[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.12989/scs.2016.22.2.257

A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates

Houari, Mohammed Sid Ahmed (Universite Mustapha Stambouli de Mascara, Department of Civil Engineering)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Bessaim, Aicha (Universite Mustapha Stambouli de Mascara, Department of Civil Engineering)
Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)

Publication Information

Steel and Composite Structures / v.22, no.2, 2016 , pp. 257-276 More about this Journal

Abstract

In this paper, a new simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded (FG) plates is developed. The significant feature of this formulation is that, in addition to including a sinusoidal variation of transverse shear strains through the thickness of the plate, it deals with only three unknowns as the classical plate theory (CPT), instead of five as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The accuracy of the present solutions is verified by comparing the obtained results with those predicted by classical theory, first-order shear deformation theory, and higher-order shear deformation theory. Verification studies show that the proposed theory is not only accurate and simple in solving the bending and free vibration behaviours of FG plates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

Keywords

a simple 3-unknown theory; bending; vibration; functionally graded plates;

Citations & Related Records

Times Cited By KSCI : 25 (Citation Analysis)

Reference
Cited By KSCI

1	Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Rogue, C.M.E., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Part B, 43(2), 711-725.
2	Pandya, B.N. and Kant, T. (1988), "Finite element analysis of laminated composite plates using a higherorder displacementmodel", Compos. Sci. Technol., 32(2), 137-155. DOI
3	Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation", J. Sound Vib., 318(1-2), 176-192. DOI
4	Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752. DOI
5	Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Methods Eng., 47(1-3), 663-684. DOI
6	Ren, J.G. (1986), "A new theory of laminated plate", Compos. Sci. Technol., 26(3), 225-239. DOI
7	Sahoo, S.S., Panda, S.K. and Mahapatra, T.R. (2016a), "Static, free vibration and transient response of laminated composite curved shallow panel - An experimental approach", Eur. J. Mech. - A/Solids, 59, 95-113. DOI
8	Sahoo, S.S., Panda, S.K. and Sen, D. (2016b), "Effect of delamination on static and dynamic behavior of laminated composite plate", AIAA J., 54(8), 2530-2544. DOI
9	Shimpi, R.P., Arya, H. and Naik, N.K. (2003), "A higher order displacement model for the plate analysis", J. Reinf. Plast. Comp., 18(22), 1667-1688.
10	Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech., 94(3), 195-220. DOI
11	Srinivas, S., Joga, C.V. and Rao, A.K. (1970), "Bending, vibration and buckling of simply supported thick orthotropic rectangular plate and laminates", Int. J. Solids Struct., 6(11), 1463-1481. DOI
12	Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916. DOI
13	Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. DOI
14	Tounsi, A., Houari, M.S.A. and Bessaim, A. (2016), "A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate", Struct. Eng. Mech., Int. J., (Accepted)
15	Vel, S.S. and Batra, R.C. (2004), "Three-dimensional exact solution for the vibration of functionally graded rectangular plates", J. Sound Vib., 272(3-5), 703-730. DOI
16	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. DOI
17	Yang, J., Liew, K.M. and Kitipornchai, S. (2005), "Stochastic analysis of compositionally graded plates with system randomness under static loading", Int. J. Mech. Sci., 47(10), 1519-1541. DOI
18	Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Free vibration analysis of functionally graded plates using the element-free kp-Ritz method", J. Sound Vib., 319(3-5), 918-939. DOI
19	Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Model., 30(1), 67-84. DOI
20	Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Tech., 34, 24-34. DOI
21	Ait Amar Meziane, M., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. DOI
22	Ait Atmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., Int. J., 19(2), 369-384. DOI
23	Boukhari, A., Atmane, H., Tounsi, A., Adda Bedia, E. and Mahmoud, S. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., Int. J., 57(5), 837-859. DOI
24	Bouchafa, A., Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., Int. J., 18(6), 1493-1515. DOI
25	Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., Int. J., 14(1), 85-104. DOI
26	Bouderba, B., Houari, M.S.A. and Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., Int. J., 58(3), 397-422. DOI
27	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. DOI
28	Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409-423. DOI
29	Bourada, F., Amara, K. and Tounsi, A. (2016), "Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory", Steel Compos. Struct., Int. J., 21(6), 1287-1306. DOI
30	Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Computat. Method., 11(6), 1350082. DOI
31	Amirpour, M., Das, R. and Saavedra Flores, E.I. (2016), "Analytical solutions for elastic deformation of functionally graded thick plates with in-plane stiffness variation using higher order shear deformation theory", Compos. Part B: Eng., 94, 109-121. DOI
