Browse > Article
http://dx.doi.org/10.12989/cac.2020.26.5.439

Porosity-dependent mechanical behaviors of FG plate using refined trigonometric shear deformation theory  

Bekkaye, Tahar Hacen Lamine (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
Fahsi, Bouazza (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes)
Bousahla, Abdelmoumen Anis (Laboratoire de Modelisation et Simulation Multi-echelle, 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)
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)
Al-Zahrani, Mesfer Mohammad (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals)
Publication Information
Computers and Concrete / v.26, no.5, 2020 , pp. 439-450 More about this Journal
Abstract
In this research, bending and buckling analyses of porous functionally graded (FG) plate under mechanical load are presented. The properties of the FG plate vary gradually across the thickness according to power-law and exponential functions. The material imperfection is considered to vary depending to a logarithmic function. The plate is modeled by a refined trigonometric shear deformation theory where the use of the shear correction factor is unnecessary. The governing equations of the FG plate are derived via virtual work principle and resolved via Navier solutions. The accuracy of the present model is checked by comparing the obtained results with those found in the literature. The various effects influencing the stresses, displacements and critical buckling loads of the plate are also examined and discussed in detail.
Keywords
static analysis; geometric imperfection; FG-plate; Navier solutions;
Citations & Related Records
Times Cited By KSCI : 56  (Citation Analysis)
연도 인용수 순위
1 Thanh, C.L., Nguyen, T.N., Vu, T.H., Khatir, S. and Abdel Wahab, M. (2020), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. Comput., 1-12. https://doi.org/10.1007/s00366-020-01154-0.
2 That, H.L.T., Nguyen-Van, H. and Chau-Dinh, T. (2020), "Nonlinear bending analysis of functionally graded plates using SQ4T elements based on twice interpolation strategy", J. Appl. Comput. Mech., 6(1), 125-136. https://doi.org/10.22055/JACM.2019.29270.1577.
3 Timesli, A. (2019), "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
4 Timesli, A. (2020a), "Prediction of the critical buckling load of SWCNT reinforced concrete cylindrical shell embedded in an elastic foundation", Comput. Concrete, 26(1), 53-62. http://dx.doi.org/10.12989/cac.2020.26.1.053.   DOI
5 Timesli, A. (2020b), "Buckling analysis of double walled carbon nanotubes embedded in Kerr elastic medium under axial compression using the nonlocal Donnell shell theory" Adv. Nano Res., 9(2), 69-82. https://doi.org/10.1007/s42452-020-2182-9.   DOI
6 Trabelsi, S., Frikha, A., Zghal, S. and Dammak, F. (2019), "A modified FSDT-based four nodes finite shell element for thermal buckling analysis of functionally graded plates and cylindrical shells", Eng. Struct., 178, 444-459. https://doi.org/10.1016/j.engstruct.2018.10.047.   DOI
7 Wattanasakulpong, N. and Ungbhakor, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32, 111-120. https://doi.org/10.1016/j.ast.2013.12.002.   DOI
8 Wattanasakulpong, N., Prusty, B.G., Kelly, D.W. and Hoffman, M. (2012), "Free vibration analysis of layered functionally graded beams with experimental validation", Mater. Des., 36, 182-190. https://doi.org/10.1016/j.matdes.2011.10.049.   DOI
9 Wu, C.P. and Li, H.Y. (2010), "An RMVT-based third-order shear deformation theory of multilayered functionally graded material plates", Compos. Struct., 92(10), 2591-2605. https://doi.org/10.1016/j.compstruct.2010.01.022.   DOI
10 Xiang, S. and Kang, G. (2013), "A nth-order shear deformation theory for the bending analysis on the functionally graded plates", Eur. J. Mech.-A/Solid., 37, 336-343. https://doi.org/10.1016/j.euromechsol.2012.08.005.   DOI
11 Yang, J. and Shen, H.S. (2001), "Dynamic response of initially stressed functionally graded rectangular thin plates", Compos. Struct., 54(4), 497-508. https://doi.org/10.1016/s0263-8223(01)00122-2.   DOI
