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http://dx.doi.org/10.12989/cac.2020.25.3.225

Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory  

Rahmani, Mohammed Cherif (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
Kaci, Abdelhakim (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
Bousahla, Abdelmoumen Anis (Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes)
Bourada, Fouad (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
Tounsi, Abdeldjebbar (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
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, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
Publication Information
Computers and Concrete / v.25, no.3, 2020 , pp. 225-244 More about this Journal
Abstract
The influence of boundary conditions on the bending and free vibration behavior of functionally graded sandwich plates resting on a two-parameter elastic foundation is examined using an original novel high order shear theory. The Hamilton's principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. 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). Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five, six or more in the case of other shear deformation theories. Galerkin's approach is utilized for FGM sandwich plates with six different boundary conditions. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.
Keywords
sandwich plates; functionally graded materials; new four-unknown refined shear deformation theory and various boundary conditions;
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1 Zhang, D.G. and Zhou, Y.H. (2008), "A theoretical analysis of FGM thin plates based on physical neutral surface", Comput. Mater. Sci., 44, 716-720. https://doi.org/10.1016/j.commatsci.2008.05.016.   DOI
2 Zhou, Y., Wang, Q., Shi, D., Liang, Q. and Zhang, Z. (2017), "Exact solutions for the free in-plane vibrations of rectangular plates with arbitrary boundary conditions", Int. J. Mech. Sci., 130, 1-10. https://doi.org/10.1016/j.ijmecsci.2017.06.004.   DOI
3 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
4 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., 25(6), 693-704. https://doi.org/10.12989/scs.2017.25.6.693.   DOI
5 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. Tran. Mech. Eng., 43, 61-73. https://doi.org/10.1007/s40997-017-0140-y.   DOI
6 Abdelrahman, A.A., Eltaher, M.A., Kabeel, A.M., Abdraboh, A.M. and Hendi, A.A. (2019), "Free and forced analysis of perforated beams", Steel Compos. Struct., 31(5), 489-502. https://doi.org/10.12989/scs.2019.31.5.489.   DOI
7 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", Ind. J. Phys., 1-12. https://doi.org/10.1007/s12648-019-01505-8.
8 Abrate S. (2008), "Functionally graded plates behave like homogeneous plates", Compos. Part B: Eng., 39, 151-158. https://doi.org/10.1016/j.compositesb.2007.02.026.   DOI
9 Akbas, S.D. (2017), "Vibration and static analysis of functionally graded porous plates", J. Appl. Comput. Mech., 3(3), 199-207. https://doi.org/10.22055/JACM.2017.21540.1107.
10 Akbas S.D. (2018), "Forced vibration analysis of functionally graded porous deep beams", Compos. Struct., 186, 293-302. https://doi.org/10.1016/j.compstruct.2017.12.013.   DOI
11 Akbas, S.D. (2019b), "Forced vibration analysis of functionally graded sandwich deep beams", Couple. Syst. Mech., 8(3), 259-271. https://doi.org/10.12989/csm.2019.8.3.259.
12 Al-Maliki, A.F., Faleh, N.M. and Alasadi, A.A. (2019), "Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities", Struct. Monit. Mainten., 6(2), 147-159. https://doi.org/10.12989/smm.2019.6.2.147.   DOI
13 Al-Osta, M.A. (2019), "Shear behaviour of RC beams retrofitted using UHPFRC panels epoxied to the sides", Comput. Concrete, 24(1), 37-49. https://doi.org/10.12989/cac.2019.24.1.037.   DOI
14 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. Aircraf. Spacecraf. Sci., 6(4), 273-282. https://doi.org/10.12989/aas.2019.6.4.273.   DOI
15 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
16 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. Aircraf. Spacecraf. Sci., 6(1), 1-18. https://doi.org/10.12989/aas.2019.6.1.001.   DOI
17 Arefi, M. (2015), "The effect of different functionalities of FGM and FGPM layers on free vibration analysis of the FG circular plates integrated with piezoelectric layers", Smart Struct. Syst., 15, 1345-1362. https://doi.org/10.12989/sss.2015.15.5.1345.   DOI
18 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
19 Akbas, S.D (2019a), "Nonlinear static analysis of laminated composite beams under hygro-thermal effect", Struct. Eng. Mech., 72(4), 433-441. https://doi.org/10.12989/sem.2019.72.4.433.   DOI
20 Barati, M.R. and Shahverdi, H. (2020), "Finite element forced vibration analysis of refined shear deformable nanocomposite graphene platelet-reinforced beams", J. Brazil Soc. Mech. Sci. Eng., 42(1), 33. https://doi.org/10.1007/s40430-019-2118-8.   DOI
21 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., 67(5), 517-525. https://doi.org/10.12989/sem.2018.67.5.517.   DOI
22 Benferhat, R., HassaineDaouadji, T., Hadji, L. and Said Mansour, M. (2016), "Static analysis of the FGM plate with porosities", Steel Compos. Struct., 21(1), 123-136. https://doi.org/10.12989/scs.2016.21.1.123.   DOI
23 Bensattalah, T., Zidour, M. and Daouadji, T.H. (2019), "A new nonlocal beam model for free vibration analysis of chiral single-walled carbon nanotubes", Compos. Mater. Eng., 1(1), 21-31. https://doi.org/10.12989/cme.2019.1.1.021.