32	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. DOI
33	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. DOI
34	Akavci, S.S. (2015), "An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Compos. Struct., 108, 667-676.
35	Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., Int. J., 19(6), 1421-1447. DOI
36	Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. DOI
37	Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., Int. J., 18(3), 659-672. DOI
38	Attia, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., Int. J., 18(1), 187-212. DOI
39	Aydogdu, M. (2006), "Comparison of various shear deformation theories for bending, buckling, and vibration of rectangular symmetric cross-ply plate with simply supported edges", J. Compos. Mater., 40(23), 2143-2155. DOI
40	Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos., Part B, 42(2), 123-133.
41	Darilmaz, K. (2015), "Vibration analysis of functionally graded material (FGM) grid systems", Steel Compos. Struct., Int. J., 18(2), 395-408. DOI
42	Draiche, K., Tounsi, A. and Khalfi, Y. (2014), "A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass", Steel Compos. Struct., Int. J., 17(1), 69-81. DOI
43	Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., Int. J., 18(1), 235-253. DOI
44	Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140(2), 374-383. DOI
45	Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011a), "Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure", Compos. Struct., 93(2), 722-735. DOI
46	Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011b), "A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates", Int. J. Mech. Sci., 53(1), 11-22. DOI
47	Jha, D.K., Kant, T. and Singh, R.K. (2013), "Free vibration response of functionally graded thick plates with shear and normal deformations effects", Compos. Struct., 96, 799-823. DOI
48	Kar, V.R. and Panda, S.K. (2015b), "Free vibration responses of temperature dependent functionally graded curved panels under thermal environment", Latin Am. J. Solid. Struct., 12(11), 2006-2024. DOI
49	Kant, T. and Pandya, B.N. (1988), "A simple finite element formulation of a higher-order theory for unsymmetrically laminated composite plates", Compos. Struct., 9(3), 215-246. DOI
50	Kar, V.R. and Panda, S.K. (2015a), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., Int. J., 18(3), 693-709. DOI
51	Kar, V.R. and Panda, S.K. (2016), "Thermal buckling and vibration analysis of laminated composite curved shell panel", Aircraft Eng. Aerosp. Technol.: Int. J., 88(1), 97-107. DOI
52	Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behaviour of laminated composite beam by the newmulti-layered laminated composite structures model with transverse shear stress continuity", Int. J. Solids Struct., 40(6), 1525-1546. DOI
53	Khalfi, Y., Houari, M.S.A. and Tounsi, A. (2014), "A Refined and Simple Shear Deformation Theory for Thermal Buckling of Solar Functionally Graded Plates on Elastic Foundation", Int. J. Computat. Method., 11(5), 1350077. DOI
54	Kitipornchai, S., Yang, J. and Liew, K.M. (2006), "Random vibration of the functionally graded laminates in thermal environments", Compos. Meth. Appl. Mech. Eng., 195(9-12), 1075-1095. DOI
55	Klouche Djedid, I., Benachour, A., Houari, M.S.A. and Tounsi, A. (2014), "A n-order four variable refined theory for bending and free vibration of functionally graded plates", Steel Compos. Struct., Int. J., 17(1), 21-46. DOI
56	Koizumi, M. (1993), "The concept of FGM", Ceram. Trans. Funct. Grad. Mater., 34, 3-10.
57	Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Braz. Soc. Mech. Sci. Eng., 38(1), 265-275. DOI
58	Bachir Bouiadjra, R., Adda Bedia, E.A. and Tounsi, A. (2013), "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory", Struct. Eng. Mech., Int. J., 48(4), 547-567. DOI
59	Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos.: Part B, 60, 274-283. DOI
60	Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygro-thermo-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. DOI
61	Belkorissat, I., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., Int. J., 18(4), 1063-1081. DOI
62	Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., Int. J., 19(3), 521-546. DOI
63	Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. DOI
64	Benveniste. Y. (1987), "A new approach to the application of Mori-Tanaka's theory in composite materials", Mech. Mat., 6(2), 147-157. DOI
65	Mahapatra, T.R., Kar, V.R. and Panda, S.K. (2016c), "Large amplitude bending behaviour of laminated composite curved panels", Eng. Computat., 33(1), 116-138. DOI
66	Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., Int. J., 18(2), 425-442. DOI
67	Mahapatra, T.R., Kar, V.R. and Panda, S.K. (2016a), "Large amplitude free vibration analysis of laminated composite spherical panel under hygrothermal environment", Int. J. Struct. Stabil. Dyn., 16(3), 1450105. DOI
68	Mahapatra, T.R., Panda, S.K. and Kar, V.R. (2016b), "Nonlinear flexural analysis of laminated composite panel under hygro-thermo-mechanical loading: A micromechanical approach", Int. J. Struct. Stabil. Dyn., 13(3), 1650015.