12 Yuan, Y., Zhao, K., Sahmani, S. and Safaei, B. (2020), "Size-dependent shear buckling response of FGM skew nanoplates modeled via different homogenization schemes", Appl. Math. Mech.-Engl. Ed., 41, 587-604. https://doi.org/10.1007/s10483-020-2600-6.   DOI
13 Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Model., 30(1), 67-84. https://doi.org/10.1016/j.apm.2005.03.009.   DOI
14 Zhao, J., Zhang, Y., Choe, K., Qu, X., Wang, A. and Wang, Q. (2019), "Three-dimensional exact solution for the free vibration of thick functionally graded annular sector plates with arbitrary boundary conditions", Compos. Part B: Eng., 159, 418-436. https://doi.org/10.1016/j.compositesb.2018.09.107.   DOI
15 Zouatnia, N. and Hadji, L. (2019), "Static and free vibration behavior of functionally graded sandwich plates using a simple higher order shear deformation theory", Adv. Mater. Res., 8(4), 313-335. https://doi.org/10.12989/amr.2019.8.4.313.   DOI
16 Abdulrazzaq, M.A., Fenjan, R.M., Ahmed, R.A. and Faleh, N.M. (2020), "Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory", Steel Compos. Struct., 35(1), 147-157. https://doi.org/10.12989/scs.2020.35.1.147.   DOI
17 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
18 Akavci, S.S. (2016), "Mechanical behavior of functionally graded sandwich plates on elastic foundation", Compos. Part B: Eng., 96, 136-152. https://doi.org/10.1016/j.compositesb.2016.04.035.   DOI
19 Akbarzadeh, A.H., Abedini, A. and Chen, Z.T. (2015), "Effect of micromechanical models on structural responses of functionally graded plates", Compos. Struct., 119, 598-609. https://doi.org/10.1016/j.compstruct.2014.09.031.   DOI
20 Akgoz, B. and Civalek, O. (2015), "A microstructure-dependent sinusoidal plate model based on the strain gradient elasticity theory", Acta Mechanica, 226, 2277-2294. https://doi.org/10.1007/s00707-015-1308-4.   DOI
21 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
22 Arani, A.J. and Kolahchi, R. (2016), "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Comput. Concrete, 17(5), 567-578. http://dx.doi.org/10.12989/cac.2016.17.5.567.   DOI
23 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
24 Bhangale, R.K. and Ganesan, N. (2006), "Static analysis of simply supported functionally graded and layered magneto-electro-elastic plates", Int. J. Solid. Struct., 43(10), 3230-3253. https://doi.org/10.1016/j.ijsolstr.2005.05.030.   DOI
25 Bodaghi, M. and Saidi, A.R. (2010), "Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory", Appl. Math. Model., 34(11), 3659-3673. https://doi.org/10.1016/j.apm.2010.03.016.   DOI
26 Ashjari, M. and Khoshravan, M.R. (2014), "Mass optimization of functionally graded plate for mechanical loading in the presence of deflection and stress constraints", Compos. Struct., 110, 118-132. https://doi.org/10.1016/j.compstruct.2013.11.025.   DOI
27 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
28 Babaei, H., Kiani, Y. and Reza Eslami, M. (2019), "Thermal buckling and post-buckling analysis of geometrically imperfect FGM clamped tubes on nonlinear elastic foundation", Appl. Math. Model., https://doi.org/10.1016/j.apm.2019.02.009.
29 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
30 Hamad, L.B., Khalaf, B.S. and Faleh, N.M. (2019), "Analysis of static and dynamic characteristics of strain gradient shell structures made of porous nano-crystalline materials", Adv. Mater. Res., 8(3), 179-196. https://doi.org/10.12989/amr.2019.8.3.179.   DOI
31 Hamed, M.A., Sadoun, A.M. and Eltaher, M.A. (2019), "Effects of porosity models on static behavior of size dependent functionally graded beam", Struct. Eng. Mech., 71(1), 89-98. https://doi.org/10.12989/sem.2019.71.1.089.   DOI
32 Hassan, A. and Kurgan, N. (2020), "Bending analysis of thin FGM skew plate resting on Winkler elastic foundation using multi-term extended Kantorovich method", Eng. Sci. Technol., 23(4), 788-800. https://doi.org/10.1016/j.jestch.2020.03.009.
