[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.12989/scs.2019.32.5.595

Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle

Medani, Mohammed (University Djillali Liabes- Sidi-Bel-Abbes)
Benahmed, Abdelillah (University Djillali Liabes- Sidi-Bel-Abbes)
Zidour, Mohamed (University Ibn Khaldoun)
Heireche, Houari (University Djillali Liabes- Sidi-Bel-Abbes)
Tounsi, Abdelouahed (Laboratory of Materials and Hydrology, University of Sidi Bel Abbes)
Bousahla, Abdelmoumen Anis (Laboratory of Modeling and Multi-Scale Simulation)
Tounsi, Abdeldjebbar (Laboratory of Materials and Hydrology, University of Sidi Bel Abbes)
Mahmoud, S.R. (GRC Department, Jeddah Community College, King Abdulaziz University)

Publication Information

Steel and Composite Structures / v.32, no.5, 2019 , pp. 595-610 More about this Journal

Abstract

This paper deals with the static and dynamic behavior of Functionally Graded Carbon Nanotubes (FG-CNT)-reinforced porous sandwich (PMPV) polymer plate. The model of nanocomposite plate is investigated within the first order shear deformation theory (FSDT). Two types of porous sandwich plates are supposed (sandwich with face sheets reinforced / homogeneous core and sandwich with homogeneous face sheets / reinforced core). Functionally graded Carbon Nanotubes (FG-CNT) and uniformly Carbon Nanotubes (UD-CNT) distributions of face sheets or core porous plates with uniaxially aligned single-walled carbon nanotubes are considered. The governing equations are derived by using Hamilton's principle. The solution for bending and vibration of such type's porous plates are obtained. The detailed mathematical derivations are provided and the solutions are compared to some cases in the literature. The effect of the several parameters of reinforced sandwich porous plates such as aspect ratios, volume fraction, types of reinforcement, number of modes and thickness of plate on the bending and vibration analyses are studied and discussed. On the question of porosity, this study found that there is a great influence of their variation on the static and vibration of porous sandwich plate.

Keywords

nanotubes; FG-CNTRC; bending; shear deformation; nanocomposite; porosities; sandwich;

Citations & Related Records

Times Cited By KSCI : 65 (Citation Analysis)

Reference
Cited By KSCI

1	Sahmani, S., Aghdam, M.M. and Rabczuk, T. (2018), "A unified nonlocal strain gradient plate model for nonlinear axial instability of functionally graded porous micro/nano-plates reinforced with graphene platelets", Mater. Res. Express, 5(4), 045048. https://doi.org/10.1088/2053-1591/aabdbb DOI
2	Semmah, A., Heireche, H., Bousahla, A.A. and Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT", Adv. Nano Res., Int. J., 7(2), 89-98. https://doi.org/10.12989/anr.2019.7.2.089
3	Shafiei, H. and Setoodeh, A.R. (2017), "Nonlinear free vibration and post-buckling of FG-CNTRC beams on nonlinear foundation", Steel Compos. Struct., Int. J., 24(1), 65-77. https://doi.org/10.12989/scs.2017.24.1.065 DOI
4	Shahsavari, D., Karami, B. and Li, L. (2018), "A high-order gradient model for wave propagation analysis of porous FG nanoplates", Steel Compos. Struct., Int. J., 29(1), 53-66. https://doi.org/10.12989/scs.2018.29.1.053
5	Sharma, N., Mahapatra, T.R., Panda, S.K. and Mehar, K. (2018), "Evaluation of vibroacoustic responses of laminated composite sandwich structure using higher-order finite-boundary element model", Steel Compos. Struct., Int. J., 28(5), 629-639. https://doi.org/10.12989/scs.2018.28.5.629
6	Shokravi, M. (2017), "Buckling of sandwich plates with FG-CNTreinforced layers resting on orthotropic elastic medium using Reddy plate theory", Steel Compos. Struct., Int. J., 23(6), 623-631. https://doi.org/10.12989/scs.2017.23.6.623
7	Mehar, K., Panda, S.K., Bui, T.Q. and Mahapatra, T.R. (2017a), "Nonlinear thermoelastic frequency analysis of functionally graded CNT-reinforced single/doubly curved shallow shell panels by FEM", J. Thermal Stress., 40(7), 899-916. https://doi.org/10.1080/01495739.2017.1318689 DOI
8	Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017b), "Theoretical and experimental investigation of vibration characteristic of carbon nanotube reinforced polymer composite structure", Int. J. Mech. Sci., 133, 319-329. https://doi.org/10.1016/j.ijmecsci.2017.08.057 DOI
9	Bensattalah, T., Daouadji, T.H., Zidour, M., Tounsi, A. and Bedia, E.A. (2016), "Investigation of thermal and chirality effects on vibration of single-walled carbon nanotubes embedded in a polymeric matrix using nonlocal elasticity theories", Mech. Compos. Mater., 52(4), 555-568. https://doi.org/10.1007/s11029-016-9606-z DOI