69	Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Modelling, 39(9), 2489-2508. DOI
70	Mantari, J.L., Ramos, I.A., Carrera, E. and Petrolo, M. (2016), "Static analysis of functionally graded plates using new non-polynomial displacement fields via Carrera Unified Formulation", Compos. Part B., 89, 127-142. DOI
71	Meradjah, M., Kaci, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2015), "A new higher order shear and normal deformation theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(3), 793-809. DOI
72	Mori, T. and Tanaka. K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta Metall, 21(5), 571-574. DOI

	H. Bakhshi Khaniki. (2018) Alexandria Engineering Journal Buckling analysis of nonuniform nonlocal strain gradient beams using generalized differential quadrature method /
	Mitsuru Endo. (2017) International Journal of Mechanical Sciences Equivalent property between the one-half order and first-order shear deformation theories under the simply supported boundary conditions / 131-132 , 245
	Jung Woo Lee. (2017) International Journal of Mechanical Sciences Free vibration analysis of functionally graded Bernoulli-Euler beams using an exact transfer matrix expression / 122 , 1
	Nitin Sharma. (2017) Composite Structures Vibro-acoustic behaviour of shear deformable laminated composite flat panel using BEM and the higher order shear deformation theory / 180 , 116
	Mohammad Reza Barati. (2017) Composite Structures A general bi-Helmholtz nonlocal strain-gradient elasticity for wave propagation in nanoporous graded double-nanobeam systems on elastic substrate / 168 , 885
	Jianguo Ding. (2018) Mechanics Based Design of Structures and Machines Nonlinear vibration analysis of functionally graded beams considering the influences of the rotary inertia of the cross section and neutral surface position / , 1
	Abdelkader Mahmoudi. (2017) Journal of Sandwich Structures & Materials A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations / , 109963621772757
3	Habib Hebali. (2016) Steel and Composite Structures A novel four variable refined plate theory for bending, buckling, and vibration of functionally graded plates / 22 (3) , 473
3	Misagh Zarepour. (2017) Applied Physics A Free vibration investigation of nano mass sensor using differential transformation method / 123 (3)
4	A. Mirafzal. (2017) Applied Physics A Dynamic characteristics of temperature-dependent viscoelastic FG nanobeams subjected to 2D-magnetic field under periodic loading / 123 (4)
	Farzad Ebrahimi. (2017) Journal of Vibration and Control Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory / , 107754631771153
	Mohammad Hadi Hajmohammad. (2018) Composite Structures Earthquake induced dynamic deflection of submerged viscoelastic cylindrical shell reinforced by agglomerated CNTs considering thermal and moisture effects / 187 , 498
6	K. Kiani. (2017) Acta Physica Polonica A Nonlocal Timoshenko Beam for Vibrations of Magnetically Affected Inclined Single-Walled Carbon Nanotubes as Nanofluidic Conveyors / 131 (6) , 1439
6	A. Chemi. (2018) Mechanics of Composite Materials Critical Buckling Load of Chiral Double-Walled Carbon Nanotubes Embedded in an Elastic Medium / 53 (6) , 827
5	M. Arefi. (2017) Applied Physics A Application of nonlocal strain gradient theory and various shear deformation theories to nonlinear vibration analysis of sandwich nano-beam with FG-CNTRCs face-sheets in electro-thermal environment / 123 (5)
	Kai Zhang. (2017) Composites Part B: Engineering Homogenization of hexagonal and re-entrant hexagonal structures and wave propagation of the sandwich plates with symplectic analysis / 114 , 80
5	Elyas Shivanian. (2017) Applied Physics A Influence of size effect on flapwise vibration behavior of rotary microbeam and its analysis through spectral meshless radial point interpolation / 123 (5)
	Davood Shahsavari. (2018) European Journal of Mechanics - A/Solids Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories / 67 , 200
4	Boumediene Kheroubi. (2016) Advances in nano research A new refined nonlocal beam theory accounting for effect of thickness stretching in nanoscale beams / 4 (4) , 251
4	Vishesh R. Kar. (2016) Advances in materials Research Thermal buckling behaviour of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties / 5 (4) , 205
	S. A. Belalia. (2017) Mechanics of Advanced Materials and Structures A new analysis of nonlinear free vibration behavior of bi-functionally graded sandwich plates using the p-version of the finite element method / , 1
	Qiliang Lin. (2017) Engineering Structures Experimental and theoretical investigation of the thermo-mechanical deformation of a functionally graded panel / 138 , 17