33 Jadhav, P.A. and Bajoria, K.M. (2012), "Buckling of piezoelectric functionally graded plate subjected to electro-mechanical loading", Smart Mater. Struct., 21(10), 105005. https://doi.org/10.1088/0964-1726/21/10/105005.   DOI
34 Boulal, A., Bensattalah, T., Karas, A., Zidour, M., Heireche, H. and Adda Bedia, E.A. (2020), "Buckling of carbon nanotube reinforced composite plates supported by Kerr foundation using Hamilton's energy principle", Struct. Eng. Mech., 73(2), 209-223. https://doi.org/10.12989/sem.2020.73.2.209.   DOI
35 Burlayenko, V.N., Altenbach, H., Sadowski, T. and Dimitrova, S.D. (2016), "Computational simulations of thermal shock cracking by the virtual crack closure technique in a functionally graded plate", Comput. Mater. Sci., 116, 11-21. https://doi.org/10.1016/j.commatsci.2015.08.038.   DOI
36 Chandra, B.M., K, Ramji, K., Kar, V.R., Panda, S.K., Lalepalli, K.A. 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
37 Cuong-Le, T., Nguyen, K.D., Nguyen-Trong, N., Khatir, S., Nguyen-Xuan, H. and Abdel-Wahab, M. (2020), "A three-dimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porous-cellular materials using IGA", Compos. Struct., 113216. https://doi.org/10.1016/j.compstruct.2020.113216.
38 Jomehzadeh, E., Saidi, A.R. and Atashipour, S.R. (2009), "An analytical approach for stress analysis of functionally graded annular sector plates", Mater. Des., 30(9), 3679-3685. https://doi.org/10.1016/j.matdes.2009.02.011.   DOI
39 Jung, W.Y., Han, S.C. and Park, W.T. (2016), "Four-variable refined plate theory for forced vibration analysis of sigmoid functionally graded plates on elastic foundation", J. Mech. Sci., 111, 73-87. https://doi.org/10.1016/j.ijmecsci.2016.03.001.   DOI
40 Kar, V.R. and Panda, S.K. (2014), "Nonlinear free vibration of functionally graded doubly curved shear deformable panels using finite element method", J. Vib. Control., 22(7), 1935-1949. https://doi.org/10.1177/1077546314545102.   DOI
41 Kar, V.R. and Panda, S.K. (2015a), "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
42 Kar, V.R. and Panda, S.K. (2015b), "Free vibration responses of temperature dependent functionally graded curved panels under thermal environment", Lat. Am. J. Solid. Struct., 12(11), 2006-2024. https://doi.org/10.1590/1679-78251691.   DOI
43 Kar, V.R. and Panda, S.K. (2015c), "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
44 Kar, V.R. and Panda, S.K. (2015d), "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
45 Kar, V.R. and Panda, S.K. (2016a), "Post-buckling behaviour of shear deformable functionally graded curved shell panel under edge compression", Int. J. Mech. Sci., 115-116, 318-324. https://doi.org/10.1016/j.ijmecsci.2016.07.014.   DOI
46 Dai, K.Y., Liu, G.R., Lim, K.M., Han, X. and Du, S.Y. (2004), "A meshfree radial point interpolation method for analysis of functionally graded material (FGM) plates", Comput. Mech., 34(3), 213-223. https://doi.org/10.1007/s00466-004-0566-0.   DOI
47 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., 16(1), 55-67. https://doi.org/10.12989/EAS.2019.16.1.055.   DOI
48 Do, T.V., Bui, T.Q., Yu, T.T., Pham, D.T. and Nguyen, C.T. (2017), "Role of material combination and new results of mechanical behavior for FG sandwich plates in thermal environment", J. Comput. Sci., 21, 164-181. https://doi.org/10.1016/j.jocs.2017.06.015.   DOI
49 Kar, V.R. and Panda, S.K. (2016b), "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
50 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
51 Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2017), "Effect of different temperature load on thermal postbuckling behaviour of functionally graded shallow curved shell panels", Compos. Struct., 160, 1236-1247. https://doi.org/10.1016/j.compstruct.2016.10.125.   DOI
52 Kar, V.R., Panda, S.K. and Mahapatra, T.R. (2016), "Thermal buckling behaviour of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties", Adv Mater. Res., 5(4), 205-221. https://doi.org/10.12989/AMR.2016.5.4.205.   DOI
53 Karami, B. and Janghorban, M. (2019), "On the dynamics of porous nanotubes with variable material properties and variable thickness", Int. J. Eng. Sci., 136, 53-66. https://doi.org/10.1016/j.ijengsci.2019.01.002   DOI
54 Khoa, N.D., Thiem, H.T. and Duc, N.D. (2017), "Nonlinear buckling and postbuckling of imperfect piezoelectric S-FGM circular cylindrical shells with metal-ceramic-metal layers in thermal environment using Reddy's third-order shear deformation shell theory", Mech. Adv. Mater. Struct., 1-12. https://doi.org/10.1080/15376494.2017.1341583.