10	Benchohra, M., Driz, H., Bakora, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "A new quasi-3D sinusoidal shear deformation theory for functionally graded plates", Struct. Eng. Mech., Int. J., 65(1), 19-31. https://doi.org/10.12989/sem.2018.65.1.019
11	Bensattalah, T., Bouakkaz, K., Zidour, M. and Daouadji, T.H. (2018a), "Critical buckling loads of carbon nanotube embedded in Kerr's medium", Adv. Nano Res., Int. J., 6(4), 339-356. https://doi.org/10.12989/anr.2018.6.4.339
12	Bouazza, M., Amara, K., Zidour, M., Tounsi, A. and Adda-Bedia, E.A. (2015), "Postbuckling Analysis of Functionally Graded Beams Using Hyperbolic Shear Deformation Theory", Rev. Info. Eng. Appl., 2(1), 1-14. https://doi.org/10.18488/journal.79/2015.2.1/79.1.1.14 DOI
13	Bensattalah, T., Zidour, M. and Hassaine Daouadji, T. (2018b), "Analytical analysis for the forced vibration of CNT surrounding elastic medium including thermal effect using nonlocal Euler-Bernoulli theory", Adv. Mater. Res., Int. J., 7(3), 163-174. https://doi.org/10.12989/amr.2018.7.3.163
14	Bensattalah, T., Zidour, M., Hassaine Daouadji, T. and Bouakaz, K. (2019), "Theoretical analysis of chirality and scale effects on critical buckling load of zigzag triple walled carbon nanotubes under axial compression embedded in polymeric matrix", Struct. Eng. Mech., Int. J., 70(3), 269-277. https://doi.org/10.12989/sem.2019.70.3.269
15	Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., Int. J., 6(2), 147-162. https://doi.org/10.12989/anr.2018.6.2.147
16	Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Houari, M.S.A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst., Int. J., 21(1), 15-25. https://doi.org/10.12989/sss.2018.21.1.015
17	Tlidji, Y., Zidour, M., Draiche, K., Safa, A., Bourada, M., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Vibration analysis of different material distributions of functionally graded microbeam", Struct. Eng. Mech., Int. J., 69(6), 637-649. https://doi.org/10.12989/sem.2019.69.6.637
18	Wattanasakulpong, N. and Chaikittiratana, A. (2015), "Exact solutions for static and dynamic analyses of carbon nanotubereinforced composite plates with Pasternak elastic foundation", Appl. Math. Model., 39(18), 5459-5472. https://doi.org/10.1016/j.apm.2014.12.058 DOI
19	Xiao, W., Yan, C., Tian, W., Tian, W. and Song, X. (2018), "Effects of face-sheet materials on the flexural behavior of aluminum foam sandwich", Steel Compos. Struct., Int. J., 29(3), 301-308. https://doi.org/10.12989/scs.2018.29.3.301
20	Youcef, D.O., Kaci, A., Benzair, A., Bousahla, A.A. and Tounsi, A. (2018), "Dynamic analysis of nanoscale beams including surface stress effects", Smart Struct. Syst., Int. J., 21(1), 65-74. https://doi.org/10.12989/sss.2018.21.1.065
21	Dash, S., Mehar, K., Sharma, N., Mahapatra, T.R. and Panda, S.K. (2018), "Modal analysis of FG sandwich doubly curved shell structure", Struct. Eng. Mech., Int. J., 68(6), 721-733. https://doi.org/10.12989/sem.2018.68.6.721
22	Younsi, A., Tounsi, A, Zaoui, F.Z., Bousahla, A.A. and Mahmoud, S.R. (2018), "Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates", Geomech. Eng., Int. J., 14(6), 519-532. https://doi.org/10.12989/gae.2018.14.6.519
23	Zaoui, F.Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B, 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051 DOI
24	Costa, M.L., De Almeida, S.F.M. and Rezende, M.C. (2001), "The influence of porosity on the interlaminar shear strength of carbon/epoxy and carbon/bismaleimide fabric laminates", Compos. Sci. Technol., 61(14), 2101-2108. https://doi.org/10.1016/S0266-3538(01)00157-9 DOI
25	Dash, S., Mehar, K., Sharma, N., Mahapatra, T.R. and Panda, S.K. (2019), "Finite element solution of stress and flexural strength of functionally graded doubly curved sandwich shell panel", Earthq. Struct., Int. J., 16(1), 55-67. https://doi.org/10.12989/eas.2019.16.1.055
26	Dihaj, A., Zidour, M., Meradjah, M., Rakrak, K., Heireche, H. and Chemi, A. (2018), "Free vibration analysis of chiral doublewalled carbon nanotube embedded in an elastic medium using non-local elasticity theory and Euler Bernoulli beam model", Struct. Eng. Mech., Int. J., 65(3), 335-342. https://doi.org/10.12989/sem.2018.65.3.335
27	Draiche, K., Tounsi, A. and Mahmoud, S.R. (2016), "A refined theory with stretching effect for the flexure analysis of laminated composite plates", Geomech. Eng., Int. J., 11(5), 671-690. https://doi.org/10.12989/gae.2016.11.5.671 DOI
28	Khetir, H., BachirBouiadjra, M., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., Int. J., 64(4), 391-402. https://doi.org/10.12989/sem.2017.64.4.391
29	Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017c), "Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure", Eur. J. Mech.-A/Solids, 65, 384-396. https://doi.org/10.1016/j.euromechsol.2017.05.005 DOI