24 Ebrahimi, F. and Barati, M.R. (2017b), "Scale-dependent effects on wave propagation in magnetically affected single/double-layered compositionally graded nanosize beams", Wave. Random Complex Media, 28(2), 326-342. https://doi.org/10.1080/17455030.2017.1346331.   DOI
25 Bensattalah, T., Zidour, M. and Hassaine Daouadji, T. (2018), "Analytical analysis for the forced vibration of CNT surrounding elastic medium including thermal effect using nonlocal Euler-Bernoulli theory", Adv. Mater. Res., 7(3), 163-174. https://doi.org/10.12989/amr.2018.7.3.163.   DOI
26 Cooke, D.W. and Levinson, M. (1983), "Thick rectangular plates-II, the generalized Levy solution", Int. J. Mech. Sci., 25(3), 207-215. https://doi.org/10.1016/0020-7403(83)90094-2.   DOI
27 Darilmaz, K. (2015), "Vibration analysis of functionally graded material (FGM) grid systems", Steel Compos. Struct., 18, 395-408. https://doi.org/10.12989/scs.2015.18.2.395.   DOI
28 Dihaj, A., Zidour, M., Meradjah, M., Rakrak, K., Heireche, H. and Chemi, A. (2018), "Free vibration analysis of chiral double-walled carbon nanotube embedded in an elastic medium using non-local elasticity theory and Euler Bernoulli beam model", Struct. Eng. Mech., 65(3), 335-342. https://doi.org/10.12989/sem.2018.65.3.335.   DOI
29 Ebrahimi, F. and Barati, M.R. (2017a), "Vibration analysis of nonlocal strain gradient embedded single-layer graphene sheets under nonuniform in-plane loads", J. Vib. Control, 107754631773408. https://doi.org/10.1177/1077546317734083.
30 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. Tran. Mech. Eng., 43, 205-220. https://doi.org/10.1007/s40997-017-0131-z.   DOI
31 Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Brazil. Soc. Mech. Sci. Eng., 40, 141. https://doi.org/10.1007/s40430-018-1065-0.   DOI
32 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
33 Eltaher, M.A., Agwa, M. and Kabeel, A (2018), "Vibration analysis of material size-dependent CNTs using energy equivalent model", J. Appl. Comput. Mech., 4(2), 75-86. https://doi.org/10.22055/JACM.2017.22579.1136.