4	S. M. Aldousari. (2017) Applied Physics A Bending analysis of different material distributions of functionally graded beam / 123 (4)
	Yang Zhong. (2017) Mathematical Problems in Engineering Analysis Bending Solutions of Clamped Rectangular Thick Plate / 2017 , 1
	Nam-Il Kim. (2017) Composites Part B: Engineering Exact solutions for coupled responses of thin-walled FG sandwich beams with non-symmetric cross-sections / 122 , 121
	Li Li. (2018) Composite Structures Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature / 184 , 1177
	Moussa Abualnour. (2018) Composite Structures A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates / 184 , 688
	Peng Hao. (2017) Composite Structures Isogeometric buckling analysis of composite variable-stiffness panels / 165 , 192
	Davood Shahsavari. (2018) Aerospace Science and Technology A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation / 72 , 134
	Rafik Meksi. (2017) Journal of Sandwich Structures & Materials An analytical solution for bending, buckling and vibration responses of FGM sandwich plates / , 109963621769844
	S. A. Belalia. (2018) Mechanics of Advanced Materials and Structures A curved hierarchical finite element method for the nonlinear vibration analysis of functionally graded sandwich elliptic plates / , 1
	Hamed Pakdel. (2017) Theoretical and Applied Fracture Mechanics Experimental observation and energy based analytical investigation of matrix cracking distribution pattern in angle-ply laminates / 92 , 146
	M. Mohammadimehr. (2017) International Journal of Smart and Nano Materials Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo-magneto-mechanical loadings using DQM / , 1
12	Farzad Ebrahimi. (2017) The European Physical Journal Plus Dynamic modeling of porous heterogeneous micro/nanobeams / 132 (12)
3	Ali Jamalpoor. (2017) Applied Physics A Vibration analysis of bonded double-FGM viscoelastic nanoplate systems based on a modified strain gradient theory incorporating surface effects / 123 (3)
	Mohammad Reza Barati. (2017) Composite Structures Post-buckling analysis of refined shear deformable graphene platelet reinforced beams with porosities and geometrical imperfection / 181 , 194
	Fahimeh Mehralian. (2017) Physica B: Condensed Matter Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes / 514 , 61
3	Yaghoub Tadi Beni. (2017) Journal of Low Frequency Noise, Vibration and Active Control Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality / 36 (3) , 277
	Farzad Ebrahimi. (2017) Arabian Journal for Science and Engineering Nonlocal and Surface Effects on Vibration Behavior of Axially Loaded Flexoelectric Nanobeams Subjected to In-Plane Magnetic Field /
	Navvab Shafiei. (2017) Computer Methods in Applied Mechanics and Engineering Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams / 322 , 615
	Mohammad Arefi. (2017) Alexandria Engineering Journal Thermal stress and deformation analysis of a size-dependent curved nanobeam based on sinusoidal shear deformation theory /
	Sid Ahmed Belalia. (2017) Journal of Sandwich Structures & Materials Investigation of the mechanical properties on the large amplitude free vibrations of the functionally graded material sandwich plates / , 109963621770129
	Peng Hao. (2017) Composite Structures Buckling optimization of variable-stiffness composite panels based on flow field function / 181 , 240
	Farzad Ebrahimi. (2017) Microsystem Technologies Damping vibration behavior of visco-elastically coupled double-layered graphene sheets based on nonlocal strain gradient theory /
2	O. Rahmani. (2018) The European Physical Journal Plus Dynamic response of a single-walled carbon nanotube under a moving harmonic load by considering modified nonlocal elasticity theory / 133 (2)
1530-7972	(2018) Journal of Sandwich Structures & Materials Thermo-acoustic analysis of higher-order shear deformable laminated composite sandwich flat panel / (1530-7972) , 109963621878484
1548-0046	(2018) Particulate Science and Technology Fracture problems, vibration, buckling, and bending analyses of functionally graded materials: A state-of-the-art review including smart FGMS / (1548-0046) , 1
1661-9897	(2018) Journal of Nano Research Buckling Analysis of Orthotropic Nanoscale Plates Resting on Elastic Foundations / 55 (1661-9897) , 42
8	(2018) Microsystem Technologies Axial magnetic field effects on dynamic characteristics of embedded multiphase nanocrystalline nanobeams / 24 (8) , 3521
11	(2018) Journal of Intelligent Material Systems and Structures Vibration and buckling analysis of a rotary functionally graded piezomagnetic nanoshell embedded in viscoelastic media / 29 (11) , 2344
