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http://dx.doi.org/10.12989/gae.2016.11.5.671

A refined theory with stretching effect for the flexure analysis of laminated composite plates  

Draiche, Kada (Departement de Genie Civil, Universite Ibn Khaldoun Tiaret)
Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
Publication Information
Geomechanics and Engineering / v.11, no.5, 2016 , pp. 671-690 More about this Journal
Abstract
This work presents a static flexure analysis of laminated composite plates by utilizing a higher order shear deformation theory in which the stretching effect is incorporated. The axial displacement field utilizes sinusoidal function in terms of thickness coordinate to consider the transverse shear deformation influence. The cosine function in thickness coordinate is employed in transverse displacement to introduce the influence of transverse normal strain. The highlight of the present method is that, in addition to incorporating the thickness stretching effect (${\varepsilon}_z{\neq}0$), the displacement field is constructed with only 5 unknowns, as against 6 or more in other higher order shear and normal deformation theory. Governing equations of the present theory are determined by employing the principle of virtual work. The closed-form solutions of simply supported cross-ply and angle-ply laminated composite plates have been obtained using Navier solution. The numerical results of present method are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy, higher order shear and normal deformation theory (HSNDT) and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory. It can be concluded that the proposed method is accurate and simple in solving the static bending response of laminated composite plates.
Keywords
shear deformation; stretching effect; static flexure; laminated plate;
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Times Cited By KSCI : 26  (Citation Analysis)
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1 Chattibi, F., Benrahou, K.H., Benachour, A., Nedri, K. and Tounsi, A. (2015), "Thermomechanical effects on the bending of antisymmetric cross-ply composite plates using a four variable sinusoidal theory", Steel Compos. Struct., Int. J., 19(1), 93-110.   DOI
2 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
3 Fekrar, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014), "A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates", Meccanica, 49(4), 795-810.   DOI
4 Grover, N., Maiti, D.K. and Singh, B.N. (2013), "A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates", Compos. Struct., 95, 667-675.   DOI
5 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
6 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
7 Hidebrand, F.B., Reissner, E. and Thomas, G.B. (1949), "Note on the foundations of the theory of small displacements of orthotropic shells", NACA TN-1883.
8 Kant, T. (1982), "Numerical analysis of thick plates", Comput. Method. Appl. Mech. Eng., 31(1), 1-18.   DOI
9 Kant, T. and Swaminathan, K. (2002), "Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory", Compos. Struct., 56(4), 329-344.   DOI
10 Kapuria, S. and Nath, J.K. (2013), "On the accuracy of recent global-local theories for bending and vibration of laminated plates", Compos. Struct., 95, 163-172.   DOI
11 Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2015), "Nonlinear flexural analysis of laminated composite flat panel under hygro-thermo-mechanical loading", Steel Compos. Struct., Int. J., 19(4), 1011-1033.   DOI
12 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
13 Levinson, M. (1980), "An accurate simple theory of statics and dynamics of elastic plates", Mech. Res. Commun., 7(6), 343-350.   DOI
14 Librescu, L. (1975), "Elastostatics and kinematics of anisotropic and heterogenous shell type structures", The Netherlands: Noordhoff.
15 Lo, K.H., Christensen, R.M. and Wu, E.M. (1977a), "A high-order theory of plate deformation, part-1: homogenous plates", J. Appl. Mech., 44(4), 663-668.   DOI
16 Meksi, A., Benyoucef, S., Houari, M.S.A. and Tounsi, A. (2015), "A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations", Struct. Eng. Mech., Int. J., 53(6), 1215-1240.   DOI
17 Lo, K.H., Christensen, R.M. and Wu, E.M. (1977b), "A high-order theory of plate deformation, part-2: homogenous plates", J. Appl. Mech., 44(4), 669-676.   DOI
18 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. Model., 39(9), 2489-2508.   DOI
19 Mantari, J.L. and Granados, E.V. (2015), "Thermoelastic analysis of advanced sandwich plates based on a new quasi-3D hybrid type HSDT with 5 unknowns", Compos.: Part B, 69, 317-334.   DOI
20 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
21 Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", ASME J. Appl. Mech., 18, 31-38.
22 Murthy, M.V.V. (1981), "An improved transverse shear deformation theory for laminated anisotropic plates", NASA Technical Paper.
