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http://dx.doi.org/10.12989/sem.2020.74.3.365

An efficient shear deformation theory with stretching effect for bending stress analysis of laminated composite plates  

Abbas, Soufiane (Laboratory of Materials and Reactive Systems (LMRS), University of Sidi Bel Abbes, Faculty of Technology, Mechanical Engineering Department)
Benguediab, Soumia (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Draiche, Kada (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Bakora, Ahmed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Benguediab, Mohamed (Laboratory of Materials and Reactive Systems (LMRS), University of Sidi Bel Abbes, Faculty of Technology, Mechanical Engineering Department)
Publication Information
Structural Engineering and Mechanics / v.74, no.3, 2020 , pp. 365-380 More about this Journal
Abstract
The focus of this paper is to develop an analytical approach based on an efficient shear deformation theory with stretching effect for bending stress analysis of cross-ply laminated composite plates subjected to transverse parabolic load and line load by using a new kinematic model, in which the axial displacements involve an undetermined integral component in order to reduce the number of unknowns and a sinusoidal function in terms of the thickness coordinate to include the effect of transverse shear deformation. The present theory contains only five unknowns and satisfies the zero shear stress conditions on the top and bottom surfaces of the plate without using any shear correction factors. The governing differential equations and its boundary conditions are derived by employing the static version of principle of virtual work. Closed-form solutions for simply supported cross-ply laminated plates are obtained applying Navier's solution technique, and the numerical case studies are compared with the theoretical results to verify the utility of the proposed model. Lastly, it can be seen that the present outlined theory is more accurate and useful than some higher-order shear deformation theories developed previously to study the static flexure of laminated composite plates.
Keywords
stress analysis; cross-ply laminated plates; parabolic load; line load; static flexure;
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Times Cited By KSCI : 79  (Citation Analysis)
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1 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. https://doi.org/10.1177/0021998306062313.   DOI
2 Baltac, A.K. (2018), "Numerical approaches for vibration response of annular and circular composite plates", Steel Compos. Struct., 29(6), 755-766. https://doi.org/10.12989/scs.2018.29.6.759.
3 Balubaid, M., Tounsi, A., Dakhel, B., Mahmoud, S.R. (2019), "Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory", Comput. Concrete., 24(6), 579-586. https://doi.org/10.12989/cac.2019.24.6.579.
4 Batou, B., Nebab, M., Bennai, R., Ait Atmane, H., Tounsi, A., Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699.   DOI
5 Behera, S., Kumari, P. (2018), "Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory", Adv. Comput. Design, 3(3), 213-232. https://doi.org/10.12989/acd.2018.3.3.213.   DOI
6 Belbachir, N., Draich, K., Bousahla, A.A., Bourada, M., Tounsi, A., Mohammadimehr, M. (2019), "Bending analysis of antisymmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings", Steel Compos. Struct., 33(1), 913-924. https://doi.org/10.12989/scs.2019.33.1.081.
7 Belkacem, A., Tahar, H.D., Abderrezak, R., Amine, B.M., Mohamed, Z., Boussad, A. (2018), "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions", Struct. Eng. Mech., 66(6), 761-769. https://doi.org/10.12989/sem.2018.66.6.761.   DOI
8 Belmahi, S., Zidour, M., Meradjah, M., Bensattalah, T., &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
9 Hirwani, C.K., Panda, S.K. (2019), "Nonlinear finite element solutions of thermoelastic deflection and stress responses of internally damaged curved panel structure", Appl. Math. Modelling, 65, 303-317. https://doi.org/10.1016/j.apm.2018.08.014.   DOI
10 Hirwani, C.K., Panda, S.K. (2018), "Numerical and experimental validation of nonlinear deflection and stress responses of pre-damaged glass-fibre reinforced composite structure", Ocean Eng., 159, 237-252. https://doi.org/10.1016/j.oceaneng.2018.04.035.   DOI
11 Hussain, M., Naeem, M.N., Tounsi, A., Taj, M. (2019a), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., 7(6), 431-442. https://doi.org/10.12989/anr.2019.7.6.431.   DOI
12 Hussain et al. (2019b), "Nonlocal vibration of DWCNTs based on Flugge shell model using wave propagation approach", Steel Compos. Struct., 34(4), 599. https://doi.org/10.12989/scs.2020.34.4.599.   DOI
13 Joshan, Y.S., Grover, N., Singh, B.N. (2018), "Assessment of non-polynomial shear deformation theories for thermo-mechanical analysis of laminated composite plates", Steel Compos. Struct., 27(6), 761-775. https://doi.org/10.12989/scs.2018.27.6.761.   DOI
14 Karami, B., Janghorban, M., Tounsi, A. (2019a), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., 7(1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055.
