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http://dx.doi.org/10.12989/gae.2020.21.5.471

A novel four-unknown integral model for buckling response of FG sandwich plates resting on elastic foundations under various boundary conditions using Galerkin's approach  

Chikr, Sara Chelahi (Department of Civil and Hydraulic Engineering, Dr Tahar Moulay University, Faculty of Technology)
Kaci, Abdelhakim (Department of Civil and Hydraulic Engineering, Dr Tahar Moulay University, Faculty of Technology)
Bousahla, Abdelmoumen Anis (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals)
Bourada, Fouad (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Tounsi, Abdeldjebbar (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Bedia, E.A. Adda (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals)
Mahmoud, S.R. (GRC Department, Jeddah Community College, King Abdulaziz University)
Benrahou, Kouider Halim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Publication Information
Geomechanics and Engineering / v.21, no.5, 2020 , pp. 471-487 More about this Journal
Abstract
In this work, the buckling analysis of material sandwich plates based on a two-parameter elastic foundation under various boundary conditions is investigated on the basis of a new theory of refined trigonometric shear deformation. This theory includes indeterminate integral variables and contains only four unknowns in which any shear correction factor not used, with even less than the conventional theory of first shear strain (FSDT). Applying the principle of virtual displacements, the governing equations and boundary conditions are obtained. To solve the buckling problem for different boundary conditions, Galerkin's approach is utilized for symmetric EGM sandwich plates with six different boundary conditions. A detailed numerical study is carried out to examine the influence of plate aspect ratio, elastic foundation coefficients, ratio, side-to-thickness ratio and boundary conditions on the buckling response of FGM sandwich plates. A good agreement between the results obtained and the available solutions of existing shear deformation theories that have a greater number of unknowns proves to demonstrate the precision of the proposed theory.
Keywords
buckling sandwich plates; functionally graded materials; new four-unknown refined shear deformation theory and various boundary conditions;
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1 Motezaker, M. and Kolahchi, R. (2017b), "Seismic response of SiO2 nanoparticles-reinforced concrete pipes based on DQ and newmark methods", Comput. Concrete, 19(6), 745-753. https://doi.org/10.12989/cac.2017.19.6.745.   DOI
2 Motezaker, M., Jamali, M. and Kolahchi, R. (2020), "Application of differential cubature method for nonlocal vibration, buckling and bending response of annular nanoplates integrated by piezoelectric layers based on surface-higher order nonlocalpiezoelasticity theory", J. Comput. Appl. Math., 369, 112625. https://doi.org/10.1016/j.cam.2019.112625.   DOI
3 Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012e), "Buckling analysis of sandwich plates with functionally graded skins using a new quasi-3D hyperbolic sine shear deformation theory and collocation with radial basis functions", ZAMM J. Appl. Math. Mech., 92(9), 749-766. https://doi.org/10.1002/zamm.201100186.   DOI
4 Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012c), "Static analysis of functionally graded sandwich plates according to a hyperbolic theory considering Zig-Zag and warping effects", Adv. Eng. Softw., 52, 30-43. https://doi.org/10.1016/j.advengsoft.2012.05.005.   DOI
5 Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2012d), "A quasi- 3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Struct., 94(5), 1814-1825. https://doi.org/10.1016/j.compstruct.2011.12.005.   DOI
6 Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Roque, C.M.C., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012a), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Part B Eng., 43(2), 711-725. https://doi.org/10.1016/j.compositesb.2011.08.009.