30	Mehar, K., Panda, S.K. and Patle, B.K. (2017d), "Thermoelastic vibration and flexural behavior of FG-CNT reinforced composite curved panel", Int. J. Appl. Mech., 9(4), 1750046. https://doi.org/10.1142/S1758825117500466 DOI
31	Kolahchi, R., Bidgoli, M.R., Beygipoor, G. and Fakhar, M.H. (2015), "A nonlocal nonlinear analysis for buckling in embedded FG-SWCNT-reinforced microplates subjected to magnetic field", J. Mech. Sci. Technol., 29(9), 3669-3677. https://doi.org/10.1007/s12206-015-0811-9 DOI
32	Kovacik, J. (1999), "Correlation between Young's modulus and porosity in porous materials", J. Mater. Sci. Lett., 18(13), 1007-1010. https://doi.org/10.1023/A:1006669914946 DOI
33	Lakshmipathi, J. and Vasudevan, R. (2019), "Dynamic characterization of a CNT reinforced hybrid uniform and nonuniform composite plates", Steel Compos. Struct., Int. J., 30(1), 31-46. https://doi.org/10.12989/scs.2019.30.1.031
34	Ahouel, M., Houari, M.S.A., Adda Bedia, E.A. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., Int. J., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963 DOI
35	Karami, B., Janghorban, M. and Li, L. (2018a), "On guided wave propagation in fully clamped porous functionally graded nanoplates", Acta Astronautica, 143, 380-390. https://doi.org/10.1007/s12206-015-0811-9 DOI
36	Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018b), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., Int. J., 28(1), 99-110. https://doi.org/10.12989/scs.2018.28.1.099
37	Katariya, P.V., Panda, S.K., Hirwani, C.K., Mehar, K. and Thakare, O. (2017), "Enhancement of thermal buckling strength of laminated sandwich composite panel structure embedded with shape memory alloy fibre", Smart Struct. Syst., Int. J., 20(5), 595-605. https://doi.org/10.12989/sss.2017.20.5.595
38	Ait Atmane, H, Tounsi, A. and Bernard, F. (2017), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 13(1), 71-84. https://doi.org/10.1007/s10999-015-9318-x DOI
39	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. https://doi.org/10.12989/sem.2015.53.6.1143 DOI
40	Draoui, A., Zidour, M., Tounsi, A. and Adim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. DOI
41	Dresselhaus, M.S. and Avouris, P. (2001), "Carbon nanotubes: synthesis, structure, properties and application", Top Appl. Phys., 80, 1-11. https://doi.org/10.1007/3-540-39947-X DOI
42	El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., Int. J., 63(5), 585-595. https://doi.org/10.12989/sem.2017.63.5.585
43	Mehar, K., Panda, S.K. and Patle, B.K. (2018d), "Stress, deflection, and frequency analysis of CNT reinforced graded sandwich plate under uniform and linear thermal environment: A finite element approach", Polym. Compos., 39(10), 3792-3809. https://doi.org/10.1002/pc.24409 DOI
44	Mehar, K., Mahapatra, T.R., Panda, S.K., Katariya, P.V. and Tompe, U.K. (2018a), "Finite-element solution to nonlocal elasticity and scale effect on frequency behavior of shear deformable nanoplate structure", J. Eng. Mech., 144(9), 04018094. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001519 DOI
45	Mehar, K., Panda, S.K. and Mahapatra, T.R. (2018b), "Nonlinear frequency responses of functionally graded carbon nanotubereinforced sandwich curved panel under uniform temperature field", Int. J. Appl. Mech., 10(3), 1850028. https://doi.org/10.1142/S175882511850028X DOI
46	Mehar, K., Panda, S.K. and Mahapatra, T.R. (2018c), "Thermoelastic deflection responses of CNT reinforced sandwich shell structure using finite element method", Scientia Iranica, 25(5), 2722-2737. https://doi.org/10.24200/SCI.2017.4525
47	Mehar, K., Panda, S.K., Devarajan, Y. and Choubey, G. (2019a), "Numerical buckling analysis of graded CNT-reinforced composite sandwich shell structure under thermal loading", Compos. Struct., 216, 406-414. https://doi.org/10.1016/j.compstruct.2019.03.002 DOI
48	Mehar, K., Panda, S.K. and Mahapatra, T.R. (2019b), "Large deformation bending responses of nanotube-reinforced polymer composite panel structure: Numerical and experimental analyses", Proceedings of the Institution of Mechanical Engineers, Part G: J. Aerosp. Eng., 233(5), 1695-1704. https://doi.org/10.1177/0954410018761192 DOI
49	Shu, D. and Fan, H. (1996), "Free vibration of a bimaterial split beam", Compos. Part B, 27(1), 79-84. https://doi.org/10.1016/1359-8368(95)00026-7 DOI
50	Lei, Z.X., Liew, K.M. and Yu, J.L. (2013), "Buckling analysis of functionally graded carbon nanotube reinforced composite plates using the element-free kp-Ritz method", Compos. Struct., 98, 160-168. https://doi.org/10.1016/j.compstruct.2012.11.006 DOI