15 Karami, B., Shahsavari, D., Janghorban, M., Tounsi, A. (2019b), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with grapheme nanoplatelets", J. Mech. Sci., 156, 94-105. https://doi.org/10.1016/j.ijmecsci.2019.03.036.   DOI
16 Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A., Al-Osta, M.A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503.   DOI
17 Karami, B., Janghorban, M. and Tounsi, A. (2019c), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 35, 1297-1316. https://doi.org/10.1007/s00366-018-0664-9.   DOI
18 Berghouti, H., AddaBedia, E.A. Benkhedda, A., Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351.   DOI
19 Bouanati, S., Benrahou, K.H., AitAtmane, H., AitYahia, S., Bernard, F., Tounsi, A., AddaBedia, E.A. (2019), "Investigation of wave propagation in anisotropic plates via quasi 3D HSDT", Geomech. Eng., 18(1), 85-96. https://doi.org/10.12989/gae.2019.18.1.085.   DOI
20 Bouazza, M., Kenouza, Y., Benseddiq, N., Zenkour, A. M. (2017), "A two-variable simplified nth-higher-order theory for free vibration behavior of laminated plates", Compos. Struc.,182, 533-541. https://doi.org/10.1016/j.compstruct.2017.09.041.   DOI
21 Katariya, P., Panda, S. and Mahapatra, T. (2018), "Bending and vibration analysis of skew sandwich plate", Aircraft Eng. Aerosp. Technol., 90(6), 885-895. https://doi.org/10.1108/AEAT-05-2016-0087.   DOI
22 Szilard, R. (1974), Theory and Analysis of Plates, Classical and Numerical Methods, Prentice-Hall Inc., Englewood Cliffs, New Jersey, U.S.A.
23 Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161.   DOI
24 Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A., Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019   DOI
25 Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A., Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197.   DOI
26 Karami, B., Janghorban, M., Tounsi, A. (2019d), "On exact wave propagation analysis of triclinic material using three dimensional bi-Helmholtz gradient plate model", Struct. Eng. Mech., 69(5), 487-497. https://doi.org/10.12989/sem.2019.69.5.487.   DOI
27 Karami, B.,Janghorban, M., Tounsi, A. (2019e), "On pre-stressed functionally graded anisotropic nanoshell in magnetic field", J. Brazilian Soc. Mech. Sci. Eng., 41, 495. https://doi.org/10.1007/s40430-019-1996-0.   DOI
28 Kar, V.R., Mahapatra, T.R., 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/10.1142/S0219876216500158.   DOI
29 Katariya, P.V., 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
30 Katariya, P.V., Panda, S.K. (2019b), "Numerical evaluation of transient deflection and frequency responses of sandwich shell structure using higher order theory and different mechanical loadings", Eng. Comput., 35(3), 1009-1026. https://doi.org/10.1007/s00366-018-0646-y.   DOI
31 Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y.   DOI
32 Timoshenko, S. P. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells, McGraw-Hill Book Company, Inc., New York, U.S.A.