7 Omurtag, M.H., Ozutok, A., Akoz, A.Y. and Ozcelikors, Y. (1997), "Free vibration analysis of kirchhoff plates resting on elastic foundation by mixed finite element formulation based on gateaux differential", Int. J. Numer. Meth. Eng., 40(2), 295-317. https://doi.org/10.1002/(sici)1097-0207(19970130)40:2<295::aid-nme66>3.0.co;2-2.   DOI
8 Othman, M.I.A., Abouelregal, A.E. and Said, S.M. (2019), "The effect of variable thermal conductivity on an infinite fiberreinforced thick plate under initial stress", J. Mech. Mater. Struct., 14(2), 277-293. https://doi.org/10.2140/jomms.2019.14.277.   DOI
9 Panjehpour, M., Loh, E.W.K. and Deepak, TJ. (2018), "Structural Insulated Panels: State-of-the-Art", Trends Civ. Eng. Architect., 3(1) 336-340. https://doi.org/10.32474/TCEIA.2018.03.000151.
10 Safa, A., Hadji, L., Bourada, M. and Zouatnia, N. (2019), "Thermal vibration analysis of FGM beams using an efficient shear deformation beam theory", Earthq. Struct., 17(3), 329-336. https://doi.org/10.12989/eas.2019.17.3.329.   DOI
11 Selmi, A. (2019), "Effectiveness of SWNT in reducing the crack effect on the dynamic behavior of aluminium alloy", Adv. Nano Res., 7(5), 365-377. https://doi.org/10.12989/anr.2019.7.5.365.   DOI
12 Sedighi, H.M. and Shirazi, K.H. (2012), "A new approach to analytical solution of cantilever beam vibration with nonlinear boundary condition", J. Comput. Nonlin. Dyn., 7(3), 034502. https://doi.org/10.1115/1.4005924.   DOI
13 Sedighi, H.M., Keivani, M. and Abadyan, M. (2015), "Modified continuum model for stability analysis of asymmetric FGM double-sided NEMS: Corrections due to finite conductivity, surface energy and nonlocal effect", Compos. Part B Eng., 83, 117-133. https://doi.org/10.1016/j.compositesb.2015.08.029.   DOI
14 Sedighi, H.M., Shirazi, K.H. and Attarzadeh, M.A. (2013), "A study on the quintic nonlinear beam vibrations using asymptotic approximate approaches", Acta Astronautica, 91, 245-250. https://doi.org/10.1016/j.actaastro.2013.06.018.   DOI
15 Shen, H.S. and Yang, D.Q. (2014), "Nonlinear vibration of anisotropic laminated cylindrical shells with piezoelectric fiber reinforced composite actuators", Ocean Eng., 80, 36-49. https://doi.org/10.1016/j.oceaneng.2014.01.016.   DOI
16 Shodja, H., Haftbaradaran, H. and Asghari, M. (2007), "A thermoelasticity solution of sandwich structures with functionally graded coating", Compos. Sci. Technol., 67(6), 1073-1080. https://doi.org/10.1016/j.compscitech.2006.06.001.   DOI
17 Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Compos. Struct, 99, 76-87. https://doi.org/10.1016/j.compstruct.2012.11.018.   DOI
18 Xiang, S., Jin, Y., Bi, Z., Jiang, S. and Yang, M. (2011). "A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates", Compos. Struct., 93(11), 2826-2832. https://doi.org/10.1016/j.compstruct.2011.05.022.   DOI
19 Timesli, A. (2020), "An efficient approach for prediction of the nonlocal critical buckling load of double-walled carbon nanotubes using the nonlocal Donnell shell theory", SN Appl. Sci., 2, 407. https://doi.org/10.1007/s42452-020-2182-9.   DOI
20 Wang, Z.X. and Shen, H.S. (2013), "Nonlinear dynamic response of sandwich plates with FGM face sheets resting on elastic foundations in thermal environments", Ocean Eng., 57, 99-110. https://doi.org/10.1016/j.oceaneng.2012.09.004.   DOI
21 Yaghoobi, H. and Yaghoobi, P. (2013), "Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach", Meccanica, 48(8), 2019-2035. https://doi.org/10.1007/s11012-013-9720-0.   DOI
22 Zamanian, M., Kolahchi, R. and Bidgoli, M.R. (2017), "Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with SiO2 nano-particles", Wind Struct., 24(1), 43-57. https://doi.org/10.12989/was.2017.24.1.043.   DOI
