The Linear and Nonlinear Bending Analyses of Functionally Graded Carbon Nanotube-Reinforced Composite Plates Based on the Novel Four-Node Quadrilateral Element

Authors

  • Hoang Lan Ton-That Faculty of Civil Engineering, Ho Chi Minh City University of Architecture, 196 Pasteur Street, District 3, Ho Chi Minh City, Viet Nam https://orcid.org/0000-0002-3544-917X

DOI:

https://doi.org/10.13052/ejcm2642-2085.2915

Keywords:

Linear and nonlinear bending, Shi theory, C0 type, four-node quadrilateral element

Abstract

This paper presents the linear and nonlinear analyses of functionally graded carbon nanotube- reinforced composite (FG-CNTRC) plates using a four-node quadrilateral element based on the C0-type of Shi’s third-order shear deformation theory (C0-STSDT). Shi’s theory is taking the advantages and desirable properties of the third-order shear deformation theory. Besides, material properties of FG-CNTRC plates are changed from the bottom to top surface and based on the rule of mixture. Numerical results and comparison with other reference solutions suggest that the advantages of present element are accuracy and efficiency in analysis of FG-CNTRC plates. Some nonlinear numerical results of FG-CNTRC plates are also given in this paper and this contributes to providing additional data for future research work.

Downloads

Download data is not yet available.

Author Biography

Hoang Lan Ton-That, Faculty of Civil Engineering, Ho Chi Minh City University of Architecture, 196 Pasteur Street, District 3, Ho Chi Minh City, Viet Nam

Hoang Lan Ton-That, an assistant professor, is a lecturer at the Ho Chi Minh City University of Architecture, Vietnam since summer 2003. He is also a visiting lecturer for universities in the south of Vietnam. He has obtained scientific degree at the University of Liege, Belgium. His areas of expertise include computational mechanics, meshfree methods, fracture mechanics, static, dynamic and buckling analysis of plate/shell structures, and smart materials.

References

P. J. F. Harris, “Carbon Nanotubes and Related Structures: New Materials for the Twenty-First Century,” American Journal of Physics, vol. 72, pp. 415–415, 2004.

S. Iijima, “Helical microtubules of graphitic carbon,” Nature, vol. 354, pp. 56–58, 1991.

Y. Han and J. Elliott, “Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites,” Computational Materials Science, vol. 39, pp. 315–323, 2007.

J. N. Coleman, U. Khan, W. J. Blau, and Y. K. Gun’ko, “Small but strong: A review of the mechanical properties of carbon nanotube–polymer composites,” Carbon, vol. 44, pp. 1624–1652, 2006.

M. M. Shokrieh and R. Rafiee, “A review of the mechanical properties of isolated carbon nanotubes and carbon nanotube composites,” Mechanics of Composite Materials, vol. 46, pp. 155–172, 2010.

A. K.-T. Lau and D. Hui, “The revolutionary creation of new advanced materials—carbon nanotube composites,” Composites Part B: Engineering, vol. 33, pp. 263–277, 2002.

E. Providas and M. A. Kattis, “An assessment of two fundamental flat triangular shell elements with drilling rotations,” Comput Struct, vol. 77, pp. 129–139, 2000.

C.-K. Choi and T.-Y. Lee, “Efficient remedy for membrane locking of 4-node flat shell elements by non-conforming modes,” Comput Method Appl M, vol. 192, pp. 1961–1971, 2003.

H. T. Y. Yang, S. Saigal, A. Masud, and R. K. Kapania, “A survey of recent shell finite elements,” Int J Numer Meth Eng, vol. 47, pp. 101–127, 2000.

A. W. Leissa, “A Review of Laminated Composite Plate Buckling,” Appl Mech Rev, vol. 40, pp. 575–591, 1987.

M. Aydogdu, “Comparison of Various Shear Deformation Theories for Bending, Buckling, and Vibration of Rectangular Symmetric Cross-ply Plate with Simply Supported Edges,” J Compos Mater, vol. 40, pp. 2143–2155, 2006.

K. M. Liew, K. C. Hung, and M. K. Lim, “Three-dimensional vibration of rectangular plates : Variance of simple support conditions and influence of in-plane inertia,” Int J Solids Struct, vol. 31, pp. 3233–3247, 1994.

K. M. Liew, K. C. Hung, and M. K. Lim, “Three-dimensional vibration of rectangular plates: Effects of thickness and edge constraints,” J Sound Vib, vol. 182, pp. 709–727, 1995.