33 Timoshenko, S. P. and Gere, J. (1961), Theory of Elastic Stability, McGraw-Hill Book Company, Inc., New York, U.S.A.
34 Tounsi, A., Al-Dulaijan, S.U., Al-Osta, M.A., Chikh, A., Al-Zahrani, M.M., Sharif, A. and Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation", Steel Compos. Struct., 34(4), 511-524. https://doi.org/10.12989/scs.2020.34.4.511   DOI
35 Ugural, A. C. (1981), Stresses in Plates and Shells, McGraw-Hill Book Company, Inc., New York, U.S.A.
36 Vo, T. P., Thai, H.T., Nguyen, T. K., Lanc, D. and Karamanli, A. (2017), "Flexural analysis of laminated composite and sandwich beams using a four unknown shear and normal deformation theory", Compos. Struct., 176, 388-397. https://doi.org/10.1016/j.compstruct.2017.05.041.   DOI
37 Wang, S. (1997), "Buckling analysis of skew fibre-reinforced composite laminates based on first-order shear deformation plate theory", Compos Struct, 37, 5-19. https://doi.org/10.1016/S0263-8223(97)00050-0.   DOI
38 Whitney, J.M. (1969), "The effect of transverse shear deformation on the bending of laminated plates", J. Compos. Mater, 3, 534-547. https://doi.org/10.1177/002199836900300316.   DOI
39 Whitney, J. M., and Pagano, N. J. (1970), "Shear deformation in heterogeneous anisotropic plates", ASME J. App. Mech., 37, 1031-1036. https://doi.org/10.1115/1.3408654   DOI
40 Katariya, P.V., Panda, S.K. (2019c), "Frequency and deflection responses of shear deformable skew sandwich curved shell panel: a finite element approach", Arabian J. Sci. Eng., 44(2), 1631-1648. https://doi.org/10.1007/s13369-018-3633-0.   DOI
41 Khiloun, M., Bousahla, A.A., Kaci, A., Bessaim, A., Tounsi, A., Mahmoud, S.R. (2019), "Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT", Eng. Comput.., https://doi.org/10.1007/s00366-019-00732-1.
42 Sahoo, R. and Singh, B.N. (2014), "A new trigonometric zigzag theory for static analysis of laminated composite and sandwich plates", Aerospace Sci. Tech., 35, 15-28. https://doi.org/10.1016/j.ast.2014.03.001.   DOI
43 Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", ASME J. App. Mec., 12, 69-77. https://doi.org/10.1177/002199836900300316.
44 Sahla, M., Saidi, H., Draiche, K., Bousahla, A.A., Bourada, F., Tounsi, A. (2019), "Free vibration analysis of angle-ply laminated composite and soft core sandwich plates", Steel Compos. Struct., 33(5), 663-679. https://doi.org/10.12989/scs.2019.33.5.663.   DOI
45 Sahouane, A., Hadji, L., 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
46 Sahoo, S.S., Panda, S.K. and Mahapatra, T.R. (2016), "Static, free vibration and transient response of laminated composite curved shallow panel-an experimental approach", Eur. J. Mec.-A/Solids, 59, 95-113. https://doi.org/10.1016/j.euromechsol.2016.03.014.   DOI
47 Carlos M.M.S., Cristovao M.M.S., and Manuel J.M.F. (1999), Mechanics of Composite Materials and Structures, Springer Science+Business Media, 517.
48 Ahmed, A. (2014), "Post buckling analysis of sandwich beams with functionally graded faces using a consistent higher order theory", Int. J. Civil Struct. Environ., 4(2), 59-64.
49 Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R., Tounsi, A. (2019), "Dynamic Analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., 7(3), 189-206. https://doi.org/10.12989/anr.2019.7.3.191.