23 Zarei, M.S., Kolahchi, R., Hajmohammad, M.H. and Maleki, M. (2017), "Seismic response of underwater fluid-conveying concrete pipes reinforced with SiO2 nanoparticles and fiber reinforced polymer (FRP) layer", Soil Dyn. Earthq. Eng., 103, 76-85. https://doi.org/10.1016/j.soildyn.2017.09.009.   DOI
24 Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 2-Buckling and free vibration", Int. J. Solids Struct., 42(18-19), 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016.   DOI
25 Zouatnia, N. and Hadji, L. (2019), "Effect of the micromechanical models on the bending of FGM beam using a new hyperbolic shear deformation theory", Earthq. Struct., 16(2), 177-183. https://doi.org/10.12989/eas.2019.16.2.177.   DOI
26 Zenkour, A.M. and Sobhy, M. (2010), "Thermal buckling of various types of FGM sandwich plates", Compos. Struct., 93(1), 93-102. https://doi.org/10.1016/j.compstruct.2010.06.012.   DOI
27 Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Mechanical and thermal buckling analysis of functionally graded plates", Compos. Struct., 90(2), 161-171. https://doi.org/10.1016/j.compstruct.2009.03.005.   DOI
28 Zhou, D., Cheung, Y.K., Lo, S.H. and Au, F.T.K. (2004), "Threedimensional vibration analysis of rectangular thick plates on Pasternak foundation", Int. J. Numer. Meth. Eng., 59(10), 1313-334. https://doi.org/10.1002/nme.915.   DOI
29 Abdou, M.A., Othman, M.I.A., Tantawi, R.S. and Mansour, N.T. (2019), "Exact solutions of generalized thermoelastic medium with double porosity under L-S theory", Indian J. Phys., 1-12. https://doi.org/10.1007/s12648-019-01505-8.
30 Abdelmalek, A., Bouazza, M., Zidour, M. and Benseddiq, N. (2019), "Hygrothermal effects on the free vibration behavior of composite plate using nth-order shear deformation theory: A Micromechanical approach", Iran. J. Sci. Technol. Trans. Mech. Eng., 43, 61-73. https://doi.org/10.1007/s40997-017-0140-y.   DOI
31 Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.   DOI
32 Akbas, S.D (2017a), "Nonlinear static analysis of functionally graded porous beams under thermal effect", Coupled Syst. Mech., 6(4), 399-415. https://doi.org/10.12989/csm.2017.6.4.399.   DOI
33 Akbas, S.D. (2019a), "Hygro-thermal post-buckling analysis of a functionally graded beam", Coupled Syst. Mech., 8(5), 459-471. https://doi.org/10.12989/csm.2019.8.5.459.   DOI
34 Akbas, S.D. (2019b), "Forced vibration analysis of functionally graded sandwich deep beams", Coupled Syst. Mech., 8(3), 259-271. https://doi.org/10.12989/csm.2019.8.3.259.   DOI
35 Eltaher, M.A. and Wagih, A. (2020), "Micromechanical modeling of damage in elasto-plastic nanocomposites using unit cell representative volume element and cohesive zone model", Ceramics Int. https://doi.org/10.1016/j.ceramint.2020.01.046.
36 Azmi, M., Kolahchi, R. and Bidgoli, M.R. (2019), "Dynamic analysis of concrete column reinforced with Sio2 nanoparticles subjected to blast load", Adv. Concrete Construct., 7(1), 51-63. https://doi.org/10.12989/acc.2019.7.1.051.   DOI
37 Barati, M.R. and Shahverdi, H. (2020), "Finite element forced vibration analysis of refined shear deformable nanocomposite graphene platelet-reinforced beams", J. Braz. Soc. Mech. Sci. Eng., 42(1), 33. https://doi.org/10.1007/s40430-019-2118-8.   DOI
38 Ebrahimi, F. and Barati, M.R. (2019), "A nonlocal strain gradient mass sensor based on vibrating hygro-thermally affected graphene nanosheets", Iran. J. Sci. Technol. Trans. Mech. Eng., 43, 205-220. https://doi.org/10.1007/s40997-017-0131-z.   DOI
39 Ebrahimi, F., Barati, M.R. and Civalek, O. (2019), "Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures", Eng. Comput., 1-12. https://doi.org/10.1007/s00366-019-00742-z.
