On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams

- Journal title : Steel and Composite Structures
- Volume 19, Issue 5, 2015, pp.1259-1277
- Publisher : Techno-Press
- DOI : 10.12989/scs.2015.19.5.1259

Title & Authors

On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams

Tagrara, S.H.; Benachour, Abdelkader; Bouiadjra, Mohamed Bachir; Tounsi, Abdelouahed;

Tagrara, S.H.; Benachour, Abdelkader; Bouiadjra, Mohamed Bachir; Tounsi, Abdelouahed;

Abstract

In this work, a trigonometric refined beam theory for the bending, buckling and free vibration analysis of carbon nanotube-reinforced composite (CNTRC) beams resting on elastic foundation is developed. The significant feature of this model is that, in addition to including the shear deformation effect, it deals with only 3 unknowns as the Timoshenko beam (TBM) without including a shear correction factor. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in polymeric matrix with different patterns of reinforcement. The material properties of the CNTRC beams are assessed by employing the rule of mixture. To examine accuracy of the present theory, several comparison studies are investigated. Furthermore, the effects of different parameters of the beam on the bending, buckling and free vibration responses of CNTRC beam are discussed.

Keywords

CNTRC beams;bending;buckling;free vibration;elastic foundation;

Language

English

Cited by

1.

Thermal post-buckling behavior of imperfect temperature-dependent sandwich FGM plates resting on Pasternak elastic foundation,;;;;

2.

A refined theory with stretching effect for the flexure analysis of laminated composite plates,;;;

3.

Buckling analysis of nanocomposite cut out plate using domain decomposition method and orthogonal polynomials,;;;;

4.

Critical buckling load of chiral double-walled carbon nanotube using non-local theory elasticity,;;;;;

5.

Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory,;;;;;;

6.

An efficient shear deformation theory for wave propagation of functionally graded material plates,;;;;;

7.

Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept,;;;;

8.

Effect of porosity on vibrational characteristics of non-homogeneous plates using hyperbolic shear deformation theory,;;;;

9.

An efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on Winkler-Pasternak elastic foundations,;;;;;;

10.

Free vibration analysis of chiral double-walled carbon nanotube using non-local elasticity theory,;;;;;

11.

Thermal stability analysis of solar functionally graded plates on elastic foundation using an efficient hyperbolic shear deformation theory,;;;;

12.

Thermal stability of functionally graded sandwich plates using a simple shear deformation theory,;;;;

13.

A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations,;;;

14.

Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory,;;;

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

References

1.

Adda Bedia, W., Benzair, A., Semmah, A., Tounsi, A. and Mahmoud, S.R. (2015), "On the thermal buckling characteristics of armchair single-walled carbon nanotube embedded in an elastic medium based on nonlocal continuum elasticity", Braz. J. Phys., 45(2), 225-233.

2.

Ait Amar Meziane, M., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318.

3.

Ait Yahia, S., Ait Atmane, H., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., Int. J., 53(6), 1143-1165.

4.

Ajayan, P.M., Stephan, O., Colliex, C. and Trauth, D. (1994), "Aligned carbon nanotube arrays formed by cutting a polymer resin-nanotube composite", Science, 256(5176), 1212-1214.

5.

Akavci, S.S. (2014), "An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Compos. Struct., 108, 667-676.

6.

Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630.

7.

Alibeigloo, A. (2014), "Three-dimensional thermoelasticity solution of functionally graded carbon nanotube reinforced composite plate embedded in piezoelectric sensor and actuator layers", Compos. Struct., 118, 482-495.

8.

Ashrafi, B. and Hubert, P. (2006), "Modeling the elastic properties of carbon nanotube array/polymer composites", Compos. Sci. Technol., 66(3-4), 387-396.

9.

Aydogdu, M. (2014), "On the vibration of aligned carbon nanotube reinforced composite beams", Adv. Nano Res., Int. J., 2(4), 199-210.

10.

Bakhti, K., Kaci, A., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2013), "Large deformation analysis for functionally graded carbon nanotube-reinforced composite plates using an efficient and simple refined theory", Steel Compos. Struct., Int. J., 14(4), 335-347.

11.

Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos.: Part B, 60, 274-283.

12.

Benachour, A., Daouadji, H.T., Ait Atmane, H., Tounsi, A. and Meftah, S.A. (2011), "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient", Compos. Part B, 42(6), 1386-1394.

13.

Benguediab, S., Tounsi, A., Zidour, M. and Semmah, A. (2014), "Chirality and scale rffects on mechanical buckling properties of zigzag double-walled carbon nanotubes", Compos. Part B, 57, 21-24.

14.

Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., Int. J., 19(3), 521-546.

15.