50 Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A., Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185.   DOI
51 Zaoui, F.Z., Ouinas, D., Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B, 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051.   DOI
52 Kim, S. E., Thai, H. T. and Lee, J. (2009), "A two variable refined plate theory for laminated composite plates", Compos.Struct.,89, 197-205. https://doi.org/10.1016/j.compstruct.2008.07.017.   DOI
53 Sahoo, S.S., Panda, S.K. and Mahapatra, T.R., Hirwani, C.K. (2019), "Numerical analysis of transient responses of delaminated layered structure using different mid-plane theories and experimental validation", Iranian J. Sci. Technol. Transactions Mech. Eng., 43(1), 41-56. https://doi.org/10.1007/s40997-017-0111-3.   DOI
54 Salah, F., Boucham, B., Bourada, F., Benzair, A., Bousahla, A.A., Tounsi, A. (2019), "Investigation of thermal buckling properties of ceramic-metal FGM sandwich plates using 2D integral plate model", Steel Compos. Struct., 33(6), 805-822. https://doi.org/10.12989/scs.2019.33.6.805.   DOI
55 Salami, S.J., Dariushi, S. (2018), "Analytical, numerical and experimental investigation of low velocity impact response of laminated composite sandwich plates using extended high order sandwich panel theory", Struct. Eng. Mech., 68(3), 325-334. https://doi.org/10.12989/sem.2018.68.3.325.   DOI
56 Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput. Concrete, 24(6), 489-498. https://doi.org/10.12989/cac.2019.24.06.489.   DOI
57 Yang, P. C., Norris, C. H., and Stavsky, Y. (1966), "Elastic wave propogation in heterogeneous plates", Int. J. Solids Struct., 2, 665-684. https://doi.org/10.1016/0020-7683(66)90045-X.   DOI
58 Zamani, H.A., Aghdam, M.M., Sadighi, M. (2017), "Free vibration analysis of thick viscoelastic composite plates on visco-Pasternak foundation using higher-order theory", Compos.Struct., 182, 25-35. https://doi.org/10.1016/j.compstruct.2017.08.101   DOI
59 Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F., Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389.   DOI
60 Zenkour, A.M. (2004), "Analytical solution for bending of cross-ply laminated plates under thermo-mechanical loading", Compos. Struct., 65, 367-379. https://doi.org/10.1016/j.compstruct.2003.11.012.   DOI
61 Zine, A., Tounsi, A., Draiche, K., Sekkal, M., and Mahmoud, S.R. (2018), "A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells", Steel Compos. Struct., 26(2), 125-137. https://doi.org/10.12989/scs.2018.26.2.125.   DOI
62 Civalek, O. (2008), "Analysis of thick rectangular plates with symmetric cross-ply laminates based on first-order shear deformation theory", J. Compos. Mater, 42, 2853-2867. https://doi.org/10.1177%2F0021998308096952.   DOI
63 Cetkovic, M. and Vuksanovic, D. (2011), "Large deflection analysis of laminated composite plates using layerwise displacement model", Struct. Eng. Mech., 40(2), 257-277. https://doi.org/10.12989/sem.2011.40.2.257.   DOI
64 Chemi, A., Zidour, M., Heireche, H., Rakrak, K. and Bousahla, A. A. (2018), "Critical buckling load of chiral double-walled carbon nanotubes embedded in an elastic medium", Mech. Compos. Mater., 53(6), 827-836. https://doi.org/10.1007/s11029-018-9708-x.   DOI
65 Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289.   DOI
66 Daouadji, T.H. (2017), "Analytical and numerical modeling of interfacial stresses in beams bonded with a thin plate", Adv. Comput. Design, 2(1), 57-69. https://doi.org/10.12989/acd.2017.2.1.057.   DOI
67 Mahmoud, S.R., Tounsi, A. (2019), "On the stability of isotropic and composite thick plates", Steel Compos. Struct., 33(4), 551-568. https://doi.org/10.12989/scs.2019.33.4.551.   DOI
68 Kirchhoff, G.R. (1850), "Uber das gleichgewicht und die bewegung einer elastischen scheibe", J. Pure and App. Math., 40, 51-88. https://doi.org/10.1515/crll.1850.40.51.
