Nonlinear dynamic analysis of functionally graded carbon nanotube-reinforced composite plates using MISQ20 element

Quoc-Hoa PHAM, Trung Thanh TRAN, Phu-Cuong NGUYEN

PDF(7521 KB)
PDF(7521 KB)
Front. Struct. Civ. Eng. ›› 2023, Vol. 17 ›› Issue (7) : 1072-1085. DOI: 10.1007/s11709-023-0951-4
RESEARCH ARTICLE

Nonlinear dynamic analysis of functionally graded carbon nanotube-reinforced composite plates using MISQ20 element

Author information +
History +

Abstract

The main objective of this study is to further extend the mixed integration smoothed quadrilateral element with 20 unknowns of displacement (MISQ20) to investigate the nonlinear dynamic responses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates with four types of carbon nanotube distributions. The smooth finite element method is used to enhance the accuracy of the Q4 element and avoid shear locking without using any shear correction factors. This method yields accurate results even if the element exhibits a concave quadrilateral shape and reduces the error when the element meshing is rough. Additionally, the element stiffness matrix is established by integrating the boundary of the smoothing domains. The motion equation of the FG-CNTRC plates is solved by adapting the Newmark method combined with the Newton–Raphson algorithm. Subsequently, the calculation program is coded in the MATLAB software and verified by comparing it with other published solutions. Finally, the effects of the input parameters on the nonlinear vibration of the plates are investigated.

Graphical abstract

Keywords

carbon nanotube / MISQ20 / FG-CNTRC plate / nonlinear vibration / nonlinear dynamic analysis / SFEM

Cite this article

Download citation ▾
Quoc-Hoa PHAM, Trung Thanh TRAN, Phu-Cuong NGUYEN. Nonlinear dynamic analysis of functionally graded carbon nanotube-reinforced composite plates using MISQ20 element. Front. Struct. Civ. Eng., 2023, 17(7): 1072‒1085 https://doi.org/10.1007/s11709-023-0951-4