55 Koizumi, M. (1993), "The concept of FGM", Ceram. Tran. Funct. Grad. Mater., 34, 3-10.
56 Kumar, R., Dutta, S.C. and Panda, S.K. (2016), "Linear and non-linear dynamic instability of functionally graded plate subjected to non-uniform loading", Compos. Struct., 154, 219-230. https://doi.org/10.1016/j.compstruct.2016.07.050.   DOI
57 Do, V.T., Pham, V.V. and Nguyen, H.N. (2020), "On the development of refined plate theory for static bending behavior of functionally graded plates", Math. Prob. Eng., 1-13. https://doi.org/10.1155/2020/2836763.
58 Duc, N.D and Cong, P.H. (2015), "Nonlinear dynamic response of imperfect symmetric thin sigmoid-functionally graded material plate with metal-ceramic-metal layers on elastic foundation", J. Vib. Control, 21, 637-646. https://doi.org/10.1177/1077546313489717.   DOI
59 Ebrahimi, F. and Barati, M.R. (2017), "Buckling analysis of nonlocal strain gradient axially functionally graded nanobeams resting on variable elastic medium", Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci., 232(11), 2067-2078. https://doi.org/10.1177/0954406217713518.   DOI
60 Ebrahimi, F. and Zia, M. (2015), "Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities", Acta Astronaut, 116, 117-125. https://doi.org/10.1016/j.actaastro.2015.06.014.   DOI
61 Ebrahimi, F., Rastgoo, A. and Atai, A.A. (2009), "A theoretical analysis of smart moderately thick shear deformable annular functionally graded plate", Eur. J. Mech.-A/Solid., 28(5), 962-973. https://doi.org/10.1016/j.euromechsol.2008.12.008.   DOI
62 Kumar, R., Lal, A., Singh, B.N. and Singh, J. (2018), "New transverse shear deformation theory for bending analysis of fgm plate under patch load", Compos. Struct., 208, 91-100. https://doi.org/10.1016/j.compstruct.2018.10.014.   DOI
63 Lanhe, W., Hongjun, W. and Daobin, W. (2007), "Dynamic stability analysis of FGM plates by the moving least squares differential quadrature method", Compos. Struct., 77(3), 383-394. https://doi.org/10.1016/j.compstruct.2005.07.011.   DOI
64 Li, Z., Zheng, J., Sun, Q. and He, H. (2019), "Nonlinear structural stability performance of pressurized thin-walled FGM arches under temperature variation field", Int. J. Nonlin. Mech., 113, 86-102. https://doi.org/10.1016/j.ijnonlinmec.2019.03.016.   DOI
65 Mantari, J.L. and Guedes Soares, C. (2012b), "Bending analysis of thick exponentially graded plates using a new trigonometric higher order shear deformation theory", Compos. Struct., 94(6), 1991-2000. https://doi.org/10.1016/j.compstruct.2012.01.005.   DOI
66 Mantari, J.L., Oktem, A.S. and Guedes Soares, C. (2012a), "Bending response of functionally graded plates by using a new higher order shear deformation theory", Compos. Struct., 94(2), 714-723. https://doi.org/10.1016/j.compstruct.2011.09.007.   DOI
67 Mehar, K. and Panda, S.K. (2016), "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
68 Mehar, K. and Panda, S.K. (2017), "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
69 Efraim, E. and Eisenberger, M. (2007), "Exact vibration analysis of variable thickness thick annular isotropic and FGM plates". J Sound Vib., 299(4-5), 720-738. https://doi.org/10.1016/j.jsv.2006.06.068.   DOI
70 Fazzolari, F.A. (2016), "Stability analysis of FGM sandwich plates by using variable-kinematics Ritz models", Mech. Adv. Mater. Struct., 23(9), 1104-1113. https://doi.org/10.1080/15376494.2015.1121559.   DOI
71 Mehar, K. and Panda, S.K. (2018), "Nonlinear finite element solutions of thermoelastic flexural strength and stress values of temperature dependent graded CNT-reinforced sandwich shallow shell structure", Struct. Eng. Mech., 67(6), 565-578. https://doi.org/10.12989/SEM.2018.67.6.565.   DOI
72 Mehar, K. and Panda, S.K. (2019), "Nonlinear deformation and stress responses of a graded carbon nanotube sandwich plate structure under thermoelastic loading", Acta Mechanica, 231(3), 1105-1123. https://doi.org/10.1007/s00707-019-02579-5.   DOI
73 Mehar, K., Kumar Panda, S., 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
74 Mehar, K., Mishra, P.K. and Panda, S.K. (2020), "Numerical investigation of thermal frequency responses of graded hybrid smart nanocomposite (CNT-SMA-Epoxy) structure", Mech. Adv. Mater. Struct., 1-13. https://doi.org/10.1080/15376494.2020.1725193.