34 Eltaher, M.A., El-Borgi, S. and Reddy, J.N. (2016), "Nonlinear analysis of size-dependent and material-dependent nonlocal CNTs", Compos. Struct., 153, 902-913. https://doi.org/10.1016/j.compstruct.2016.07.013.   DOI
35 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 non-uniform porosities", Coupl. Syst. Mech., 8(3), 247-257. https://doi.org/10.12989/csm.2019.8.3.247.   DOI
36 Nguyen, H.X., Nguyen, T.N., Abdel-Wahab, M., Bordas, S.P.A., Nguyen Xuan, H. and Vo, T.P. (2017), "A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory", Comput. Meth. Appl. Mech. Eng., 313, 904-940. https://doi.org/10.1016/j.cma.2016.10.002.   DOI
37 Eltaher, M.A., Mohamed, S.A. and Melaibari, A. (2020), "Static stability of a unified composite beams under varying axial loads", Thin Wall. Struct., 147, 106488. https://doi.org/10.1016/j.tws.2019.106488.   DOI
38 Eltaher, M.A., Wagih, A., Melaibari, A., Fathy, A. and Lubineau, G. (2019), "Effect of $Al_2O_3$ particles on mechanical and tribological properties of Al-Mg dual-matrix nanocomposites", Ceram. Int., 46(5), 5779-5787. https://doi.org/10.1016/j.ceramint.2019.11.028.   DOI
39 Fadoun, O.O., Borokinni, A.S., Layeni, O.P. and Akinola, A.P. (2017), "Dynamics analysis of a transversely isotropic non-classical thin plate", Wind Struct., 25(1), 25-38. https://doi.org/10.12989/was.2017.25.1.025.   DOI
40 Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007.   DOI
41 Ghorbanpour, A.A., Cheraghbak, A. and Kolahchi, R. (2016), "Dynamic buckling of FGM viscoelastic nano-plates resting on orthotropic elastic medium based on sinusoidal shear deformation theory", Struct. Eng. Mech., 60, 489-505. https://doi.org/10.12989/sem.2016.60.3.489.   DOI
42 Giunta, G., Belouettar, S. and Ferreira, A.J.M. (2016), "A static analysis of three-dimensional functionally graded beams by hierarchical modelling and a collocation meshless solution method", Acta Mechanica, 227(4), 969-991. https://doi.org/10.1007/s00707-015-1503-3.   DOI
43 Goldsmith, W., Wang, G., Li, K. and Crane, D. (1997), "Perforation of cellular sandwich plates", Int. J. Impact Eng., 19(5-6), 361-379. https://doi.org/10.1016/S0734-743X(97)00003-1.   DOI
44 Pandey, H.K., Hirwani, C.K., Sharma, N., Katariya, P.V. and Panda, S.K. (2019), "Effect of nano glass cenosphere filler on hybrid composite eigenfrequency responses-An FEM approach and experimental verification", Adv. Nano Res., 7(6), 419-429. https://doi.org/10.12989/anr.2019.7.6.419.   DOI
45 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
46 Nguyen, N.D., Nguyen, T.K., Nguyen, T.N. and Thai, H.T. (2018), "New Ritz-solution shape functions for analysis of thermo-mechanical buckling and vibration of laminated composite beams", Compos. Struct., 184, 452-460. https://doi.org/10.1016/j.compstruct.2017.10.003.   DOI
47 Nguyen, N.T., Hui, D., Lee, J. and Nguyen-Xuan, H. (2015), "An efficient computational approach for size-dependent analysis of functionally graded nanoplates", Comput. Meth. Appl. Mech. Eng., 297, 191-218. https://doi.org/10.1016/j.cma.2015.07.021.   DOI
48 Nguyen, V.H, Nguyen, T.K., Thai, H.T. and Vo, T.P. (2014), "A new inverse trigonometric shear deformation theory for isotropic and functionally graded sandwich plates", Compos. Part B: Eng., 66, 233-246. https://doi.org/10.1016/j.compositesb.2014.05.012.   DOI
49 Othman, M.I.A. and Lotfy, K. (2009), "Two-dimensional problem of generalized Magneto-Thermoelasticity with temperature dependent elastic moduli for different theories", Multidisc. Model. Mater. Struct., 5(3), 235-242. https://doi.org/10.1163/157361109789016961.   DOI
50 Thai, C.H., Ferreira, A., Bordas, S., Rabczuk, T. and Nguyen-Xuan, H. (2014), "Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory", Eur. J. Mech.-A/Solid., 43, 89-108. https://doi.org/10.1016/j.euromechsol.2013.09.001.   DOI
51 Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29, 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y.   DOI
52 Woo, J., Meguid, S.A. and Ong, L.S. (2006), "Nonlinear free vibration behavior of functionally graded plates", J. Sound Vib., 289, 595-611. https://doi.org/10.1016/j.jsv.2005.02.031.   DOI
53 Yazdani, R. and Mohammadimehr, M. (2019), "Double bonded Cooper-Naghdi micro sandwich cylindrical shells with porous core and CNTRC face sheets: Wave propagation solution", Comput. Concrete, 24(6), 499-511. https://doi.org/10.12989/cac.2019.24.6.499.   DOI
54 Yuksela, Y.Z. and Akbas, S.D. (2018), "Free vibration analysis of a Cross-Ply laminated plate in thermal environment", Int. J. Eng. Appl. Sci. (IJEAS)., 10(3), 176-189. http://dx.doi.org/10.24107/ijeas.456755.