51	Li, H., Tu, S., Liu, Y., Lu, X. and Zhu, X. (2019), "Mechanical Properties of L-joint with composite sandwich structure", Compos. Struct., 217, 165-174. https://doi.org/10.1016/j.compstruct.2019.03.011 DOI
52	Bousahla, A.A., Benyoucef, S., Tounsi, A. and Mahmoud, S.R. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., Int. J., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313 DOI
53	Abdelaziz, H.H., Meziane, M.A.A, Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., Int. J., 25(6), 693-704. https://doi.org/10.12989/scs.2017.25.6.693
54	Bouhadra, A., Tounsi, A., Bousahla, A.A., Benyoucef, S. and Mahmoud, S.R. (2018), "Improved HSDT accounting for effect of thickness stretching in advanced composite plates", Struct. Eng. Mech., Int. J., 66(1), 61-73. https://doi.org/10.12989/sem.2018.66.1.061
55	Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A. and Al-Osta, M.A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., Int. J., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503
56	Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., Int. J., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161
57	Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., Int. J., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227 DOI
58	Bourada, F., Amara, K., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel refined plate theory for stability analysis of hybrid and symmetric S-FGM plates", Struct. Eng. Mech., Int. J., 68(6), 661-675. https://doi.org/10.12989/sem.2018.68.6.661
59	Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A. and Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., Int. J., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019
60	Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., Int. J., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389
61	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. https://doi.org/10.12989/sem.2015.54.4.693 DOI
62	Mehar, K. and Panda, S.K. (2016b), "Geometrical nonlinear free vibration analysis of FG-CNT reinforced composite flat panel under uniform thermal field", Compos. Struct., 143, 336-346. https://doi.org/10.1016/j.compstruct.2016.02.038 DOI
63	Liu, L., Zhang, B.D., Wang, D.F. and Wu, Z.J. (2006), "Effects of cure cycles on void content and mechanical properties of composites laminates", Compos. Struct., 73(3), 303-309. https://doi.org/10.1016/j.compstruct.2005.02.001 DOI
64	Mahapatra, T.R., Mehar, K., Panda, S.K., Dewangan, S. and Dash, S. (2017), "Flexural strength of functionally graded nanotube reinforced sandwich spherical panel", Proceedings of IOP conference series: Mater. Sci. Eng., Vol. 178, No. 1, p. 012031. https://doi.org/10.1088/1757-899X/178/1/012031 DOI
65	Mehar, K. and Panda, S.K. (2016a), "Free vibration and bending behaviour of CNT reinforced composite plate using different shear deformation theory", Proceedings of IOP Conference Series: Mater. Sci. Eng., Vol. 115, No. 1, p. 012014. https://doi.org/10.1088/1757-899X/115/1/012014 DOI
66	Alankaya, V. and Erdonmez, C. (2017), "Bending performance of laminated sandwich shells in hyperbolic paraboloidal form", Steel Compos. Struct., Int. J., 25(3), 337-346. https://doi.org/10.12989/scs.2017.25.3.337
67	Abualnour, M., Houari, M.S.A., Tounsi, A., AddaBedia, E.A., Mahmoud, S.R. (2018), "A novel quasi 3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047 DOI
68	Ajayan, P.M., Stephen, O., Colliex, C. and Trauth, D. (1994), "Aligned carbon nanotube arrays formed by cutting a polymer resin-nanotube composite", Science, 256, 1212-1214. https://doi.org/10.1126/science.265.5176.1212
69	Akgoz, B. and Civalek, O. (2011), "Nonlinear vibration analysis of laminated plates resting on nonlinear two-parameters elastic foundations", Steel Compos. Struct., Int. J., 11(5), 403-421. https://doi.org/10.12989/scs.2011.11.5.403 DOI
70	Allahkarami, F., Nikkhah-Bahrami, M. and Saryazdi, M.G. (2017), "Damping and vibration analysis of viscoelastic curved microbeam reinforced with FG-CNTs resting on viscoelastic medium using strain gradient theory and DQM", Steel Compos. Struct., Int. J., 25(2), 141-155. https://doi.org/10.12989/scs.2017.25.2.141
71	Panda, K.C., Bhattacharyya, S.K. and Barai, S.V. (2012), "Shear behaviour of RC T-beams strengthened with U-wrapped GFRP sheet", Steel Compos. Struct., Int. J., 12(2), 149-166. https://doi.org/10.12989/scs.2012.12.2.149 DOI
72	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, 1450-1460. https://doi.org/10.1016/j.compstruct.2011.11.010 DOI
73	Zidour, M., Hadji, L., Bouazza, M., Tounsi, A. and Bedia, E.A. (2015), "The mechanical properties of Zigzag carbon nanotube using the energy-equivalent model", J. Chem. Mater. Res., 3, 9-14.
