Journal of Applied and Computational Mechanics
Nonlinear Bending Analysis of Functionally Graded Plates Using SQ4T Elements based on Twice Interpolation Strategy
Document Type : Research Paper
Authors
1 Faculty of Civil Engineering, Ho Chi Minh City University of Technology and Education, 01 Vo Van Ngan Street, Thu Duc District, Ho Chi Minh City, Vietnam
2 Faculty of Civil Engineering, Ho Chi Minh City University of Architecture, 196 Pasteur Street, District 3, Ho Chi Minh City, Vietnam
Abstract
This paper develops a computational model for nonlinear bending analysis of functionally graded (FG) plates using a four-node quadrilateral element SQ4T within the context of the first order shear deformation theory (FSDT). In particular, the construction of the nonlinear geometric equations are based on Total Lagrangian approach in which the motion at the present state compared with the initial state is considered to be large. Small strain-large displacement theory of von Kármán is used in nonlinear formulations of the quadrilateral element SQ4T with twice interpolation strategy (TIS). The solution of the nonlinear equilibrium equations is obtained by the iterative method of Newton-Raphson with the appropriate convergence criteria. The present numerical results are compared with the other numerical results available in the literature in order to demonstrate the effectiveness of the developed element. These results also contribute a better knowledge and understanding of nonlinear bending behaviors of these structures.
Keywords
- Functionally graded material
- Nonlinear bending
- First-order shear deformation theory (FSDT)
- Twice interpolation strategy (TIS)
- Von Kármán theory
Main Subjects
[1] G. Udupa, S. S. Rao, and K. V. Gangadharan, Functionally Graded Composite Materials: An Overview, Procedia Materials Science, 5, 2014, 1291-1299.
[2] V.-H. Nguyen, T.-K. Nguyen, H.-T. Thai, and 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.
[3] T. Thai and D.-H. Choi, A simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates, Composite Structures, 101, 2013, 332-340.
[4] S. S. Vel and R. C. Batra, Exact Solution for Thermoelastic Deformations of Functionally Graded Thick Rectangular Plates, AIAA Journal, 40, 2002, 1421-1433.
[5] E. Carrera, S. Brischetto, and A. Robaldo, Variable Kinematic Model for the Analysis of Functionally Graded Material plates, AIAA Journal, 46, 2008, 194-203.
[6] G. N. Praveen and J. N. Reddy, Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates, International Journal of Solids and Structures, 35, 1998, 4457-4476.
[7] J. R. Xiao, R. C. Batra, D. F. Gilhooley, J. Gillespie Jr, and M. McCarthy, Analysis of thick plates by using a higher-order shear and normal deformable plate theory and MLPG method with radial basis functions, Computer Methods in Applied Mechanics and Engineering, 196, 2007, 979-987.
[8] A. M. A. Neves, A. J. M. Ferreira, E. Carrera, M. Cinefra, C. M. C. Roque, R. M. N. Jorge, et al., Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique, Composites Part B: Engineering, 44, 2013, 657-674.
[9] C. H. Thai, A. M. Zenkour, M. Abdel Wahab, and H. Nguyen-Xuan, A simple four-unknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric analysis, Composite Structures, 139, 2016, 77-95.
[10] X. Zhao and K. M. Liew, Geometrically nonlinear analysis of functionally graded plates using the element-free kp-Ritz method, Computer Methods in Applied Mechanics and Engineering, 198, 2009, 2796-2811.
[11] T. T. Yu, S. Yin, T. Q. Bui, and S. Hirose, A simple FSDT-based isogeometric analysis for geometrically nonlinear analysis of functionally graded plates, Finite Elements in Analysis and Design, 96, 2015, 1-10.
[12] T. Q. Bui, T. V. Do, L. H. T. Ton, D. H. Doan, S. Tanaka, D. T. Pham, et al., On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory, Composites Part B: Engineering, 92, 2016, 218-241.
[13] V. N. Van Do and C.-H. Lee, Nonlinear analyses of FGM plates in bending by using a modified radial point interpolation mesh-free method, Applied Mathematical Modelling, 57, 2018, 1-20.
[14] H. Nguyen-Van, N. Nguyen-Hoai, T. Chau-Dinh, and T. Nguyen-Thoi, Geometrically nonlinear analysis of composite plates and shells via a quadrilateral element with good coarse-mesh accuracy, Composite Structures, 112, 2014, 327-338.