69 Love, A. E. H., (1944), A Treatise on the Mathematical Theory of Elasticity, 4th ed., Dover Publ., New York, U.S.A.
70 Mahi, A., Adda Bedia, E.A, 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. Model, 39, 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045.   DOI
71 Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Adda Bedia, E.A., Mahmoud, S.R. (2019), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandwich Struct. Mater., 21(6), 1906-1926. https://doi.org/10.1177%2F1099636217727577.   DOI
72 Mantari, J.L., Oktem, A.S., GuedesSoares, C. (2012), "A new trigonometric layerwise shear deformation theory for the finite element analysis of laminated composite and sandwich plates", Comput. and Struct., 94-95, 45-53. https://doi.org/10.1016/j.compstruc.2011.12.003.   DOI
73 Matsunaga, H. (2000), "Vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory", Compos.Struct.,48(4), 231-244. https://doi.org/10.1016/S0263-8223(99)00110-5.   DOI
74 Sherafat, M.H., Ghannadpour, S.A.M., Ovesy, H.R. (2013), "Pressure loading, end-shortening and through-thickness shearing effects on geometrically nonlinear response of composite laminated plates using higher order finite strip method", Struct. Eng. Mech., 45(5), 677-691. https://doi.org/10.12989/sem.2013.45.5.677.   DOI
75 Sayyad, A. S. and Ghugal, Y. M. (2013), "Effect of Stress Concentration on Laminated Plates", J. Mech., 29(02), 241-252. https://doi.org/10.1017/jmech.2012.131.   DOI
76 Sayyad, A. S., Ghugal, Y. M., Shinde, B. M. (2016), "Thermal stress analysis of laminated composite plates using exponential shear deformation theory", Int. J. Automotive Compos., 2(1), 23-40.   DOI
77 Sayyad, A.S. and Ghugal, Y.M. (2017), "A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates", Int. J. App. Mec., 9(1), 1- 36. https://doi.org/10.1142/S1758825117500077.
78 Sehoul, M., Benguediab, M., Bakora, A. and Tounsi, A. (2017), "Free vibrations of laminated composite plates using a novel four variable refined plate theory", Steel Compos. Struct., 24(5), 603-613. https://doi.org/10.12989/scs.2017.24.5.603.   DOI
79 Semmah, A., Heireche, H., Bousahla, A.A., Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT", Adv. Nano Res., 7(2), 89-98. https://doi.org/10.12989/anr.2019.7.2.089.   DOI
80 Singh D. B. and Singh, B. N. (2017), "New higher order shear deformation theories for free vibration and buckling analysis of laminated and braided composite plates", J. Mec. Sci., 131, 265-277. https://doi.org/10.1016/j.ijmecsci.2017.06.053.   DOI
81 Soldatos, KP, Timarci, T. (1993), "A unified formulation of laminated composite, shear deformable, five-degrees-of-freedom cylindrical shell theories", Compos. Struct., 1993, 25, 165-171. https://doi.org/10.1016/0263-8223(93)90162-J.   DOI
82 Avcar, M. (2015), "Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam", Struct. Eng. Mech., 55(4), 871-884. https://doi.org/10.12989/sem.2015.55.4.871.   DOI
83 Addou, F.Y., Meradjah, M., Bousahla, A.A, Benachour, A., Bourada, F., Tounsi, A., Mahmoud, S.R. (2019), "Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT", Comput. Concrete, 24(4), 347-367. https://doi.org/10.12989/cac.2019.24.4.347.   DOI
84 Akavci, S. S. (2007), "Buckling and free vibration analysis of symmetric and antisymmetric laminated composite plates on an elastic foundation", J. Reinf. Plastics Compos., 26(18), 1907-1919. https://doi.org/10.1177/0731684407081766.   DOI
85 Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magnetoelastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485.   DOI