74	Muller, E., Drasar, C., Schilz, J. and Kaysser, W.A. (2003), "Functionally graded materials for sensor and energy applications", Mater. Sci. Eng. A, 362(1-2), 17-39. https://doi.org/10.1016/S0921-5093(03)00581-1 DOI
75	Rakrak, K., Zidour, M., Heireche, H., Bousahla, A.A. and Chemi, A. (2016), "Free vibration analysis of chiral double-walled carbon nanotube using non-local elasticity theory", Adv. Nano Res., Int. J., 4(1), 31-44. https://doi.org/10.12989/anr.2016.4.1.031 DOI
76	Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, (2nd Edition), Taylor & Francis eBooks, CRC Press.
77	Fourn, H., AitAtmane, H., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., Int. J., 27(1), 109-122. https://doi.org/10.12989/scs.2018.27.1.109
78	Ghiorse, S.R. (1993), "Effect of void content on the mechanical properties of carbon/epoxy laminates", Samp. Quarter., 1, 54-59.
79	Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., Int. J., 25(2), 157-175. https://doi.org/10.12989/scs.2017.25.2.157
80	Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., 21(2), 727-757. https://doi.org/10.1177/1099636217698443 DOI
81	Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., Int. J., 21(4), 397-405. https://doi.org/10.12989/sss.2018.21.4.397
82	Moradi-Dastjerdi, R. (2016), "Wave propagation in functionally graded composite cylinders reinforced by aggregated carbon nanotube", Struct. Eng. Mech., Int. J., 57(3), 441-456. https://doi.org/10.12989/sem.2016.57.3.441 DOI
83	Mouffoki, A., Adda Bedia, E.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory", Smart Struct. Syst., Int. J., 20(3), 369-383. https://doi.org/10.12989/sss.2017.20.3.369
84	Mehar, K. and Panda, S.K. (2017b), "Thermoelastic analysis of FG-CNT reinforced shear deformable composite plate under various loadings", Int. J. Computat. Methods, 14(2), 1750019. https://doi.org/10.1142/S0219876217500190 DOI
85	Avcar, M. (2015), "Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam", Struct. Eng. Mech., Int. J., 55(4), 871-884. https://doi.org/10.12989/sem.2015.55.4.871 DOI
86	Mehar, K. and Panda, S.K. (2016c), "Nonlinear static behavior of FG-CNT reinforced composite flat panel under thermomechanical load", J. Aerosp. Eng., 30(3), 04016100. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000706 DOI
87	Mehar, K. and Panda, S.K. (2017a), "Numerical investigation of nonlinear thermomechanical deflection of functionally graded CNT reinforced doubly curved composite shell panel under different mechanical loads", Compos. Struct., 161, 287-298. https://doi.org/10.1016/j.compstruct.2016.10.135 DOI
88	Guessas, H., Zidour, M., Meradjah, M. and Tounsi, A. (2018), "The critical buckling load of reinforced nanocomposite porous plates", Struct. Eng. Mech., Int. J., 67(2), 115-123. https://doi.org/10.12989/sem.2018.67.2.115
89	Asadi, H. and Wang, Q. (2017), "Dynamic stability analysis of a pressurized FG-CNTRC cylindrical shell interacting with supersonic airflow", Compos. Part B: Eng., 118, 15-25. https://doi.org/10.1016/j.compositesb.2017.03.001 DOI
90	Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., Int. J., 65(4), 453-464. https://doi.org/10.12989/sem.2018.65.4.453
91	Benahmed, A., Fahsi, B., Benzair, A., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., Int. J., 69(4), 457-466. https://doi.org/10.12989/sem.2019.69.4.457
92	Mehar, K. and Panda, S.K. (2018a), "Thermal free vibration behavior of FG-CNT reinforced sandwich curved panel using finite element method", Polym. Compos., 39(8), 2751-2764. https://doi.org/10.1002/pc.24266 DOI
93	Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygrothermo mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., Int. J., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755 DOI
94	Belkacem, A., Tahar, H.D., Abderrezak, R., Amine, B.M., Mohamed, Z. and Boussad, A. (2018), "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions", Struct. Eng. Mech., Int. J., 66(6), 761-769. https://doi.org/10.12989/sem.2018.66.6.761
95	Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017a), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., Int. J., 25(3), 257-270. https://doi.org/10.12989/scs.2017.25.3.257
96	Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017b), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., Int. J., 62(6), 695-702. https://doi.org/10.12989/sem.2017.62.6.695
97	Belmahi, S., Zidour, M., Meradjah, M., Bensattalah, T. and Dihaj, A. (2018), "Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix", Struct. Eng. Mech., Int. J., 67(5), 517-525. https://doi.org/10.12989/sem.2018.67.5.517