[15] H. Nguyen-Van, N. Nguyen-Hoai, T. Chau-Dinh, and T. Tran-Cong, Large deflection analysis of plates and cylindrical shells by an efficient four-node flat element with mesh distortions, Acta Mechanica, 226, 2015, 2693-2713.
[16] L. T. That-Hoang, H. Nguyen-Van, T. Chau-Dinh, and C. Huynh-Van, Enhancement to four-node quadrilateral plate elements by using cell-based smoothed strains and higher-order shear deformation theory for nonlinear analysis of composite structures, Journal of Sandwich Structures & Materials, 2018, doi: 10.1177/1099636218797982.
[17] D. Jha, T. Kant, and R. Singh, A critical review of recent research on functionally graded plates, Composite Structures, 96, 2013, 833–849.
[18] H. Nguyen-Van, H. L. Ton-That, T. Chau-Dinh, and N. D. Dao, Nonlinear Static Bending Analysis of Functionally Graded Plates Using MISQ24 Elements with Drilling Rotations, in International Conference on Advances in Computational Mechanics Singapore, 2018, 461-475.
[19] H. L. Ton-That, H. Nguyen-Van, and T. Chau-Dinh, An Improved Four-Node Element for Analysis of Composite Plate/Shell Structures Based on Twice Interpolation Strategy, International Journal of Computational Methods, 2019, doi: 10.1142/S0219876219500208.
[20] J. S. Moita, A. L. Araújo, V. F. Correia, C. M. Mota Soares, and J. Herskovits, Buckling and nonlinear response of functionally graded plates under thermo-mechanical loading, Composite Structures, 202, 2018, 719-730.
[21] J. S.Moita, V. Franco Correia, C. M. Mota Soares, and J. Herskovits, Higher-order finite element models for the static linear and nonlinear behaviour of functionally graded material plate-shell structures, Composite Structures, 212, 2019, 465-475.
[22] N. Valizadeh, S. Natarajan, O. A. Gonzalez-Estrada, T. Rabczuk, T. Q. Bui, and S. P. A. Bordas, NURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter, Composite Structures, 99, 2013, 309-326.
[23] S. Shojaee and N. Valizadeh, NURBS-based isogeometric analysis for thin plate problems, Structural Engineering and Mechanics, 41, 2012, 617-632.
[24] S. Shojaee, N. Valizadeh, E. Izadpanah, T. Bui, and T.-V. Vu, Free vibration and buckling analysis of laminated composite plates using the NURBS-based isogeometric finite element method, Composite Structures, 94, 2012, 1677-1693.
[25] N. Nguyen-Thanh, N. Valizadeh, M. N. Nguyen, H. Nguyen-Xuan, X. Zhuang, P. Areias, et al., An extended isogeometric thin shell analysis based on Kirchhoff–Love theory, Computer Methods in Applied Mechanics and Engineering, 284, 2015, 265-291.
[26] P. K. Karsh, T. Mukhopadhyay, and S. Dey, Stochastic dynamic analysis of twisted functionally graded plates, Composites Part B: Engineering, 147, 2018, 259-278.
[27] P. K. Karsh, T. Mukhopadhyay, and S. Dey, Stochastic low-velocity impact on functionally graded plates: Probabilistic and non-probabilistic uncertainty quantification, Composites Part B: Engineering, 159, 2019, 461-480.
[28] L. W. Zhang, K. M. Liew, and J. N. Reddy, Geometrically nonlinear analysis of arbitrarily straight-sided quadrilateral FGM plates, Composite Structures, 154, 2016, 443-452.
[29] T. N. Nguyen, C. H. Thai, H. Nguyen-Xuan, and J. Lee, Geometrically nonlinear analysis of functionally graded material plates using an improved moving Kriging meshfree method based on a refined plate theory, Composite Structures, 193, 2018, 268-280.
[30] T. Quoc Bui, D. Quang Vo, Chuanzeng Zhang, and D. Dinh Nguyen, A consecutive-interpolation quadrilateral element (CQ4): Formulation and applications, Finite Elements in Analysis and Design, 84, 2014, 14-31.
[31] C. Zheng, S. C. Wu, X. H. Tang, and J. H. Zhang, A novel twice-interpolation finite element method for solid mechanics problems, Acta Mechanica Sinica, 26, 2010, 265-278.
[32] S. C. Wu, W. H. Zhang, X. Peng, and B. R. Miao, A twice-interpolation finite element method (TFEM) for crack propagation problems, International Journal of Computational Methods, 9, 2012, 1250055.
)