23 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", Mech. Compos. Mater., 49(6), 629-640.   DOI
24 Nguyen, K.T., Thai, T.H. and Vo, T.P. (2015), "A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates", Steel Compos. Struct., Int. J., 18(1), 91-120.   DOI
25 Reddy, J.N. (1984), "A simple higher order shear deformation theory for laminated composite plates", J. Appl. Mech., 51(4), 745-753.   DOI
26 Nelson, R.B. and Lorch, D.R. (1974), "A refined theory for laminated orthotropic plates", ASME J. Appl. Mech., 41(1), 177-183.   DOI
27 Pagano, N.J. (1970), "Exact solutions for bidirectional composites and sandwich plates", J. Compos. Mater., 4, 20-34.   DOI
28 Pandit, M.K., Sheikh, A.H. and Singh, B.N. (2010), "Analysis of laminated sandwich plates based on an improved higher order zigzag theory", J. Sandw. Struct. Mater., 12, 307-326.   DOI
29 Ren, J.G. (1990), "Bending, vibration and buckling of laminated plates", In: Cheremisinoff NP, editor. Handbook of ceramics and composites, vol. 1. New York: Marcel Dekker; pp. 413-450.
30 Sadoune, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2014), "A novel first-order shear deformation theory for laminated composite plates", Steel Compos. Struct., Int. J., 17(3), 321-338.   DOI
31 Sahoo, R. and Singh, B.N. (2013), "A new shear deformation theory for the static analysis of laminated composite and sandwich plates", Int. J. Mech. Sci., 75, 324-336.   DOI
32 Saidi, H., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2013), "Thermo-mechanical bending response with stretching effect of functionally graded sandwich plates using a novel shear deformation theory", Steel Compos. Struct., Int. J., 15, 221-245.   DOI
33 Sallai, B., Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E.A. (2015), "Analytical solution for bending analysis of functionally graded beam", Steel Compos. Struct., Int. J., 19(4), 829-841.   DOI
34 Sayyad, A.S. and Ghugal, Y.M. (2014a), "Flexure of cross-ply laminated plates using equivalent single layer trigonometric shear deformation theory", Struct. Eng. Mech., Int. J., 51(5), 867-891.   DOI
35 Tebboune, W., Benrahou, K.H., Houari, M.S.A. and Tounsi, A. (2015), "Thermal buckling analysis of FG plates resting on elastic foundation based on an efficient and simple trigonometric shear deformation theory", Steel Compos. Struct., Int. J., 18(2), 443-465.   DOI
36 Sayyad, A.S. and Ghugal, Y.M. (2014b), "A new shear and normal deformation theory for isotropic, transversely isotropic, laminated composite and sandwich plates", Int. J. Mech. Mater. Des., 10(3), 247-267.   DOI
37 Soldatos, K.P. (1988), "On certain refined theories for plate bending", ASME J. Appl. Mech., 55(4), 994-995.   DOI
38 Tagrara, S.H., Benachour, A., Bachir Bouiadjra, M. and Tounsi, A. (2015), "On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams", Steel Compos. Struct., Int. J., 19(5), 1259-1277.   DOI
39 Zenkour, A.M. (2007), "Three-dimensional elasticity solution for uniformly loaded cross-ply laminates and sandwich plates", J. Sandw. Struct. Mater., 9(3), 213-238.   DOI
40 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
41 Zhen, W. and Wanji, C. (2010), "A $C^{\circ}$-type higher-order theory for bending analysis of laminated composite and sandwich plates", Compos. Struct., 92(3), 653-661.   DOI
42 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. Technol., 34, 24-34.   DOI
43 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
44 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
45 Akavci, S.S. (2007), "Buckling and free vibration analysis of symmetric and antisymmetric laminated composite plates on an elastic foundation", J. Reinf. Plast. Compos., 26(18), 1907-1919.   DOI
46 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
47 Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2012), "Thermal buckling of functionally graded plates according to a four-variable refined plate theory", J. Therm. Stresses, 35(8), 677-694.   DOI
48 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
49 Bakora, A. and Tounsi, A. (2015)," Thermo-mechanical post-buckling behavior of thick functionally graded plates resting on elastic foundations", Struct. Eng. Mech., Int. J., 56(1), 85-106.   DOI
50 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", Composites: Part B, 60, 274-283.   DOI
51 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
52 Bhimaradi A. and Stevens, L.K. (1984), "A higher order theory for free vibration of orthotropic, homogenous and laminated rectangular plates", J. Appl. Mech., 51(1),195-198.   DOI
53 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
54 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
55 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
56 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
57 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
58 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
59 Boukhari, A., Ait Atmane, H., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., Int. J., 57(5), 837-859.   DOI
60 Bouderba, B., Houari, M.S.A., 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
61 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
62 Bourada, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandw. Struct. Mater., 14(1), 5-33.   DOI
63 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
64 Chalak, H.D., Chakrabarti, A., Iqbal M.A. and Sheikh, A.H. (2012), "An improved $C^{\circ}$ FE model for the analysis of laminated sandwich plate with soft core", Finite Elem. Anal. Des., 56, 20-31.   DOI
65 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
66 Brischetto, S., Carrera, E. and Demasi, L. (2009), "Improved response of unsymmetrically laminated sandwich plates by using zig-zag functions", J. Sandw. Struct. Mater., 11(2-3), 257-267.   DOI