86 Avcar, M. (2016), "Effects of material non-homogeneity and two parameter elastic foundation on fundamental frequency parameters of Timoshenko beams", Acta Physica Polonica A, 130(1), 375-378.   DOI
87 Avcar, M. and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci., 11, 232. https://doi.org/10.1007/s12517-018-3579-2.   DOI
88 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
89 Ayat, H., Kellouche, Y., Ghrici, M., Boukhatem, B. (2018), "Compressive strength prediction of limestone filler concrete using artificial neural networks", Adv. Comput. Design, 3(3), 289-302. https://doi.org/10.12989/acd.2018.3.3.289.   DOI
90 Draoui, A., Zidour, M., Tounsi, A., Adim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117.   DOI
91 Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", J. App. Mec., 18, 31-38.   DOI
92 Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate", Steel Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595.   DOI
93 Mehar, K., Panda, S.K. (2019), "Theoretical deflection analysis of multi-walled carbon nanotube reinforced sandwich panel and experimental verification", Compos. Part B Eng., 167, 317-328. https://doi.org/10.1016/j.compositesb.2018.12.058.   DOI
94 Meksi, R, Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, SR. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater.,21(2), 727-757. https://doi.org/10.1177/1099636217698443.   DOI
95 Nedri, K., El Meiche, N. and Tounsi, A. (2014), "Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory", Mec. Compos. Mater.,49(6), 629-640. https://doi.org/10.1007/s11029-013-9379-6.   DOI
96 Nor Hafizah, A.K., Lee, J.H., Aziz, Z.A. and Viswanatha, K.K. (2018), "Vibration of antisymmetric angle-ply laminated plates of higher-order theory with variable thickness", Math. Prob. in Eng., Article ID 7323628, 14. https://doi.org/10.1155/2018/7323628.
97 Rezaiee-Pajand, M., Shahabian, F., Tavakoli, F.H. (2012), "A new higher-order triangular plate bending element for the analysis of laminated composite and sandwich plates", Struct. Eng. Mech., 43(2), 253-271. https://doi.org/10.12989/sem.2012.43.2.253.   DOI
98 Reddy, J. N. (1984), "A simple high-order theory of laminated composite plate", J. App. Mec. (Trans. ASME), 51, 745-752.   DOI
99 Ghugal, Y.M. and Sayyad, A.S. (2013), "Stress analysis of thick laminated plates using trigonometric shear deformation theory", Int. J. Appl. Mec., 5(1), 23. https://doi.org/10.1142/S1758825113500038.
100 Ferreira, A.J.M., Castro, L.M.S., Bertoluzza, S. (2009), "A high order collocation method for the static and vibration analysis of composite plates using a first-order theory", Compos. Struct, 89, 424-432. https://doi.org/10.1016/j.compstruct.2008.09.006.   DOI
101 Hadji, L., Zouatnia, N., 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
102 Hellal, H., Bourada, M., Hebali, H., Bourada, F., Tounsi, A., Bousahla, A.A., Mahmoud, S.R. (2019), "Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory", J. Sandwich Struct. Mater., https://doi.org/10.1177/1099636219845841.
103 Hirwani, C.K., Panda, S.K., Patle, B.K. (2018a), "Theoretical and experimental validation of nonlinear deflection and stress responses of an internally debonded layer structure using different higher-order theories", Acta Mechanica, 229(8), 3453-3473. https://doi.org/10.1007/s00707-018-2173-8.   DOI
104 Hirwani, C.K., Panda, S.K., Mahapatra, T.R., Mandal, S.K., Mahapatra, S.S. and De, A.K. (2018b), "Delamination effect on flexural responses of layered curved shallow shell panel-experimental and numerical analysis", J. Comput. Methods, 15(4), 1850027. https://doi.org/10.1142/S0219876218500275.   DOI