P.-S. Lee and K.-J. Bathe, “The quadratic MITC plate and MITC shell elements in plate bending,” Adv Eng Softw, vol. 41, pp. 712–728, 2010.

C. H. Thai, A. J. M. Ferreira, S. P. A. Bordas, T. Rabczuk, and H. Nguyen-Xuan, “Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory,” Eur J Mech A-Solid, vol. 43, pp. 89–108, 2014.

C. H. Thai, L. V. Tran, D. T. Tran, T. Nguyen-Thoi, and H. Nguyen-Xuan, “Analysis of laminated composite plates using higher-order shear deformation plate theory and node-based smoothed discrete shear gap method,” Appl Math Model, vol. 36, pp. 5657–5677, 2012.

C. Thai-Hoang, N. Nguyen-Thanh, H. Nguyen-Xuan, and T. Rabczuk, “An alternative alpha finite element method with discrete shear gap technique for analysis of laminated composite plates,” Appl Math Comput, vol. 217, pp. 7324–7348, 2011.

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, vol. 22, pp. 2302–2329, 2018.

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, vol. 92, pp. 218–241, 2016.

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, vol. 17, 1950020, 2019.

H. L. Ton That, H. Nguyen-Van, and T. Chau-Dinh, “Nonlinear Bending Analysis of Functionally Graded Plates Using SQ4T Elements based on Twice Interpolation Strategy,” Journal of Applied and Computational Mechanics, vol. 6, pp. 125–136, 2020.

H. L. Ton-That, “Finite Element Analysis of Functionally Graded Skew Plates in Thermal Environment based on the New Third-order Shear Deformation Theory,” Journal of Applied and Computational Mechanics, vol. 6, pp. 1044–1057, 2020.

H. L. Ton-That, “Improvement on eight-node quadrilateral element (IQ8) using twice-interpolation strategy for linear elastic fracture mechanics,” Engineering Solid Mechanics, vol. 8, pp. 323–336, 2020.

S. Ahmad, B. M. Irons, and O. C. Zienkiewicz, “Analysis of thick and thin shell structures by curved finite elements,” International Journal for Numerical Methods in Engineering, vol. 2, pp. 419–451, 1970.

T. J. R. Hughes and E. Carnoy, “Nonlinear finite element shell formulation accounting for large membrane strains,” Computer Methods in Applied Mechanics and Engineering, vol. 39, pp. 69–82, 1983.

H. L. Ton That, “A Novel Quadrilateral Element for Dynamic Response of Plate ?Structures Subjected to Blast Loading,” Journal of Applied and Computational Mechanics, 2020.

J. Argyris and L. Tenek, “Linear and geometrically nonlinear bending of isotropic and multilayered composite plates by the natural mode method,” Computer Methods in Applied Mechanics and Engineering, vol. 113, pp. 207–251, 1994.

F. van Keulen, “A geometrically nonlinear curved shell element with constant stress resultants,” Computer Methods in Applied Mechanics and Engineering, vol. 106, pp. 315–352, 1993.

C. Sansour and H. Bednarczyk, “The Cosserat surface as a shell model, theory and finite-element formulation,” Computer Methods in Applied Mechanics and Engineering, vol. 120, pp. 1–32, 1995.

A. Kamoulakos, “Understanding and improving the reduced integration of Mindlin shell elements,” International Journal for Numerical Methods in Engineering, vol. 26, pp. 2009–2029, 1988.

W. K. Liu, Y.-K. Hu, and T. Belytschko, “Multiple quadrature underintegrated finite elements,” International Journal for Numerical Methods in Engineering, vol. 37, pp. 3263–3289, 1994.

X. Hu, T. Q. Bui, J. Wang, W. Yao, L. H. T. Ton, I. V. Singh, et al., “A new cohesive crack tip symplectic analytical singular element involving plastic zone length for fatigue crack growth prediction under variable amplitude cyclic loading,” European Journal of Mechanics - A/Solids, vol. 65, pp. 79–90, 2017.

J. C. Simo and M. S. Rifai, “A class of mixed assumed strain methods and the method of incompatible modes,” International Journal for Numerical Methods in Engineering, vol. 29, pp. 1595–1638, 1990.

J. C. Simo, F. Armero, and R. L. Taylor, “Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems,” Computer Methods in Applied Mechanics and Engineering, vol. 110, pp. 359–386, 1993.

H. Parisch, “An investigation of a finite rotation four node assumed strain shell element,” International Journal for Numerical Methods in Engineering, vol. 31, pp. 127–150, 1991.