75 Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017a), "Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure", Eur. J. Mech.-A/Solid., 65, 384-396. https://doi.org/10.1016/j.euromechsol.2017.05.005.   DOI
76 Mehar, K., Panda, S.K. and Mahapatra, T.R. (2018a), "Nonlinear frequency responses of functionally graded carbon nanotube-reinforced sandwich curved panel under uniform temperature field", Int. J. Appl. Mech., 10(3), 1850028. https://doi.org/10.1142/s175882511850028x.   DOI
77 Mehar, K., Panda, S.K. and Patle, B.K. (2018b), "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
78 Fenjan, N.M., Moustafa, N.M. and Faleh, N.M. (2020), "Scale-dependent thermal vibration analysis of FG beams having porosities based on DQM", Adv. Nano Res., 8(4), 283-292. https://doi.org/10.12989/anr.2020.8.4.283.   DOI
79 Forsat, M., Badnava, S., Mirjavadi, S.S., Barati. M.R. and Hamouda, A. (2020), "Small scale effects on transient vibrations of porous FG cylindrical nanoshells based on nonlocal strain gradient theory", Eur. Phys. J. Plus., 135, 81. https://doi.org/10.1140/epjp/s13360-019-00042-x.   DOI
80 Gafour, Y., Hamidi, A., Benahmed, A., Zidour, M. and Bensattalah, T. (2020), "Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle", Adv. Nano Res., 8(1), 49-58. https://doi.org/10.12989/anr.2020.8.1.049.   DOI
81 Ghannadpour, S.A.M., Ovesy, H.R. and Nassirnia, M. (2012), "Buckling analysis of functionally graded plates under thermal loadings using the finite strip method", Comput. Struct., 108-109, 93-99. https://doi.org/10.1016/j.compstruc.2012.02.011.   DOI
82 Gupta, A. and Talha, M. (2017), "Influence of porosity on the flexural and vibration response of gradient plate using nonpolynomial higher-order shear and normal deformation theory", Int. J. Mech. Mater. Des., 14(2), 277-296. https://doi.org/10.1007/s10999-017-9369-2.   DOI
83 Hadji, L. (2020), "Influence of the distribution shape of porosity on the bending of FGM beam using a new higher order shear deformation model", Smart Struct. Syst., 26(2), 253-262. https://doi.org/10.12989/sss.2020.26.2.253.   DOI
84 Mehar, K., Panda, S.K., Bui, T.Q. and Mahapatra, T.R. (2017b), "Nonlinear thermoelastic frequency analysis of functionally graded CNT-reinforced single/doubly curved shallow shell panels by FEM", J. Therm. Stress., 40(7), 899-916. https://doi.org/10.1080/01495739.2017.1318689.   DOI
85 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
86 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
87 Merzoug, M., Bourada, M., Sekkal, M., Abir, A.C., Chahrazed, B., Benyoucef, S. and Benachour, A. (2020), "2D and quasi 3D computational models for thermoelastic bending of FG beams on variable elastic foundation: Effect of the micromechanical models", Geomech. Eng., 22(4), 361-374. https://doi.org/10.12989/GAE.2020.22.4.361.   DOI
88 Mohammadi, M., Saidi, A.R. and Jomehzadeh, E. (2010), "A novel analytical approach for the buckling analysis of moderately thick functionally graded rectangular plates with two simply-supported opposite edges", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 224(9), 1831-1841. https://doi.org/10.1243/09544062jmes1804.   DOI
89 Moita, J.S., Araujo, A.L., Correia, V.F., Mota Soares, C.M. and Herskovits, J. (2019), "Buckling behavior of composite and functionally graded material plates", Eur. J. Mech.-A/Solid., 103921. https://doi.org/10.1016/j.euromechsol.2019.103921.