References

[1]
Thostenson E T, Ren Z, Chou T W. Advances in the science and technology of carbon nanotubes and their composites: A review. Composites Science and Technology, 2001, 61(13): 1899–1912
CrossRef Google scholar
[2]
Fiedler B, Gojny F H, Wichmann M H G, Nolte M C M, Schulte K. Fundamental aspects of nano-reinforced composites. Composites Science and Technology, 2006, 66(3): 115–125
[3]
Cooper C A, Cohen S R, Barber A H, Wagner H D. Detachment of nanotubes from a polymer matrix. Applied Physics Letters, 2002, 81(20): 3873–3875
CrossRef Google scholar
[4]
Barber A H, Cohen S R, Wagner H D. Measurement of carbon nanotube–polymer interfacial strength. Applied Physics Letters, 2003, 82(4): 140–142
[5]
GouJMinaieBWangBLiangZZhangC. Computational and experimental study of interfacial bonding of single-walled nanotube reinforced composites. Computational Materials Science, 2004, 31(3−4): 225−236
[6]
Frankland S J V, Caglar A, Brenner D W, Griebel M. Molecular simulation of the influence of chemical cross-links on the shear strength of carbon nanotube polymer interfaces. Journal of Physical Chemistry B, 2002, 106(12): 3046–3048
CrossRef Google scholar
[7]
Ma P C, Mo S Y, Tang B Z, Kim J K. Dispersion, interfacial interaction and reagglomeration of functionalized carbon nanotubes in epoxy composites. Carbon, 2010, 48(6): 1824–1834
CrossRef Google scholar
[8]
Coleman J N, Khan U, Blau W J, Gun’ko Y K. Small but strong: A review of the mechanical properties of carbon nanotube–polymer composites. Carbon, 2006, 44(9): 1624–1652
CrossRef Google scholar
[9]
Wagner H D, Lourie O, Feldman Y, Tenne R. Stress-induced fragmentation of multiwall carbon nanotubes in a polymer matrix. Applied Physics Letters, 1998, 72(2): 188–190
CrossRef Google scholar
[10]
Qian D, Dickey E C, Andrews R, Rantell T. Load transfer and deformation mechanisms in carbon nanotube–polystyrene composites. Applied Physics Letters, 2000, 76(20): 2868–2870
CrossRef Google scholar
[11]
Odegard G M, Gates T S, Nicholson L M, Wise K E. Equivalent-continuum modeling of nano-structured materials. Composites Science and Technology, 2002, 62(14): 1869–1880
CrossRef Google scholar
[12]
Odegard G M, Gates T S, Wise K E, Park C, Siochi E J. Constitutive modeling of nanotube-reinforced polymer composites. Composites Science and Technology, 2003, 63(11): 1671–1687
CrossRef Google scholar
[13]
Liu Y J, Chen X L. Evaluations of the effective material properties of carbon nanotube-based composites using a nanoscale representative volume element. Mechanics of Materials, 2003, 35(1−2): 69–81
CrossRef Google scholar
[14]
Hu N, Fukunaga H, Lu C, Kameyama M, Yan B. Prediction of elastic properties of carbon nanotube reinforced composites. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2005, 461(2058): 1685–1710
CrossRef Google scholar
[15]
Frankland S J V, Harik V M, Odegard G M, Brenner D W, Gates T S. The stress–strain behaviour of polymer–nanotube composites from molecular dynamics simulation. Composites Science and Technology, 2003, 63(11): 1655–1661
CrossRef Google scholar
[16]
Griebel M, Hamaekers J. Molecular dynamics simulations of the elastic moduli of polymer–carbon nanotube composites. Computer Methods in Applied Mechanics and Engineering, 2004, 193(17−20): 1773–1788
CrossRef Google scholar
[17]
Wernik J M, Meguid S A. Multiscalemodeling of the nonlinear response of nanoreinforced polymers. Acta Mechanica, 2011, 217(1−2): 1–16
CrossRef Google scholar
[18]
Wuite J, Adali S. Deflection and stress behaviour of nanocomposite reinforced beams using a multiscale analysis. Composite Structures, 2005, 71(3−4): 388–396
CrossRef Google scholar
[19]
Vodenitcharova T, Zhang L C. Bending and local buckling of a nanocomposite beam reinforced by a single-walled carbon nanotube. International Journal of Solids and Structures, 2006, 43(10): 3006–3024
CrossRef Google scholar
[20]
Ray M C, Batra R C. A single-walled carbon nanotube reinforced 1–3 piezoelectric composite for active control of smart structures. Smart Materials and Structures, 2007, 16(5): 1936–1947
CrossRef Google scholar
[21]
Formica G, Lacarbonara W, Alessi R. Vibrations of carbon nanotube-reinforced composites. Journal of Sound and Vibration, 2010, 329(10): 1875–1889
CrossRef Google scholar
[22]
Arani A, Maghamikia S, Mohammadimehr M, Arefmanesh A. Buckling analysis of laminated composite rectangular plates reinforced by SWCNTS using analytical and finite element methods. Journal of Mechanical Science and Technology, 2011, 25(3): 809–820
CrossRef Google scholar
[23]
Shen S H. Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Composite Structures, 2009, 91(1): 9–19
CrossRef Google scholar
[24]