4	(2018) The European Physical Journal Plus Wave dispersion characteristics of embedded graphene platelets-reinforced composite microplates / 133 (4)
None	(2016) The open civil engineering journal Finite Element Method of Composite Steel-Concrete Beams Considering Interface Slip and Uplift / 11 (None) , 531
5	(2018) The European Physical Journal Plus Free vibration analysis of a piezoelectric curved sandwich nano-beam with FG-CNTRCs face-sheets based on various high-order shear deformation and nonlocal elasticity theories / 133 (5)
1530-7972	(2018) Journal of Sandwich Structures & Materials Smart electrical and magnetic stability analysis of exponentially graded shear deformable three-layered nanoplate based on nonlocal piezo-magneto-elasticity theory / (1530-7972) , 109963621876066
1661-9897	(2018) Journal of Nano Research Thermal and Small-Scale Effects on Vibration of Embedded Armchair Single-Walled Carbon Nanotubes / 51 (1661-9897) , 24
8	(2018) Journal of Thermal Stresses Thermodynamic effect on the bending response of elastic foundation FG plate by using a novel four variable refined plate theory / 41 (8) , 1042
02	(2018) International Journal of Applied Mechanics Thermoacoustic Behavior of Laminated Composite Curved Panels Using Higher-Order Finite-Boundary Element Model / 10 (02) , 1850017
1539-7742	(2019) Mechanics Based Design of Structures and Machines A novel approach for nonlinear bending response of macro- and nanoplates with irregular variable thickness under nonuniform loading in thermal environment / (1539-7742) , 1
3	(2016) Advances in materials research : AMR An analytical approach for buckling of functionally graded plates / 5 (3) , 141
5	(2016) Steel & Composite structures : an international journal A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates / 22 (5) , 975
3	(2016) Steel & Composite structures : an international journal A non-polynomial four variable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation / 23 (3) , 317
1	(2016) Advances in materials research : AMR Static deflection and dynamic behavior of higher-order hyperbolic shear deformable compositionally graded beams / 6 (1) , 13
1	(2017) Advances in materials research : AMR Bending and stability analysis of size-dependent compositionally graded Timoshenko nanobeams with porosities / 6 (1) , 45
3	(2016) Smart structures and systems Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT / 19 (3) , 289
2	(2016) Structural engineering and mechanics : An international journal Wave propagation in functionally graded beams using various higher-order shear deformation beams theories / 62 (2) , 143
4	(2017) Structural engineering and mechanics : An international journal A novel and simple HSDT for thermal buckling response of functionally graded sandwich plates / 62 (4) , 401
6	(2017) Structural engineering and mechanics : An international journal A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams / 62 (6) , 695
6	(2016) Smart structures and systems Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory / 19 (6) , 601
5	(2017) Steel & Composite structures : an international journal A new shear deformation plate theory with stretching effect for buckling analysis of functionally graded sandwich plates / 24 (5) , 569
5	(2017) Steel & Composite structures : an international journal Free vibrations of laminated composite plates using a novel four variable refined plate theory / 24 (5) , 603
2	(2016) Computers & concrete Dynamic bending response of SWCNT reinforced composite plates subjected to hygro-thermo-mechanical loading / 20 (2) , 229
4	(2017) Structural engineering and mechanics : An international journal An original single variable shear deformation theory for buckling analysis of thick isotropic plates / 63 (4) , 439
4	(2016) Structural engineering and mechanics : An international journal Rotating effects on hygro-mechanical vibration analysis of FG beams based on Euler-Bernoulli beam theory / 63 (4) , 471
5	(2016) Structural engineering and mechanics : An international journal A simple analytical approach for thermal buckling of thick functionally graded sandwich plates / 63 (5) , 585
3	(2016) Earthquakes and structures An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities / 13 (3) , 255
3	(2016) Geomechanics & engineering A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates / 13 (3) , 385
3	(2016) Smart structures and systems Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory / 20 (3) , 369
2	(2016) Steel & Composite structures : an international journal A new and simple HSDT for thermal stability analysis of FG sandwich plates / 25 (2) , 157