98	Belmahi, S., Zidour, M. and Meradjah, M. (2019), "Small-scale effect on the forced vibration of a nano beam embedded an elastic medium using nonlocal elasticity theory", Adv. Aircr. Spacecr. Sci., 6(1), 1-18. https://doi.org/10.12989/aas.2019.6.1.001 DOI
99	Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Tounsi, A. (2019), "Dynamic Analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., Int. J., 7(3), 189-206. https://doi.org/10.12989/anr.2019.7.3.189
100	Zine, A., Tounsi, A., Draiche, K., Sekkal, M. and Mahmoud, S.R. (2018), "A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells", Steel Compos. Struct., Int. J., 26(2), 125-137. https://doi.org/10.12989/scs.2018.26.2.125
101	Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A. and Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., Int. J., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185
102	Chemi, A., Heireche, H., Zidour, M., Rakrak, K. and Bousahla, A.A. (2015), "Critical buckling load of chiral double-walled carbon nanotube using non-local theory elasticity", Adv. Nano Res., Int. J., 3(4), 193-206. https://doi.org/10.12989/anr.2015.3.4.193 DOI
103	Chemi, A., Zidour, M., Heireche, H., Rakrak, K. and Bousahla, A.A. (2018), "Critical buckling load of chiral double-walled carbon nanotubes embedded in an elastic medium", Mech. Compos. Mater., 53(6), 827-836. https://doi.org/10.1007/s11029-018-9708-x DOI
104	Chen, D., Yang, J. and Kitipornchai, S. (2017), "Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams", Compos. Sci. Technol., 142, 235-245. https://doi.org/10.1016/j.compscitech.2017.02.008 DOI
105	Cherif, R.H., Meradjah, M., Zidour, M., Tounsi, A., Belmahi, H. and Bensattalah, T. (2018), "Vibration analysis of nano beam using differential transform method including thermal effect", J. Nano Res., 54, 1-14. DOI
106	Avcar, M. and Alwan, H.H.A. (2017), "Free vibration of functionally graded Rayleigh beam", Int. J. Eng. Appl. Sci., 9(2), 127-137. http://dx.doi.org/10.24107/ijeas.322884
107	Hajmohammad, M.H., Zarei, M.S., Farrokhian, A. and Kolahchi, R. (2018), "A layerwise theory for buckling analysis of truncated conical shells reinforced by CNTs and carbon fibers integrated with piezoelectric layers in hygrothermal environment", Adv. Nano Res., Int. J., 6(4), 299-321. https://doi.org/10.12989/anr.2018.6.4.299 DOI
108	Hamidi, A., Zidour, M., Bouakkaz, K. and Bensattalah, T. (2018), "Thermal and small-scale effects on vibration of embedded armchair single-walled carbon nanotubes", J. Nano Res., 51, 24-38. https://doi.org/10.4028/www.scientific.net/JNanoR.51.24 DOI
109	Avcar, M. (2016), "Effects of material non-homogeneity and two parameter elastic foundation on fundamental frequency parameters of Timoshenko beams", Acta Physica Polonica A, 130(1), 375-378. https://doi.org/10.12693/APhysPolA.130.375 DOI
110	Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., Int. J., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603
111	Avcar, M. and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci., 11(10), 232. https://doi.org/10.1007/s12517-018-3579-2 DOI
112	Mehar, K. and Panda, S.K. (2019), "Theoretical deflection analysis of multi-walled carbon nanotube reinforced sandwich panel and experimental verification", Compos. Part B: Eng., 167, 317-328. https://doi.org/10.1016/j.compositesb.2018.12.058 DOI
113	Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., Int. J., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289 DOI
114	Rezaiee-Pajand, M., Sani, A.A. and Hozhabrossadati, S.M. (2019), "Deflection of axially functionally graded rectangular plates by Green's function method", Steel Compos. Struct., Int. J., 30(1), 57-67. https://doi.org/10.12989/scs.2019.30.1.057
115	Safaei, B., Moradi-Dastjerdi, R., Qin, Z. and Chu, F. (2019), "Frequency-dependent forced vibration analysis of nanocomposite sandwich plate under thermo-mechanical loads", Composites Part B: Eng., 161, 44-54. https://doi.org/10.1016/j.compositesb.2018.10.049 DOI
116	Mehar, K. and Panda, S.K. (2018b), "Dynamic response of functionally graded carbon nanotube reinforced sandwich plate", Proceedings of IOP Conference Series: Mater. Sci. Eng., Vol. 338, No. 1, p. 012017. https://doi.org/10.1088/1757-899X/338/1/012017 DOI
117	Mehar, K. and Panda, S.K. (2018c), "Elastic bending and stress analysis of carbon nanotube-reinforced composite plate: Experimental, numerical, and simulation", Adv. Polym. Technol., 37(6), 1643-1657. https://doi.org/10.1002/adv.21821 DOI