Wang Z X, Shen H S. Nonlinear vibration of nanotube-reinforced composite plates in thermal environments. Computational Materials Science, 2011, 50(8): 2319–2330
CrossRef Google scholar
[25]
Wang Z X, Shen H S. Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets. Composites. Part B, Engineering, 2011, 43(2): 411–421
CrossRef Google scholar
[26]
Zhang L, Cui W, Liew K. Vibration analysis of functionally graded carbon nanotube reinforced composite thick plates with elastically restrained edges. International Journal of Mechanical Sciences, 2015, 103: 9–21
CrossRef Google scholar
[27]
Natarajan S, Haboussi M, Manickam G. Application of higher-order structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite facesheets. Composite Structures, 2014, 113: 197–207
CrossRef Google scholar
[28]
Sankar A, Natarajan S, Haboussi M, Ramajeyathilagam K, Ganapathi M. Panel flutter characteristics of sandwich plates with CNT reinforced facesheets using an accurate higher-order theory. Journal of Fluids and Structures, 2014, 50: 376–391
CrossRef Google scholar
[29]
Sankar A, Natarajan S, Zineb T B, Ganapathi M. Investigation of supersonic flutter of thick doubly curved sandwich panels with CNT reinforced facesheets using higher-order structural theory. Composite Structures, 2015, 127: 340–355
CrossRef Google scholar
[30]
Sankar A, Natarajan S, Merzouki T, Ganapathi M. Nonlinear dynamic thermal buckling of sandwich spherical and conical shells with CNT reinforced facesheets. International Journal of Structural Stability and Dynamics, 2017, 17(9): 1750100
CrossRef Google scholar
[31]
Rodrigues J, Natarajan S, Ferreira A, Carrera E, Cinefra M, Bordas S. Analysis of composite plates through cell-based smoothed finite element and 4-noded mixed interpolation of tensorial components techniques. Computers & Structures, 2014, 135: 83–87
CrossRef Google scholar
[32]
HughesT J RCottrellJ ABazilevsY. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 2005, 194(39−41): 4135−4195
[33]
BordenM JScottM AEvamsJ AHughesT J R. Isogeometric finite element data structures based on Bezier extraction of NURBS. International Journal for Numerical Methods in Engineering, 2011, 87 (1−5): 15−47
[34]
Phung-Van P, Thai C H, Nguyen-Xuan H, Abdel-Wahab M. An isogeometric approach of static and free vibration analyses for porous FG nanoplates. European Journal of Mechanics. A, Solids, 2019, 78: 103851
CrossRef Google scholar
[35]
Thanh C L, Nguyen T N, Vu T H, Khatir S, Abdel Wahab M. A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate. Engineering with Computers, 2022, 38(Suppl 1): 449–460
CrossRef Google scholar
[36]
Cuong-Le T, Nguyen K D, Hoang-Le M, Sang-To T, Phan-Vu P, Wahab M A. Nonlocal strain gradient IGA numerical solution for static bending, free vibration and buckling of sigmoid FG sandwich nanoplate. Physica B, Condensed Matter, 2022, 631: 413726
CrossRef Google scholar
[37]
PhamQ HNguyenP CTranV KLieuQ XTranT T. Modified nonlocal couple stress isogeometric approach for bending and free vibration analysis of functionally graded nanoplates. Engineering with Computers, 2022: 1−26
[38]
Pham Q H, Nguyen P C, Tran T T. Dynamic response of porous functionally graded sandwich nanoplates using nonlocal higher-order isogeometric analysis. Composite Structures, 2022, 290: 115565
CrossRef Google scholar
[39]
Guo H, Zheng H. The linear analysis of thin shell problems using the numerical manifold method. Thin-walled Structures, 2018, 124: 366–383
CrossRef Google scholar
[40]
Guo H, Zheng H, Zhuang X. Numerical manifold method for vibration analysis of Kirchhoff’s plates of arbitrary geometry. Applied Mathematical Modelling, 2019, 66: 695–727
CrossRef Google scholar
[41]
Zhuang X, Guo H, Alajlan N, Zhu H, Rabczuk T. Deep autoencoder based energy method for the bending, vibration, and buckling analysis of Kirchhoff plates with transfer learning. European Journal of Mechanics. A, Solids, 2021, 87: 104225
CrossRef Google scholar
[42]
Guo H, Zhuang X, Rabczuk T. A deep collocation method for the bending analysis of Kirchhoff plate. Computers Materials & Continua, 2021, 59(2): 433–456
[43]
Samaniego E, Anitescu C, Goswami S, Nguyen-Thanh V M, Guo H, Hamdia K, Zhuang X, Rabczuk T. An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications. Computer Methods in Applied Mechanics and Engineering, 2020, 362: 112790
CrossRef Google scholar
[44]
Ganapathi M, Varadan T K, Sarma B S. Nonlinear flexural vibrations of laminated orthotropic plates. Computers & Structures, 1991, 39(6): 685–688
CrossRef Google scholar
[45]
Kant T, Kommineni J R. Large amplitude free vibration analysis of cross-ply composite and sandwich laminates with a refined theory and C0 finite elements. Computers & Structures, 1994, 50(1): 123–134
[46]