40 Eltaher, M.A. and Mohamed, S.A. (2020), "Buckling and stability analysis of sandwich beams subjected to varying axial loads", Steel Compos. Struct., 34(2), 241-260. https://doi.org/10.12989/scs.2020.34.2.241.   DOI
41 Fakhar, A. and Kolahchi, R. (2018), "Dynamic buckling of magnetorheological fluid integrated by visco-piezo-GPL reinforced plates", Int. J. Mech. Sci., 144, 788-799. https://doi.org/10.1016/j.ijmecsci.2018.06.036.   DOI
42 Farrokhian, A. and Kolahchi, R. (2020), "Frequency and instability responses in nanocomposite plate assuming different distribution of CNTs", Struct. Eng. Mech., 73(5), 555-563. https://doi.org/10.12989/sem.2020.73.5.555.   DOI
43 Hadji, L., Zouatnia, N. and Bernard, F. (2019), "An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models", Struct. Eng. Mech., 69(2), 231-241. https://doi.org/10.12989/sem.2019.69.2.231.   DOI
44 Fenjan, R.M., Ahmed, R.A., Alasadi, A.A. and Faleh, N.M. (2019), "Nonlocal strain gradient thermal vibration analysis of double-coupled metal foam plate system with uniform and nonuniform porosities", Coupled Syst. Mech., 8(3), 247-257. https://doi.org/10.12989/csm.2019.8.3.247.   DOI
45 Filipich, C.P. and Rosales, M.B. (2002), "A further study about the behaviour of foundation piles and beams in a Winkler-Pasternak soil", Int. J. Mech. Sci., 44(1), 21-36. https://doi.org/10.1016/s0020-7403(01)00087-x.   DOI
46 Golabchi, H., Kolahchi, R. and Bidgoli, M.R. (2018), "Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects", Comput. Concrete, 21(4), 431-440. https://doi.org/10.12989/cac.2018.21.4.431.   DOI
47 Hajmohammad, M.H., Maleki, M. and Kolahchi, R. (2018b), "Seismic response of underwater concrete pipes conveying fluid covered with nano-fiber reinforced polymer layer", Soil Dyn. Earthq. Eng., 110, 18-27. https://doi.org/10.1016/j.soildyn.2018.04.002.   DOI
48 Hajmohammad, M.H., Farrokhian, A. and Kolahchi, R. (2018a), "Smart control and vibration of viscoelastic actuator-multiphase nanocomposite conical shells-sensor considering hygrothermal load based on layerwise theory", Aerosp. Sci. Technol., 78, 260-270. https://doi.org/10.1016/j.ast.2018.04.030.   DOI
49 Hajmohammad, M.H., Kolahchi, R., Zarei, M.S. and Maleki, M. (2018c), "Earthquake induced dynamic deflection of submerged viscoelastic cylindrical shell reinforced by agglomerated CNTs considering thermal and moisture effects", Compos. Struct., 187, 498-508. https://doi.org/10.1016/j.compstruct.2017.12.004.   DOI
50 Hajmohammad, M.H., Kolahchi, R., Zarei, M.S. and Nouri, A.H. (2019), "Dynamic response of auxetic honeycomb plates integrated with agglomerated CNT-reinforced face sheets subjected to blast load based on visco-sinusoidal theory", Int. J. Mech. Sci., 153, 391-401. https://doi.org/10.1016/j.ijmecsci.2019.02.008.   DOI
51 Hajmohammad, M.H., Zarei, M.S., Nouri, A. and Kolahchi, R. (2017), "Dynamic buckling of sensor/functionally gradedcarbon nanotube-reinforced laminated plates/actuator based on sinusoidal-visco-piezoelasticity theories", J. Sandw. Struct. Mater. https://doi.org/10.1177/1099636217720373.