Berrabah, H.M., Tounsi, A., Semmah, A. and Adda Bedia, E.A. (2013), "Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams", Struct. Eng. Mech., Int. J., 48(3), 351-365.

16.

Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Adda Bedia, E.A. (2013), "A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets", J. Sandw. Struct. Mater., 15(6), 671-703.

17.

Besseghier, A., Heireche, H., Bousahla, A.A., Tounsi, A. and Benzair, A. (2015), "Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix", Adv. Nano Res., Int. J., 3(1), 29-37.

18.

Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., Int. J., 14(1), 85-104.

19.

Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409-423.

20.

Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Computat. Method., 11(6), 1350082.

21.

Draiche, K., Tounsi, A. and Khalfi, Y. (2014), "A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass", Steel Compos. Struct., Int. J., 17(1), 69-81.

22.

El Meiche, N., Tounsi, A., Ziane, N., Mechab, I. and Adda Bedia, E.A. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53(4), 237-247.

23.

Esawi, A.M.K. and Farag, M.M. (2007), "Carbon nanotube reinforced composites: Potential and current challenges", Mater. Des., 28(9), 2394-2401.

24.

Fekrar, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014), "A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates", Meccanica, 49(4), 795-810.

25.

Fidelus, J.D., Wiesel, E., Gojny, F.H., Schulte, K. and Wagner, H.D. (2005), "Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites", Compos. Part A, 36(11), 1555-1561.

26.

Griebel, M. and Hamaekers, J. (2004), "Molecular dynamics simulations of the elastic moduli of polymer-carbon nanotube composites", Comput. Method. Appl. Mech. Eng., 193(17-20), 1773-1788.

27.

Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., Int. J., 18(1), 235-253.

28.

Han, Y. and Elliott, J. (2007), "Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites", Comp. Mater. Sci., 39(2), 315-323.

29.

Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140(2), 374-383.

30.

Houari, M.S.A., Tounsi, A. and Anwar Beg, O. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 467-479.

31.

Hu, N., Fukunaga, H., Lu, C., Kameyama, M. and Yan, B. (2005), "Prediction of elastic properties of carbon nanotube reinforced composites", P. Roy. Soc. A,, 461(2058), 1685-1710.

32.

Jha, D.K., Kant, T. and Singh, R.K. (2012), "Higher order shear and normal deformation theory for natural frequency of functionally graded rectangular plates", Nucl. Eng. Des., 250, 8-13.

33.

Jha, D.K., Kant, T. and Singh, R.K. (2013), "A critical review of recent research on functionally graded plates", Compos. Struct., 96, 833-849.

34.

Kaci, A., Tounsi, A., Bakhti, K. and Adda Bedia, E.A. (2012), "Nonlinear cylindrical bending of functionally graded carbon nanotube-reinforced composite plates", Steel Compos. Struct., Int. J., 12(6), 491-504.

35.

Ke, L.L., Yang, J. and Kitipornchai, S. (2013), "Dynamic stability of functionally graded carbon nanotube-reinforced composite beams", Mech. Adv. Mater. Struct., 20(1), 28-37.

36.

Khalfi, Y., Houari, M.S.A. and Tounsi, A. (2014), "A refined and simple shear deformation theory for thermal buckling of solar functionally graded plates on elastic foundation", Int. J. Computat. Method., 11(5), 135007.

37.

Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., Int. J., 18(2), 425-442.

38.

Lei, Z.X., Liew, K.M. and Yu, J.L. (2013a), "Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment", Compos. Struct., 106, 128-138.

39.

Lei, Z.X., Liew, K.M. and Yu, J.L. (2013b), "Large deflection analysis of functionally graded carbon nanotube-reinforced composite plates by the element-free kp-Ritz method", Comput. Method. Appl. Mech. Eng., 256, 189-199.

40.

Li, X.F., Wang, B.L. and Han, J.C. (2010), "A higher-order theory for static and dynamic analyses of functionally graded beams", Arch. Appl. Mech., 80(10), 1197-1212.

41.

Liew, K.M., Yang, J. and Kitipornchai, S. (2003), "Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading", Int. J. Solid Strut., 40(15), 3869-3892.

42.

Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489-2508.

43.

Meradjah, M., Kaci, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2015), "A new higher order shear and normal deformation theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(3), 793-809.

44.

Nedri, K., El Meiche, N. and Tounsi, A. (2014), "Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory", Mech. Compos. Mater., 49(6), 641-650.

45.

Odegard, G.M., Gates, T.S., Wise, K.E., Park, C. and Siochi, E.J. (2003), "Constitutive modelling of nanotube-reinforced polymer composites", Compos. Sci. Technol., 63(11), 1671-1687.

46.

Ould Larbi, L, Kaci, A., Houari, M.S.A. and Tounsi, A. (2013), "An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams", Mech. Based Des. Struct. Mach., 41(4), 421-433.