AnilK D. Large amplitude free vibration analysis of composite plates by finite element method. Thesis for the Master’s Degree. Rourkela: National Institute of Technology, 2010
[47]
JavedA. Dynamic stability of delaminated cross ply composite plates and shells. International Journal of Mechanical Sciences, 1998, 40(8): 805–823
[48]
Parhi P K, Bhattacharyya S K, Sinha P K. Hygrothermal effects on the dynamic behaviour of multiple delamated composite plates and shells. Journal of Sound and Vibration, 2001, 248(2): 195–214
CrossRef Google scholar
[49]
Providas E, Kattis M A. An assessment of two fundamental flat triangular shell elements with drilling rotations. Computers & Structures, 2000, 77(2): 129–139
CrossRef Google scholar
[50]
Groenwold A A, Slander N. An efficient 4-node 24 DOF thick shell finite element with 5-point quadrature. Engineering Computations, 1995, 12(8): 723–747
CrossRef Google scholar
[51]
Choi C K, Lee T Y. Efficient remedy for membrane locking of 4-node flat shell elements by non-conforming modes. Computer Methods in Applied Mechanics and Engineering, 2003, 192(16–18): 1961–1971
CrossRef Google scholar
[52]
Pimpinelli G. An assumed strain quadrilateral element with drilling degrees of freedom. Finite Elements in Analysis and Design, 2004, 41(3): 267–283
CrossRef Google scholar
[53]
Thai-Hoang C, Nguyen-Thanh N, Nguyen-Xuan H, Rabczuk T. An alternative alpha finite element method with discrete shear gap technique for analysis of laminated composite plates. Applied Mathematics and Computation, 2011, 217(17): 7324–7348
CrossRef Google scholar
[54]
Phan-Dao H, Nguyen-Xuan H, Thai-Hoang C, Nguyen-Thoi T, Rabczuk T. An edge-based smoothed finite element method for analysis of laminated composite plates. International Journal of Computational Methods, 2013, 10(1): 1340005
CrossRef Google scholar
[55]
Nguyen-Thanh N, Rabczuk T, Nguyen-Xuan H, Bordas S. A smoothed finite element method for shell analysis. Computer Methods in Applied Mechanics and Engineering, 2008, 198(2): 165–177
CrossRef Google scholar
[56]
Nguyen-XuanHRabczukTBordasSDebongnieJ F. A smoothed finite element method for plate analysis. Computer Methods in Applied Mechanics and Engineering, 2008, 197(13−16): 1184−1203
[57]
Shen H S. Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially loaded shells. Composite Structures, 2011, 93(8): 2096–2108
CrossRef Google scholar
[58]
Nguyen-Van H, Nguyen-Hoai N, Chau-Dinh T, Nguyen-Thoi T. Geometrically nonlinear analysis of composite plates and shells via a quadrilateral element with good coarse-mesh accuracy. Composite Structures, 2014, 112: 327–338
CrossRef Google scholar
[59]
ReddyJ N. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. Boca Raton: CRC Press, 2004
[60]
ChopraA K. Dynamics of Structures: Theory and Applications to Earthquake Engineering. Upper Saddle River: Pearson Prentice Hall, 2007
[61]
Nguyen P C, Kim S E. Investigating effects of various base restraints on the nonlinear inelastic static and seismic responses of steel frames. International Journal of Non-linear Mechanics, 2017, 89: 151–167
CrossRef Google scholar
[62]
TranTTPhamQHNguyen-ThoiT. Dynamic analysis of sandwich auxetic honeycomb plates subjected to moving oscillator load on elastic foundation. Advances in Materials Science and Engineering, 2020, 6309130
[63]
Nguyen H N, Canh T N, Thanh T T, Ke T V, Phan V D, Thom D V. Finite element modelling of a composite shell with shear connectors. Symmetry, 2019, 11(4): 527
CrossRef Google scholar
[64]
Tran T T, Tran V K, Le P B, Phung V M, Do V T, Nguyen H N. Forced vibration analysis of laminated composite shells reinforced with graphene nanoplatelets using finite element method. Advances in Civil Engineering, 2020, 2020: 1471037
CrossRef Google scholar
[65]
Reddy J. Analysis of functionally graded plates. International Journal for Numerical Methods in Engineering, 2000, 47(1–3): 663–684
CrossRef Google scholar
[66]
Sundararajan N, Prakash T, Ganapathi M. Nonlinear free exural vibrations of functionally graded rectangular and skew plates under thermal environments. Finite Elements in Analysis and Design, 2005, 42(2): 152–168
CrossRef Google scholar
[67]
Balamurugan V, Ganapathi M, Varadan T. Nonlinear dynamic instability of laminated composite plates using finite element method. Computers & Structures, 1996, 60(1): 125–130
CrossRef Google scholar
[68]
Phung-Van P, Abdel-Wahab M, Liew K, Bordas S, Nguyen-Xuan H. Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory. Composite Structures, 2015, 123: 137–149
CrossRef Google scholar

Conflict of Interest

The authors declare that they have no conflict of interest.

RIGHTS & PERMISSIONS

2023 Higher Education Press
AI Summary AI Mindmap
PDF(7521 KB)

Accesses

Citations

Detail

Sections
Recommended

/