52 Katariya, P.V., Panda, S.K. and Mahapatra, T.R. (2017), "Prediction of nonlinear eigen frequency of laminated curved sandwich structure using higher-order equivalent single-layer theory", J. Sandw. Struct. Mater., 109963621772842. https://doi.org/10.1177/1099636217728420.
53 Hamed, M.A., Mohamed, S.A. and Eltaher, M.A. (2020), "Buckling analysis of sandwich beam rested on elastic foundation and subjected to varying axial in-plane loads", Steel Compos. Struct., 34(1), 75-89. https://doi.org/10.12989/scs.2020.34.1.075.   DOI
54 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
55 Hieu, D. and Hai, N.Q. (2019), "Free vibration analysis of quintic nonlinear beams using equivalent linearization method with a weighted averaging", J. Appl. Comput. Mech., 5(1), 46-57. https://doi.org/10.22055/jacm.2018.24919.1217.
56 Hosseini, H. and Kolahchi, R. (2018), "Seismic response of functionally graded-carbon nanotubes-reinforced submerged viscoelastic cylindrical shell in hygrothermal environment", Physica E Low-dimens. Syst. Nanostruct., 102, 101-109. https://doi.org/10.1016/j.physe.2018.04.037.   DOI
57 Jamali, M., Shojaee, T., Mohammadi, B. and Kolahchi, R. (2019), "Cut out effect on nonlinear post-buckling behavior of FGCNTRC micro plate subjected to magnetic field via FSDT", Adv. Nano Res., 7(6), 405-417. https://doi.org/10.12989/anr.2019.7.6.405.   DOI
58 Keshtegar, B., Bagheri, M., Meng, D., Kolahchi, R. and Trung, N.T. (2020a), "Fuzzy reliability analysis of nanocomposite ZnO beams using hybrid analytical-intelligent method", Eng. Comput., 1-16. https://doi.org/10.1007/s00366-020-00965-5.
59 Koizumi M. (1997), "FGM activities in Japan", Compos. Part B Eng., 28(1-2), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9.   DOI
60 Keshtegar, B., Tabatabaei, J., Kolahchi, R. and Trung, N.T. (2020b), "Dynamic stress response in the nanocomposite concrete pipes with internal fluid under the ground motion load", Adv. Concrete Construct., 9(3), 327-335. https://doi.org/10.12989/acc.2020.9.3.327.   DOI
61 Kolahchi, R. (2017), "A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods", Aerosp. Sci. Technol., 66, 235-248. https://doi.org/10.1016/j.ast.2017.03.016.   DOI
62 Kolahchi, R. and Moniri Bidgoli, A.M. (2016), "Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes", Appl. Math. Mech. Engl. Ed., 37, 265-274. https://doi.org/10.1007/s10483-016-2030-8.   DOI
63 Kolahchi, R. and Cheraghbak, A. (2017), "Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method", Nonlin. Dyn., 90, 479-492. https://doi.org/10.1007/s11071-017-3676-x.   DOI
64 Kolahchi, R., Hosseini, H., Fakhar, M.H., Taherifar, R. and Mahmoudi, M. (2019), "A numerical method for magnetohygro-thermal postbuckling analysis of defective quadrilateral graphene sheets using higher order nonlocal strain gradient theory with different movable boundary conditions", Comput. Math. Appl., 78(6), 2018-2034. https://doi.org/10.1016/j.camwa.2019.03.042.   DOI
65 Kolahchi, R., Keshtegar, B. and Fakhar, M.H. (2020a), "Optimization of dynamic buckling for sandwich nanocomposite plates with sensor and actuator layer based on sinusoidal-visco-piezoelasticity theories using Grey Wolf algorithm", J. Sandw. Struct. Mater., 22(1). https://doi.org/10.1177/1099636217731071.