55 Yuksela, Y.Z. and Akbas, S.D. (2019), "Buckling analysis of a fiber reinforced laminated composite plate with porosity", J. Comput. Appl. Mech., 50(2), 375-380. https://doi.org/10.22059/jcamech.2019.291967.448.
56 Zenkour, A.M. and Radwan, A.F. (2018), "Compressive study of functionally graded plates resting on Winkler-Pasternak foundations under various boundary conditions using hyperbolic shear deformation theory", Arch. Civil Mech. Eng., 18, 645-658. https://doi.org/10.1016/j.acme.2017.10.003.   DOI
57 Hamed, M.A., Salwa, A., Mohamed, S.A., Mohamed, 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
58 Haciyev, V.C., Sofiyev, A.H. and Kuruoglu, N. (2018), "Free bending vibration analysis of thin bidirectionally exponentially graded orthotropic rectangular plates resting on two-parameter elastic foundations", Compos. Struct., 184, 372-377. https://doi.org/10.1016/j.compstruct.2017.10.014.   DOI
59 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
60 Hajmohammad, M.H., Zarei, M.S., Nouri, A. and Kolahchi, R. (2017), "Dynamic buckling of sensor/functionally graded-carbon nanotube-reinforced laminated plates/actuator based on sinusoidal-visco-piezoelasticity theories", J. Sandw. Struct. Mater., 1099636217720373. https://doi.org/10.1177/1099636217720373.
61 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
62 He, X.Q., Ng, T.Y., Sivashanker, S. and Liew, K.M. (2001), "Active control of FGM plates with integrated piezoelectric sensors and actuators", Int. J. Solid. Struct., 38, 1641-1655. https://doi.org/10.1016/S0020-7683(00)00050-0.   DOI
63 Kar, V.R. and Panda, S.K. (2015c), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693.   DOI
64 Panjehpour, M., Loh, E.W.K. and Deepak, T.J. (2018), "Structural insulated panels: State-of-the-Art", Trend. Civil Eng. Arch., 3(1) 336-340. https://doi.org/10.32474/TCEIA.2018.03.000151.
65 Pradhan, K.K. and Chakraverty, S. (2015), "Free vibration of functionally graded thin elliptic plates with various edge supports", Struct. Eng. Mech., 53, 337-354. https://doi.org/10.12989/sem.2015.53.2.337.   DOI
66 Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermoelastic analysis of func-tionally graded ceramic-metal plates", Int. J. Solid. Struct., 35, 4457-4471. https://doi.org/10.1016/S0020-7683(97)00253-9.   DOI
67 Hussain, M. and Naeem, M.N. (2019), "Effects of ring supports on vibration of armchair and zigzag FGM rotating carbon nanotubes using Galerkin's method", Compos. Part B: Eng., 163, 548-561. https://doi.org/10.1016/j.compositesb.2018.12.144.   DOI
68 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. https://doi.org/10.1016/j.nucengdes.2012.05.001.   DOI
69 Kar, V.R. and Panda, S.K. (2015a), "Thermoelastic analysis of functionally graded doubly curved shell panels using nonlinear finite element method", Compos. Struct., 129, 202-212. https://doi.org/10.1016/j.compstruct.2015.04.006.   DOI
70 Kar, V.R. and Panda, S.K. (2015b), "Large deformation bending analysis of functionally graded spherical shell using FEM", Struct. Eng. Mech., 53(4), 661-679. https://doi.org/10.12989/sem.2015.53.4.661.   DOI
71 Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51, 745-752. https://doi.org/10.1115/1.3167719.   DOI
72 Radford, D.D., Fleck, N.A. and Deshpande, V.S. (2006), "The response of clamped sandwich beams subjected to shock loading", Int. J. Impact Eng., 32(6), 968-987. https://doi.org/10.1016/j.ijimpeng.2004.08.007.   DOI
73 Rajabi, J. and Mohammadimehr, M. (2019), "Bending analysis of a micro sandwich skew plate using extended Kantorovich method based on Eshelby-Mori-Tanaka approach", Comput. Concrete, 23(5), 361-376. https://doi.org/10.12989/cac.2019.23.5.361.   DOI