90 Monge, J.C. and Mantari, J.L. (2020), "3D elasticity numerical solution for the static behavior of FGM shells", Eng. Struct., 208, 110159. https://doi.org/10.1016/j.engstruct.2019.110159.   DOI
91 Nejadi, M.M. and Mohammadimehr, M. (2020), "Analysis of a functionally graded nanocomposite sandwich beam considering porosity distribution on variable elastic foundation using DQM: Buckling and vibration behaviors", Comput. Concrete, 25(3), 215-224. https://doi.org/10.12989/cac.2020.25.3.215   DOI
92 Nguyen, T.K. (2014), "A higher-order hyperbolic shear deformation plate model for analysis of functionally graded materials", Int. J. Mech. Mater. Des., 11(2), 203-219. https://doi.org/10.1007/s10999-014-9260-3.   DOI
93 Nguyen, T.K., Sab, K. and Bonnet, G. (2008), "First-order shear deformation plate models for functionally graded materials", Compos. Struct., 83(1), 25-36. https://doi.org/10.1016/j.compstruct.2007.03.004.   DOI
94 Othman, M. and Fekry, M. (2018), "Effect of rotation and gravity on generalized thermo-viscoelastic medium with voids", Multidisc. Model. Mater. Struct., 14(2), 322-338. https://doi.org/10.1108/MMMS-08-2017-0082.   DOI
95 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.
96 Rachedi, M. A., Benyoucef, S., Bouhadra, A., Bouiadjra, R.B., Sekkal, M. and Benachour, A. (2020), "Impact of the homogenization models on the thermoelastic response of FG plates on variable elastic foundation", Geomech. Eng., 22(1), 65-80. https://doi.org/10.12989/GAE.2020.22.1.065.   DOI
97 Ramteke, P.M., Mahapatra, B.P., Panda, S.K. and Sharma, N. (2020a), "Static deflection simulation study of 2D Functionally graded porous structure", Mater. Today: Proc., https://doi.org/10.1016/j.matpr.2020.03.537.
98 Ramteke, P.M., Mehar, K., Sharma, N. and Panda, S. (2020b), "Numerical prediction of deflection and stress responses of functionally graded structure for grading patterns (Power-law, sigmoid and exponential) and variable porosity (even/uneven)", Scientia Iranica. https://doi.org/10.24200/sci.2020.55581.4290.
99 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
100 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
101 Sahraee, S. (2009), "Bending analysis of functionally graded sectorial plates using Levinson plate theory", Compos. Struct., 88(4), 548-557. https://doi.org/10.1016/j.compstruct.2008.05.014.   DOI
102 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
103 Singha, M.K., Prakash, T. and Ganapathi, M. (2011), "Finite element analysis of functionally graded plates under transverse load", Finite Elem. Anal. Des., 47(4), 453-460. https://doi.org/10.1016/j.finel.2010.12.001.   DOI
104 Tayeb, T.S., Zidour, M., Bensattalah, T., Heireche, H., Benahmed, A. and Bedia, E.A. (2020), "Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle", Adv. Nano Res., 8(2), 135-148. https://doi.org/10.12989/anr.2020.8.2.135.   DOI
105 Thai, H.T. and Choi, D.H. (2012), "An efficient and simple refined theory for buckling analysis of functionally graded plates", Appl. Math. Model., 36(3), 1008-1022. https://doi.org/10.1016/j.apm.2011.07.062.   DOI
106 Thai, H.T. and Kim, S.E. (2013), "A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates", Compos. Struct., 96, 165-173. https://doi.org/10.1016/j.compstruct.2012.08.025.   DOI