118	Mehar, K. and Panda, S.K. (2018d), "Nonlinear finite element solutions of thermoelastic flexural strength and stress values of temperature dependent graded CNT-reinforced sandwich shallow shell structure", Struct. Eng. Mech., Int. J., 67(6), 565-578. https://doi.org/10.12989/sem.2018.67.6.565
119	Mehar, K. and Panda, S.K. (2018e), "Thermoelastic flexural analysis of FG-CNT doubly curved shell panel", Aircraft Eng. Aerospace Technol., 90(1), 11-23. https://doi.org/10.1108/AEAT-11-2015-0237 DOI
120	Mehar, K., Panda, S.K., Dehengia, A. and Kar, V.R. (2016), "Vibration analysis of functionally graded carbon nanotube reinforced composite plate in thermal environment", J. Sandw. Struct. Mater., 18(2), 151-173. https://doi.org/10.1016/j.compstruct.2019.03.002 DOI
121	Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of sheardeformable composite beams using a novel simple twounknown beam theory", Struct. Eng. Mech., Int. J., 65(5), 621-631. https://doi.org/10.12989/sem.2018.65.5.621
122	Hamza-Cherif, R., Meradjah, M., Zidour, M., Tounsi, A., Belmahi, S. and Bensattalah, T. (2018), "Vibration analysis of nano beam using differential transform method including thermal effect", J. Nano Res., 54, 1-14. https://doi.org/10.4028/www.scientific.net/JNanoR.54.1 DOI
123	Hu, J.S. and Hwu, C. (1995), "Free vibration of delaminated composite sandwich beams", AIAA J., 33(10), 1911-1918. https://doi.org/10.2514/3.12745 DOI
124	Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354, 56-58. https://doi.org/10.1038/354056a0 DOI
125	Kadari, B., Bessaim, A., Tounsi, A., Heireche, H., Bousahla, A.A. and Houari, M.S.A. (2018), "Buckling analysis of orthotropic nanoscale plates resting on elastic foundations", J. Nano Res., 55, 42-56. https://doi.org/10.4028/www.scientific.net/JNanoR.55.42 DOI
126	Kar, V.R. and Panda, S.K. (2015), "Large deformation bending analysis of functionally graded spherical shell using FEM", Struct. Eng. Mech., Int. J., 53(4), 661-679. https://doi.org/10.12989/sem.2015.53.4.661 DOI
127	Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A new 3-unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate", Earthq. Struct., Int. J., 14(2), 103-115. https://doi.org/10.12989/eas.2018.14.2.103
128	Bakhadda, B., Bouiadjra, M.B., Bourada, F., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation", Wind Struct., Int. J., 27(5), 311-324. https://doi.org/10.12989/was.2018.27.5.311
129	Baltacioglu, A.K. and Civalek, O. (2018), "Numerical approaches for vibration response of annular and circular composite plates", Steel Compos. Struct., Int. J., 29(6), 755-766. https://doi.org/10.12989/scs.2018.29.6.759
130	Baseri, V., Jafari, G.S. and Kolahchi, R. (2016), "Analytical solution for buckling of embedded laminated plates based on higher order shear deformation plate theory", Steel Compos. Struct., Int. J., 21(4), 883-919. https://doi.org/10.12989/scs.2016.21.4.883 DOI

6	(2019) Advances in nano research The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory / 7 (6) , 443
5	(2019) Steel & Composite structures : an international journal Wave dispersion properties in imperfect sigmoid plates using various HSDTs / 33 (5) , 699
6	(2019) Coupled systems mechanics Axisymmetric deformation in transversely isotropic thermoelastic medium using new modified couple stress theory / 8 (6) , 501
2	(2019) Steel & Composite structures : an international journal Effect of thermal conductivity on isotropic modified couple stress thermoelastic medium with two temperatures / 34 (2) , 309
5	(2019) Steel & Composite structures : an international journal The effect of voltage and nanoparticles on the vibration of sandwich nanocomposite smart plates / 34 (5) , 733
3	(2019) Advances in concrete construction Numerical study for nonlocal vibration of orthotropic SWCNTs based on Kelvin's model / 9 (3) , 301
3	(2019) Computers & concrete Analysis of a functionally graded nanocomposite sandwich beam considering porosity distribution on variable elastic foundation using DQM: Buckling and vibration behaviors / 25 (3) , 215
3	(2019) Computers & concrete Non-local orthotropic elastic shell model for vibration analysis of protein microtubules / 25 (3) , 245
1	(2019) Geomechanics & engineering Effect of the rotation on the thermal stress wave propagation in non-homogeneous viscoelastic body / 21 (1) , 1
1	(2020) Steel & Composite structures : an international journal Buckling response of smart plates reinforced by nanoparticles utilizing analytical method / 35 (1) , 1
4	(2019) Advances in concrete construction Analysis of post-buckling of higher-order graphene oxide reinforced concrete plates with geometrical imperfection / 9 (4) , 397