2	(2016) Structural engineering and mechanics : An international journal A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams / 64 (2) , 145
4	(2017) Smart structures and systems Free vibration of functionally graded plates resting on elastic foundations based on quasi-3D hybrid-type higher order shear deformation theory / 20 (4) , 509
3	(2016) Steel & Composite structures : an international journal An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates / 25 (3) , 257
4	(2017) Structural engineering and mechanics : An international journal Vibration analysis of micro composite thin beam based on modified couple stress / 64 (4) , 403
4	(2017) Steel & Composite structures : an international journal A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate / 25 (4) , 389
5	(2016) Earthquakes and structures A simple quasi-3D sinusoidal shear deformation theory with stretching effect for carbon nanotube-reinforced composite beams resting on elastic foundation / 13 (5) , 509
4	(2016) Structural engineering and mechanics : An international journal A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates / 64 (4) , 391
6	(2016) Structural engineering and mechanics : An international journal Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermo-mechanical loading using nonlocal strain gradient theory / 64 (6) , 683
6	(2016) Structural engineering and mechanics : An international journal A new quasi-3D HSDT for buckling and vibration of FG plate / 64 (6) , 737
6	(2016) Steel & Composite structures : an international journal An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions / 25 (6) , 693
6	(2016) Steel & Composite structures : an international journal A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations / 25 (6) , 717
6	(2016) Steel & Composite structures : an international journal An original HSDT for free vibration analysis of functionally graded plates / 25 (6) , 735
1	(2018) Structural engineering and mechanics : An international journal A nonlocal strain gradient theory for nonlinear free and forced vibration of embedded thick FG double layered nanoplates / 68 (1) , 103
5	(2016) Structural engineering and mechanics : An international journal Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory / 65 (5) , 621
1	(2016) Advances in nano research Forced vibration analysis of cracked functionally graded microbeams / 6 (1) , 39
6	(2018) Structural engineering and mechanics : An international journal Wave dispersion characteristics of nonlocal strain gradient double-layered graphene sheets in hygro-thermal environments / 65 (6) , 645
6	(2016) Structural engineering and mechanics : An international journal Development of super convergent Euler finite elements for the analysis of sandwich beams with soft core / 65 (6) , 657
1	(2018) Steel & Composite structures : an international journal A novel four variable refined plate theory for wave propagation in functionally graded material plates / 27 (1) , 109
1	(2016) Structural engineering and mechanics : An international journal Improved HSDT accounting for effect of thickness stretching in advanced composite plates / 66 (1) , 61
2	(2016) Steel & Composite structures : an international journal Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles / 27 (2) , 201
2	(2016) Structural engineering and mechanics : An international journal Three dimensional dynamic response of functionally graded nanoplates under a moving load / 66 (2) , 249
4	(2016) Smart structures and systems A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory / 21 (4) , 397
6	(2016) Geomechanics & engineering Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates / 14 (6) , 519
3	(2018) Steel & Composite structures : an international journal Bending of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment using an accurate theory / 27 (3) , 311
3	(2018) Structural engineering and mechanics : An international journal Analytical investigation of bending response of FGM plate using a new quasi 3D shear deformation theory: Effect of the micromechanical models / 66 (3) , 317
3	(2016) Structural engineering and mechanics : An international journal Free vibration of FGM plates with porosity by a shear deformation theory with four variables / 66 (3) , 353
4	(2018) Steel & Composite structures : an international journal Nonlocal free vibration analysis of a doubly curved piezoelectric nano shell / 27 (4) , 479
4	(2018) Structural engineering and mechanics : An international journal Three dimensional finite elements modeling of FGM plate bending using UMAT / 66 (4) , 487
6	(2016) Steel & Composite structures : an international journal Quasi-3D static analysis of two-directional functionally graded circular plates / 27 (6) , 789