66 Kolahchi, R., Safari, M. and Esmailpour, M. (2016c), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. https://doi.org/10.1016/j.compstruct.2016.05.023.   DOI
67 Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017b), "Wave propagation of embedded viscoelastic FGCNT-reinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", Int. J. Mech. Sci., 130, 534-545. https://doi.org/10.1016/j.ijmecsci.2017.06.039.   DOI
68 Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Oskouei, A.N. (2017a), "Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods", Thin-Walled Struct., 113, 162-169. https://doi.org/10.1016/j.tws.2017.01.016.   DOI
69 Kolahchi, R., Zhu, S.P., Keshtegar, B. and Trung, N.T. (2020b), "Dynamic buckling optimization of laminated aircraft conical shells with hybrid nanocomposite martial", Aerosp. Sci. Technol., 98, 105656. https://doi.org/10.1016/j.ast.2019.105656.   DOI
70 Kolahchi, R., Hosseini, H. and Esmailpour, M. (2016b), "Differential cubature and quadrature-Bolotin methods for dynamic stability of embedded piezoelectric nanoplates based on visco-nonlocal-piezoelasticity theories", Compos. Struct., 157, 174-186. https://doi.org/10.1016/j.compstruct.2016.08.032.   DOI
71 Kolahchi, R., Safari, M. and Esmailpour, M. (2016a), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. https://doi.org/10.1016/j.ijmecsci.2017.06.039.   DOI
72 Matsunaga, H. (2000), "Vibration and stability of thick plates on elastic foundations", J. Eng. Mech., 126(1), 27-34. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:1(27).   DOI
73 Li, Z.M. and Yang, D.Q. (2016), "Thermal postbuckling analysis of anisotropic laminated beams with tubular cross-section based on higher-order theory", Ocean Eng., 115, 93-106. https://doi.org/10.1016/j.oceaneng.2016.02.017.   DOI
74 Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNTreinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel Compos. Struct., 22(4), 889-913. https://doi.org/10.12989/scs.2016.22.4.889.   DOI
75 Malikan, M. (2019), "On the buckling response of axially pressurized nanotubes based on a novel nonlocal beam theory", J. Appl. Comput. Mech., 5(1), 103-112. https://doi.org/10.22055/jacm.2018.25507.1274.
76 Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82(4), 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030.   DOI
77 Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012b), "Buckling analysis of sandwich plates with functionally graded skins using a new quasi-3D hyperbolic sine shear deformation theory and collocation with radial basis functions", ZAMM J. Appl. Math. Mech., 92(9), 749-766. https://doi.org/10.1002/zamm.201100186.   DOI
78 Motezaker, M. and Eyvazian, A. (2020a), "Post-buckling analysis of Mindlin cut out-plate reinforced by FG-CNTs", Steel Compos. Struct., 34(2), 289-297. https://doi.org/10.12989/scs.2020.34.2.289.   DOI
79 Motezaker, M. and Eyvazian, A. (2020b), "Buckling load optimization of beam reinforced by nanoparticles", Struct. Eng. Mech., 73(5), 481-486. https://doi.org/10.12989/sem.2020.73.5.481.   DOI
80 Motezaker, M. and Kolahchi, R. (2017a), "Seismic response of concrete columns with nanofiber reinforced polymer layer", Comput. Concrete, 20(3), 361-368. https://doi.org/10.12989/cac.2017.20.3.361.   DOI