4	(2020) Computers & concrete Finite element based post-buckling analysis of refined graphene oxide reinforced concrete beams with geometrical imperfection / 25 (4) , 283
11	(2020) Polymer composites Multiphysical theoretical prediction and experimental verification of vibroacoustic responses of fruit fiber‐reinforced polymeric composite / 41 (11) , 4461
3	(2019) Structural engineering and mechanics : An international journal Nonlocal nonlinear stability of higher-order porous beams via Chebyshev-Ritz method / 76 (3) , 413
8	(2019) International journal of applied mechanics Thermal Buckling of Graphene Platelets Toughening Sandwich Functionally Graded Porous Plate with Temperature-Dependent Properties / 12 (8) , 2050089
1	(2019) International journal of concrete structures and materials Stressing State Analysis of Reinforcement Concrete Beams Strengthened with Carbon Fiber Reinforced Plastic / 14 (1) , 38
4	(2019) Advances in materials research : AMR Predictions of the maximum plate end stresses of imperfect FRP strengthened RC beams: study and analysis / 9 (4) , 265
6	(2020) Coupled systems mechanics Time Harmonic interactions in the axisymmetric behaviour of transversely isotropic thermoelastic solid using New M-CST / 9 (6) , 521
6	(2020) Coupled systems mechanics Effect of porosity distribution rate for bending analysis of imperfect FGM plates resting on Winkler-Pasternak foundations under various boundary conditions / 9 (6) , 575
	(2021) Mathematical problems in engineering On the Finite Element Model of Rotating Functionally Graded Graphene Beams Resting on Elastic Foundation / 2021 , 1
	(2019) Mathematical problems in engineering Free Vibration Exploration of Rotating FGM Porosity Beams under Axial Load considering the Initial Geometrical Imperfection / 2021 , 1
1	(2019) Structural engineering and mechanics : An international journal Thermal frequency analysis of FG sandwich structure under variable temperature loading / 77 (1) , 57
1	(2021) Advances in nano research On thermally induced instability of FG-CNTRC cylindrical panels / 10 (1) , 43
2	(2019) Structural engineering and mechanics : An international journal Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity / 77 (2) , 217
2	(2019) Advances in nano research Geometrically nonlinear thermo-mechanical analysis of graphene-reinforced moving polymer nanoplates / 10 (2) , 151
2	(2019) Advances in nano research Frequency characteristics and sensitivity analysis of a size-dependent laminated nanoshell / 10 (2) , 175
4	(2021) Steel & Composite structures : an international journal Dual-phase-lag model on thermo-microstretch elastic solid Under the effect of initial stress and temperature-dependent / 38 (4) , 355
7	(2019) Applied sciences Buckling Analysis of CNTRC Curved Sandwich Nanobeams in Thermal Environment / 11 (7) , 3250
1	(2021) Steel & Composite structures : an international journal Exact third-order static and free vibration analyses of functionally graded porous curved beam / 39 (1) , 1
1	(2021) Structural engineering and mechanics : An international journal Electromagnetic field and initial stress on a porothermoelastic medium / 78 (1) , 1
4	(2019) Computers & concrete Computer simulation for stability analysis of the viscoelastic annular plate with reinforced concrete face sheets / 27 (4) , 369
4	(2021) Mechanics based design of structures and machines Stability analysis of single-walled carbon nanotubes embedded in winkler foundation placed in a thermal environment considering the surface effect using a new refined beam theory / 49 (4) , 581
1	(2019) Advances in nano research Temperature jump and concentration slip effects on bioconvection past a vertical porous plate in the existence of nanoparticles and gyrotactic microorganism with inclined MHD / 11 (1) , 27
2	(2021) Steel & Composite structures : an international journal Free vibration analysis of open-cell FG porous beams: analytical, numerical and ANN approaches / 40 (2) , 157
8	(2019) Engineering computations Surface wave scattering analysis in an initially stressed stratified media / 38 (8) , 3153
2	(2021) Advances in nano research Free vibration analysis of carbon nanotube RC nanobeams with variational approaches / 11 (2) , 157
6	(2021) Steel & Composite structures : an international journal Numerical forced vibration analysis of compositionally gradient porous cylindrical microshells under moving load and thermal environment / 40 (6) , 893
12	(2019) Materials research express Compressive mechanical behavior and model of composite elastic-porous metal materials / 8 (12) , 126518