5	(2016) Steel & Composite structures : an international journal Large deflection analysis of a fiber reinforced composite beam / 27 (5) , 567
5	(2016) Steel & Composite structures : an international journal A novel four-unknown quasi-3D shear deformation theory for functionally graded plates / 27 (5) , 599
2	(2016) Advances in nano research A new nonlocal HSDT for analysis of stability of single layer graphene sheet / 6 (2) , 147
6	(2018) Structural engineering and mechanics : An international journal A new quasi-3D higher shear deformation theory for vibration of functionally graded carbon nanotube-reinforced composite beams resting on elastic foundation / 66 (6) , 771
1	(2016) Steel & Composite structures : an international journal Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter / 28 (1) , 13
1	(2016) Smart structures and systems Size-dependent free vibration and dynamic analyses of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory / 22 (1) , 27
1	(2018) Smart structures and systems Eigenfrequencies of advanced composite plates using an efficient hybrid quasi-3D shear deformation theory / 22 (1) , 121
3	(2016) Structural engineering and mechanics : An international journal Single variable shear deformation model for bending analysis of thick beams / 67 (3) , 291
4	(2016) Structural engineering and mechanics : An international journal A new plate model for vibration response of advanced composite plates in thermal environment / 67 (4) , 369
5	(2016) Steel & Composite structures : an international journal Evaluation of vibroacoustic responses of laminated composite sandwich structure using higher-order finite-boundary element model / 28 (5) , 629
5	(2016) Structural engineering and mechanics : An international journal Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix / 67 (5) , 517
5	(2018) Structural engineering and mechanics : An international journal Effect of homogenization models on stress analysis of functionally graded plates / 67 (5) , 527
4	(2018) Earthquakes and structures Analysis of wave propagation and free vibration of functionally graded porous material beam with a novel four variable refined theory / 15 (4) , 369
4	(2016) Wind & structures An analytical solution for free vibration of functionally graded beam using a simple first-order shear deformation theory / 27 (4) , 247
4	(2016) Wind & structures A refined quasi-3D hybrid-type higher order shear deformation theory for bending and Free vibration analysis of advanced composites beams / 27 (4) , 269
6	(2016) Advances in aircraft and spacecraft science Surface effects on nonlinear vibration and buckling analysis of embedded FG nanoplates via refined HOSDPT in hygrothermal environment considering physical neutral surface position / 5 (6) , 691
5	(2018) Wind & structures Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation / 27 (5) , 311
4	(2016) Advances in nano research Critical buckling loads of carbon nanotube embedded in Kerr's medium / 6 (4) , 339
1	(2016) Steel & Composite structures : an international journal A novel hyperbolic shear deformation theory for the mechanical buckling analysis of advanced composite plates resting on elastic foundations / 30 (1) , 13
2	(2016) Structural engineering and mechanics : An international journal Nonlinear vibration of functionally graded nano-tubes using nonlocal strain gradient theory and a two-steps perturbation method / 69 (2) , 205
1	(2016) Wind & structures Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory / 28 (1) , 19
1	(2016) Wind & structures Dynamic and wave propagation investigation of FGM plates with porosities using a four variable plate theory / 28 (1) , 49
3	(2019) Structural engineering and mechanics : An international journal A novel refined shear deformation theory for the buckling analysis of thick isotropic plates / 69 (3) , 335
3	(2016) European physical journal Plus Application of the nonlocal strain gradient elasticity on the wave dispersion behaviors of inhomogeneous nanosize beams / 134 (3) , 112
None	(2016) Journal of nano research Static and Dynamic Behavior of Nanotubes-Reinforced Sandwich Plates Using (FSDT) / 57 (None) , 117
5	(2016) Structural engineering and mechanics : An international journal Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT / 69 (5) , 511
2	(2016) Advances in nano research Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT / 7 (2) , 89
6	(2016) Structural engineering and mechanics : An international journal Vibration analysis of different material distributions of functionally graded microbeam / 69 (6) , 637
None	(2016) Journal of nano research A New Hyperbolic Two-Unknown Beam Model for Bending and Buckling Analysis of a Nonlocal Strain Gradient Nanobeams / 57 (None) , 175