81 Ayat, H., Kellouche, Y., Ghrici, M. and Boukhatem, B. (2018), "Compressive strength prediction of limestone filler concrete using artificial neural networks", Adv. Comput. Des., 3(3), 289-302. https://doi.org/10.12989/acd.2018.3.3.289.   DOI
82 Sahouane, A., Hadji, L. and Bourada, M. (2019), "Numerical analysis for free vibration of functionally graded beams using an original HSDBT", Earthq. Struct., 17(1), 31-37. https://doi.org/10.12989/eas.2019.17.1.031.   DOI
83 Zenkour, A.M. and Alghamdi, N.A. (2008), "Thermoelastic bending analysis of functionally graded sandwich plates", J. Mater. Sci., 43(8), 2574-2589. https://doi.org/10.1007/s10853-008-2476-6.   DOI
84 Al-Maliki, A.F.H., Faleh, N.M., Abbas, A. and Alasadi, A.A. (2019), "Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities", Struct. Monit. Maint., 6(2), 147-159. https://doi.org/10.12989/smm.2019.6.2.147.   DOI
85 Alasadi, A.A., Ahmed, R.A. and Faleh, N.M. (2019), "Analyzing nonlinear vibrations of metal foam nanobeams with symmetric and non-symmetric porosities", Adv. Aircraft Spacecraft Sci., 6(4), 273-282. https://doi.org/10.12989/aas.2019.6.4.273.   DOI
86 Amnieh, H.B., Zamzam, M.S. and Kolahchi, R. (2018), "Dynamic analysis of non-homogeneous concrete blocks mixed by SiO2 nanoparticles subjected to blast load experimentally and theoretically", Construct. Build. Mater., 174, 633-644. https://doi.org/10.1016/j.conbuildmat.2018.04.140.   DOI
87 Anderson, T.A. (2003), "A 3-D elasticity solution for a sandwich composite with functionally graded core subjected to transverse loading by a rigid sphere", Compos. Struct., 60(3), 265-274. https://doi.org/10.1016/s0263-8223(03)00013-8.   DOI
88 Arani, A.J. and Kolahchi, R. (2016), "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Comput. Concrete, 17(5), 567-578. https://doi.org/10.12989/cac.2016.17.5.567.   DOI
89 Arbabi, A., Kolahchi, R. and Bidgoli, M.R, (2020), "Experimental study for ZnO nanofibers effect on the smart and mechanical properties of concrete", Smart Struct. Syst., 25(1), 97-104. https://doi.org/10.12989/sss.2020.25.1.097.   DOI
90 Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603.   DOI
91 Bilouei, B.S., Kolahchi, R. and Bidgoli, M.R. (2016), "Buckling of concrete columns retrofitted with nano-fiber reinforced Polymer (NFRP)", Comput. Concrete, 18(5), 1053-1063. https://doi.org/10.12989/cac.2016.18.6.1053.   DOI
92 Behera, S. and Kumari, P. (2018), "Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory", Adv. Comput. Des., 3(3), 213-232. https://doi.org/10.12989/acd.2017.2.3.165.   DOI
93 Behravan Rad, A. (2012), "Static response of 2-D functionally graded circular plate with gradient thickness and elastic foundations to compound loads", Struct. Eng. Mech., 44(2), 139-161. https://doi.org/10.12989/sem.2012.44.2.139.   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., 66(6), 761-769. https://doi.org/10.12989/sem.2018.66.6.761.   DOI
95 Das, M., Barut, A., Madenci, E. and Ambur, D.R. (2006), "A triangular plate element for thermo-elastic analysis of sandwich panels with a functionally graded core", Int. J. Numer. Meth. Eng., 68(9), 940-966. https://doi.org/10.1002/nme.1724.   DOI
96 Ebrahimi, F. and Barati, M.R. (2018), "Hygro-thermal vibration analysis of bilayer graphene sheet system via nonlocal strain gradient plate theory", J. Braz. Soc. Mech. Sci. Eng., 40(9), 428. https://doi.org/10.1007/s40430-018-1350-y.   DOI