J. Jang and P. M. Pinsky, “Convergence of curved shell elements based on assumed covariant strain interpolations,” International Journal for Numerical Methods in Engineering, vol. 26, pp. 329–347, 1988.

H. L. Ton-That and H. Nguyen-Van, “A Combined Strain Element in Static, Frequency and Buckling Analyses of Laminated Composite Plates and Shells,” Periodica Polytechnica Civil Engineering, 2020.

T. Kant, S. Kumar, and U. P. Singh, “Shell dynamics with three-dimensional degenerate finite elements,” Computers & Structures, vol. 50, pp. 135–146, 1994.

F. Gruttmann and W. Wagner, “Coupling of two- and three-dimensional composite shell elements in linear and non-linear applications,” Computer Methods in Applied Mechanics and Engineering, vol. 129, pp. 271–287, 1996.

A. Ibrahimbegoviæ and F. Frey, “Stress resultant geometrically nonlinear shell theory with drilling rotations—Part II. Computational aspects,” Computer Methods in Applied Mechanics and Engineering, vol. 118, pp. 285–308, 1994.

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,” International Conference on Advances in Computational Mechanics, Singapore, pp. 461–475, 2018.

H. L. Ton-That;, H. Nguyen-Van;, and T. Chau-Dinh, “Static and buckling analyses of stiffened plate/shell structures using the quadrilateral element SQ4C,” Comptes Rendus. Mécanique, vol. 348, pp. 285–305, 2020.

L. Jiang, M. W. Chernuka, and N. G. Pegg, “A co-rotational, updated Lagrangian formulation for geometrically nonlinear finite element analysis of shell structures,” Finite Elements in Analysis and Design, vol. 18, pp. 129–140, 1994.

G. F. Moita and M. A. Crisfield, “A finite element formulation for 3-D continua using the co-rotational technique,” International Journal for Numerical Methods in Engineering, vol. 39, pp. 3775–3792, 1996.

C. L. Liao and J. N. Reddy, “Continuum-based stiffened composite shell element for geometrically nonlinear analysis,” AIAA Journal, vol. 27, pp. 95–101, 1989.

W. C. Chao and J. N. Reddy, “Analysis of laminated composite shells using a degenerated 3-D element,” International Journal for Numerical Methods in Engineering, vol. 20, pp. 1991–2007, 1984.

G. Shi, “A new simple third-order shear deformation theory of plates,” International Journal of Solids and Structures, vol. 44, pp. 4399–4417, 2007.

S. Imani Yengejeh, S. A. Kazemi, and A. Öchsner, “Carbon nanotubes as reinforcement in composites: A review of the analytical, numerical and experimental approaches,” Computational Materials Science, vol. 136, pp. 85–101, 2017.

F. T. Fisher, R. D. Bradshaw, and L. C. Brinson, “Fiber waviness in nanotube-reinforced polymer composites—I: Modulus predictions using effective nanotube properties,” Composites Science and Technology, vol. 63, pp. 1689–1703, 2003.

H.-S. Shen, “Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments,” Composite Structures, vol. 91, pp. 9–19, 2009.

S. Sharma, R. Chandra, P. Kumar, and N. Kumar, “Molecular dynamics simulation of polymer/carbon nanotube composites,” Acta Mechanica Solida Sinica, vol. 28, pp. 409–419, 2015.

P. Zhu, Z. X. Lei, and K. M. Liew, “Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory,” Composite Structures, vol. 94, pp. 1450–1460, 2012.

T. Truong-Thi, T. Vo-Duy, V. Ho-Huu, and T. Nguyen-Thoi, “Static and Free Vibration Analyses of Functionally Graded Carbon Nanotube Reinforced Composite Plates using CS-DSG3,” International Journal of Computational Methods, vol. 17, 1850133, 2020.

P. Phung-Van, M. Abdel-Wahab, K. M. Liew, S. P. A. Bordas, and H. Nguyen-Xuan, “Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory,” Composite Structures, vol. 123, pp. 137–149, 2015.

A. Alibeigloo and A. Emtehani, “Static and free vibration analyses of carbon nanotube-reinforced composite plate using differential quadrature method,” Meccanica, vol. 50, pp. 61–76, 2015.

Published

2020-11-30

How to Cite

Ton-That, H. L. (2020). The Linear and Nonlinear Bending Analyses of Functionally Graded Carbon Nanotube-Reinforced Composite Plates Based on the Novel Four-Node Quadrilateral Element. European Journal of Computational Mechanics, 29(1), 139–172. https://doi.org/10.13052/ejcm2642-2085.2915

Issue

Section

Original Article