None	(2016) Nano hybrids and composites Free Vibration Analysis of Composite Material Plates "Case of a Typical Functionally Graded FG Plates Ceramic/Metal" with Porosities / 25 (None) , 69
1	(2019) Structural engineering and mechanics : An international journal Buckling behavior of rectangular plates under uniaxial and biaxial compression / 70 (1) , 113
3	(2019) Structural engineering and mechanics : An international journal A simple HSDT for bending, buckling and dynamic behavior of laminated composite plates / 70 (3) , 325
3	(2016) Advances in nano research Hygro-thermal effects on wave dispersion responses of magnetostrictive sandwich nanoplates / 7 (3) , 157
3	(2016) Advances in nano research Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT / 7 (3) , 191
2	(2016) Geomechanics & engineering The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate / 18 (2) , 161
5	(2016) Steel & Composite structures : an international journal A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation / 31 (5) , 503
5	(2019) Structural engineering and mechanics : An international journal Numerical analysis for free vibration of hybrid laminated composite plates for different boundary conditions / 70 (5) , 535
7	(2019) Microsystem technologies : sensors, actuators, systems integration Chaotic dynamics of a non-autonomous nonlinear system for a smart composite shell subjected to the hygro-thermal environment / 25 (7) , 2587
7	(2019) European physical journal Plus Stability analysis of embedded graphene platelets reinforced composite plates in thermal environment / 134 (7) , 349
5	(2019) Advances in nano research Vibration analysis of nonlocal porous nanobeams made of functionally graded material / 7 (5) , 351
10	(2019) European physical journal Plus Nonlinear forced vibrations of sandwich smart nanobeams with two-phase piezo-magnetic face sheets / 134 (10) , 508
4	(2016) Computers & concrete Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT / 24 (4) , 347
6	(2016) Advances in nano research The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory / 7 (6) , 443
12	(2016) European physical journal Plus Dynamic modeling of a multi-scale sandwich composite panel containing flexible core and MR smart layer / 134 (12) , 622
4	(2016) Strojnícky &ccaron;asopis Free Vibration Analysis of Simply Supported P-FGM Nanoplate Using a Nonlocal Four Variables Shear Deformation Plate Theory / 69 (4) , 9
5	(2019) Structural engineering and mechanics : An international journal A new higher-order shear and normal deformation theory for the buckling analysis of new type of FGM sandwich plates / 72 (5) , 653
6	(2016) Wind & structures On the modeling of dynamic behavior of composite plates using a simple nth-HSDT / 29 (6) , 371
2	(2020) Structural engineering and mechanics : An international journal Transfer matrix formulations and single variable shear deformation theory for crack detection in beam-like structures / 73 (2) , 109
2	(2020) Smart structures and systems A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates / 25 (2) , 197
1	(2020) Structural monitoring and maintenance A numerical method for dynamic characteristics of nonlocal porous metal-ceramic plates under periodic dynamic loads / 7 (1) , 27
5	(2016) Structural engineering and mechanics : An international journal A comprehensive review on the modeling of smart piezoelectric nanostructures / 74 (5) , 611
2	(2020) Structural engineering and mechanics : An international journal Buckling and free vibration analyses of nanobeams with surface effects via various higher-order shear deformation theories / 74 (2) , 175
4	(2016) Smart structures and systems Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory / 25 (4) , 409
3	(2020) Coupled systems mechanics Vibration analysis of nonlocal strain gradient porous FG composite plates coupled by visco-elastic foundation based on DQM / 9 (3) , 201
3	(2016) Engineering with computers Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT / 36 (3) , 807
3	(2016) Smart structures and systems Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam / 26 (3) , 361
4	(2020) Technologies Nonlinear Dynamic Behavior of Porous and Imperfect Bernoulli-Euler Functionally Graded Nanobeams Resting on Winkler Elastic Foundation / 8 (4) , 56
1	(2021) Archive of applied mechanics : Ingenieur-Archiv Higher-order semi-layerwise models for doubly curved delaminated composite shells / 91 (1) , 61
2	(2021) Aircraft engineering and aerospace technology Free vibration and buckling analysis of FGM plates using inverse trigonometric shear deformation theory / 93 (2) , 298