74 Ramteke, P.M., Panda, S.K. and Sharma, N. (2019), "Effect of grading pattern and porosity on the eigen characteristics of porous functionally graded structure", Steel Compos. Struct., 33(6), 865-875. https://doi.org/10.12989/scs.2019.33.6.865.   DOI
75 Reddy, J.N., Wang, C.M., Lim, G.T. and Ng, K.H. (2001), "Bending solutions of Levinson beams and plates in terms of the classical theories", Int. J. Solid. Struct., 38(26-27), 4701-4720. https://doi.org/10.1016/S0020-7683(00)00298-5.   DOI
76 Katariya, P., Panda, S. and Mahapatra, T. (2018), "Bending and vibration analysis of skew sandwich plate", Aircraf. Eng. Aerosp. Technol., 90(6), 885-895. https://doi.org/10.1108/AEAT-05-2016-0087.   DOI
77 Kar, V.R. and Panda, S.K. (2016), "Nonlinear thermomechanical behavior of functionally graded material Cylindrical/Hyperbolic/Elliptical shell panel with temperature-dependent and temperature-independent properties", J. Press. Ves. Technol., 138(6), 061202. https://doi.org/10.1115/1.4033701.   DOI
78 Kar, V.R. and Panda, S.K. (2017), "Large-amplitude vibration of functionally graded Doubly-Curved panels under heat conduction", AIAA J., 55(12), 4376-4386. https://doi.org/10.2514/1.j055878.   DOI
79 Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2015), "Nonlinear flexural analysis of laminated composite flat panel under hygro-thermo-mechanical loading", Steel Compos. Struct., 19(4),1011-1033. https://doi.org/10.12989/scs.2015.19.4.1011.   DOI
80 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
81 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
82 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
83 Sedighi, H.M. and Shirazi, K.H. (2013), "Vibrations of micro-beams actuated by an electric field via Parameter Expansion Method", Acta Astronautica, 85, 19-24. https://doi.org/10.1016/j.actaastro.2012.11.014.   DOI
84 Kolahchi, R., Keshtegar, B. and Fakhar, M.H. (2020), "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), 3-27. https://doi.org/10.1177/1099636217731071.   DOI
85 Katariya, P.V. and Panda, S.K. (2019a), "Numerical frequency analysis of skew sandwich layered composite shell structures under thermal environment including shear deformation effects", Struct. Eng. Mech., 71(6), 657-668. https://doi.org/10.12989/sem.2019.71.6.657.   DOI
86 Katariya, P.V. and Panda, S.K. (2019b), "Frequency and deflection responses of shear deformable skew sandwich curved shell panel: A finite element approach", Arab. J. Sci. Eng., 44(2), 1631-1648. https://doi.org/10.1007/s13369-018-3633-0.   DOI
87 Katariya, P.V., Hirwani, C.K. and Panda, S.K. (2019), "Geometrically nonlinear deflection and stress analysis of skew sandwich shell panel using higher-order theory", Eng. Comput., 35, 467-485. https://doi.org/10.1007/s00366-018-0609-3.   DOI
88 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
89 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
90 Katariya, P.V., Panda, S.K. and Mahapatra, T.R. (2017), "Prediction of nonlinear eigenfrequency of laminated curved sandwich structure using higher-order equivalent single-layer theory", J. Sandw. Struct. Mater., 109963621772842. https://doi.org/10.1177/1099636217728420.
91 Kolahchi, R., Safari, M. and Esmailpour, M. (2016), "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
92 Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017a), "Wave propagation of embedded viscoelastic FG-CNT-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
93 Shahadat, M.R.B., Alam, M.F., Mandal, M.N.A. and Ali, M.M. (2018), "Thermal transportation behaviour prediction of defective graphene sheet at various temperature: A Molecular Dynamics Study", Am. J. Nanomater., 6(1), 34-40. https://doi.org/10.12691/ajn-6-1-4.
