022.100817
[17]. N. Vasiraja, P. Nagaraj, The effect of material gradient on the static and dynamic response of layered functionally graded material plate using finite element method, Bulletin of the Polish Academy of Sciences: Technical Sciences, 67 (2019) 827-838. https://doi.org/10.24425/bpasts.2019.130191
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Received
20/12/2023
Revised
02/03/2023
Accepted
31/03/2024
Published
15/04/2024
Type
Research Article
How to Cite
Dương Mạnh, T. (1713114000). Static bending analysis of functionally graded material sandwich plates using a finite element method . Transport and Communications Science Journal, 75(3), 1359-1373. https://doi.org/10.47869/tcsj.75.3.4
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