47.

Ray, M.C. and Batra, R.C. (2007), "A single-walled carbon nanotube reinforced 1-3 piezoelectric composite for active control of smart structures", Smart Mater. Struct., 16(5), 1936-1947.

48.

Saidi, H., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2013), "Thermo-mechanical bending response with stretching effect of functionally graded sandwich plates using a novel shear deformation theory", Steel Compos. Struct., Int. J., 15(2), 221-245.

49.

Sayyad, A.S. and Ghugal, Y.M. (2014), "Flexure of cross-ply laminated plates using equivalent single layer trigonometric shear deformation theory", Struct. Eng. Mech., Int. J., 51(5), 867-891.

50.

Shahrjerdi, A., Mustapha, F., Bayat, M. and Majid, D.L.A. (2011), "Free vibration analysis of solar functionally graded plates with temperature-dependent material properties using second order shear deformation theory", J. Mech. Sci. Technol., 25(9), 2195-2209.

51.

Swaminathan, K. and Naveenkumar, D.T. (2014), "Higher order refined computational models for the stability analysis of FGM plates: Analytical solutions", Eur. J. Mech. A/Solids, 47, 349-361.

52.

Talha, M. and Singh, B.N. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., 34(12), 3991-4011.

53.

Thostenson, E.T. and Chou, T.W. (2003), "On the elastic properties of carbon nanotube-based composites: Modelling and characterization", J. Phys. A-Appl. Phys., 36(5), 573-582.

54.

Thostenson, E.T., Ren, Z.F. and Chou, T.W. (2001), "Advances in the science and technology of carbon nanotubes and their composites: A review", Compos. Sci. Technol., 61(13), 1899-1912.

55.

Tounsi, A., Benguediab, S., Adda Bedia, E.A., Semmah, A. and Zidour, M. (2013a), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., Int. J., 1(1), 1-11.

56.

Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013b), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220.

57.

Vodenitcharova, T. and Zhang, L.C. (2006), "Bending and local buckling of a nanocomposite beam reinforced by a single-walled carbon nanotube", Int. J. Solids Struct., 43(10), 3006-3024.

58.

Wattanasakulpong, N. and Ungbhakorn, V. (2013), "Analytical solutions for bending, buckling and vibration responses of carbon nanotube-reinforced composite beams resting on elastic foundation", Computat. Mater. Sci., 71, 201-208.

59.

Wu, C.-P. and Li, H.-Y. (2014), "Three-dimensional free vibration analysis of functionally graded carbon nanotube-reinforced composite plates with various boundary conditions", J. Vib. Control, 1077546314528367.

60.

Wuite, J. and Adali, S. (2005), "Deflection and stress behaviour of nanocomposite reinforced beams using a multiscale analysis", Compos. Struct., 71(3-4), 388-396.

61.

Xu, Y.S., Ray, G. and Abdel-Magid, B. (2006), "Thermal behavior of single walled carbon nanotube polymer-matrix composites", Compos. Part A, 37(1), 114-121.

62.

Yas, M.H. and Samadi, N. (2012), "Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation", Int. J. Pres. Vess. Pip., 98, 119-128.

63.

Yaghoobi, H. and Fereidoon, A. (2014), "Mechanical and thermal buckling analysis of functionally graded plates resting on elastic foundations: An assessment of a simple refined nth-order shear deformation theory", Compos.: Part B, 62, 54-64.

64.

Yaghoobi, H., Valipour, M.S., Fereidoon, A. and Khoshnevisrad, P. (2014), "Analytical study on postbuckling and nonlinear free vibration analysis of FG beams resting on nonlinear elastic foundation under thermo-mechanical loading using VIM", Steel Compos. Struct., Int. J., 17(5), 753-776.

65.

Yesilce, Y. (2010), "Effect of axial force on the free vibration of Reddy-Bickford multi- span beam carrying multiple spring-mass systems", J. Vib. Control, 16(1), 11-32.

66.

Yesilce, Y. and Catal, S. (2009), "Free vibration of axially loaded Reddy-Bickford beam on elastic soil using the differential transform method", Struct. Eng. Mech., Int. J., 31(4), 453-476.

67.

Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: An assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., Int. J., 54(4), 693-710.

68.

Zhu, R., Pan, E. and Roy, A.K. (2007), "Molecular dynamics study of the stress-strain behavior of carbon-nanotube reinforced Epon 862 composites", Mater. Sci. Eng. A., 447(1-2), 51-57.

69.

Zhu, P., Lei, Z.X. and Liew, K.M. (2012), "Static and free vibration analyses of carbon nanotube reinforced composite plates using finite element method with first order shear deformation plate theory", Compos. Struct., 94(4), 1450-1460.