94 Sedighi, H.M., Shirazi, K.H. and Zare, J. (2012a), "Novel equivalent function for deadzone nonlinearity: applied to analytical solution of beam vibration using He's Parameter Expanding Method", Lat. Am. J. Solid. Struct., 9(4), 443-452. https://doi.org/10.1590/s1679-78252012000400002.   DOI
95 Sedighi, H.M., Shirazi, K.H., Reza, A. and Zare, J. (2012b), "Accurate modeling of preload discontinuity in the analytical approach of the nonlinear free vibration of beams", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 226(10), 2474-2484. https://doi.org/10.1177/0954406211435196.   DOI
96 Selmi, A. and Bisharat, A. (2018), "Free vibration of functionally graded SWNT reinforced aluminum alloy beam", J. Vibroeng., 20(5), 2151-2164. https://doi.org/10.21595/jve.2018.19445.   DOI
97 Sharma, J.N., Chand, R. and Othman, M.I.A. (2009), "On the propagation of Lamb waves in viscothermoelastic plates under fluid loadings", Int. J. Eng. Sci., 47(3), 391-404. https://doi.org/10.1016/j.ijengsci.2008.10.008.   DOI
98 Shi, G. (2007), "A new simple third-order shear deformation theory of plates", Int. J. Solid. Struct., 44, 4399-4417. https://doi.org/10.1016/j.ijsolstr.2006.11.031.   DOI
99 Kunche, M.C., Mishra, P.K., Nallala, H.B., Hirwani, C.K., Katariya, P.V., Panda, S. and Panda, S.K. (2019), "Theoretical and experimental modal responses of adhesive bonded T-joints", Wind Struct., 29(5), 361-369. https://doi.org/10.12989/was.2019.29.5.361.   DOI
100 Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017b), "Wave propagation of embedded viscoelastic FG-CNT-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
101 Majeed, W.I. and Ghani, R.A. (2017), "Free vibration analysis of laminated composite plates with general elastic boundary supports", J. Eng., 23(4),100-124.
102 Lee, K.H., Lim, G.T. and Wang, C.M. (2002), "Thick Levy plates revisited", Int. J. Solid. Struct., 39, 127-144. https://doi.org/10.1016/S0020-7683(01)00205-0   DOI
103 Liu, Y. (2011), "A refined shear deformation plate theory", Int. J. Comput. Meth. Eng. Sci. Mech., 12, 141-149. https://doi.org/10.1080/15502287.2011.564267.   DOI
104 Majeed, W.I. and Abdul Kareem Abed, Z. (2019)," Buckling and pre-stressed dynamics analysis of laminated composite plate with different boundary conditions", Al-Khwarizmi Eng. J., 15(1), 46-55. https://doi.org/10.22153/kej.2019.07.002.   DOI
105 Mehar, K., Panda, S.K., Dehengia, A. and Kar, V.R. (2015), "Vibration analysis of functionally graded carbon nanotube reinforced composite plate in thermal environment", J. Sandw. Struct. Mater., 18(2), 151-173. https://doi.org/10.1177/1099636215613324.   DOI
106 Mehar, K., Panda, S.K., Devarajan, Y. and Choubey, G. (2019), "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
107 Mouli, C.B., Ramji, K., Kar, V.R., Panda, S.K., Anil, L.K. and Pandey, H.K. (2018), "Numerical study of temperature dependent eigenfrequency responses of tilted functionally graded shallow shell structures", Struct. Eng. Mech., 68(5), 527-536. https://doi.org/10.12989/sem.2018.68.5.527.   DOI
108 Merdaci, S., Tounsi, A., Houari, M.S.A., Mechab, I., Hebali, H. and Benyoucef, S. (2011), "Two new refined shear displacement models for functionally graded sandwich plates", Arch. Appl. Mech., 81(11), 1507-1522. https://doi.org/10.1007/s00419-010-0497-5.   DOI
109 Mirjavadi, S.S., Forsat, M., Nikookar, M., Barati, M.R. and Hamouda, A.M.S. (2019b), "Nonlinear forced vibrations of sandwich smart nanobeams with two-phase piezo-magnetic face sheets", Eur. Phys. J. Plus., 134, 508. https://doi.org/10.1140/epjp/i2019-12806-8.   DOI
110 Mohamed, N., Mohamed, A., Eltaher, M.A., Mohamed, S.A and Seddek. L.F. (2019), "Energy equivalent model in analysis of postbuckling of imperfect carbon nanotubes resting on nonlinear elastic foundation", Struct. Eng. Mech., 70(6), 737-750. https://doi.org/10.12989/sem.2019.70.6.737.   DOI
111 Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Jorge, R.M.N., MotaSoares, C.M. and Araujo, A.L. (2017), "Influence of zig-zag and warping effects on buckling of functionally graded sandwich plates according to sinusoidal shear deformation theories", Mech. Adv. Mater. Struct., 24(5), 360-376. https://doi.org/10.1080/15376494.2016.1191095.   DOI
112 Nguyen-Xuan, H., Thai, C.H. and Nguyen-Thoi, T. (2013), "Isogeometric finite element analysis of composite sandwich plates using a higher order shear deformation theory", Compos. Part B: Eng., 55, 558-574. https://doi.org/10.1016/j.compositesb.2013.06.044.   DOI