An efficient and simple higher order shear deformation theory for bending analysis of composite plates under various boundary conditions

• Journal title : Earthquakes and Structures
• Volume 11, Issue 1,  2016, pp.63-82
• Publisher : Techno-Press
• DOI : 10.12989/eas.2016.11.1.063
Title & Authors
An efficient and simple higher order shear deformation theory for bending analysis of composite plates under various boundary conditions
Abstract
In this study, the bending and dynamic behaviors of laminated composite plates is examined by using a refined shear deformation theory and developed for a bending analysis of orthotropic laminated composite plates under various boundary conditions. The displacement field of the present theory is chosen based on nonlinear variations in the in-plane displacements through the thickness of the plate. By dividing the transverse displacement into the bending and shear parts and making further assumptions, the number of unknowns and equations of motion of the present theory is reduced and hence makes them simple to use. In the analysis, the equation of motion for simply supported thick laminated rectangular plates is obtained through the use of Hamilton`s principle. Numerical results for the bending and dynamic behaviors of antisymmetric cross-ply laminated plate under various boundary conditions are presented. The validity of the present solution is demonstrated by comparison with solutions available in the literature. Numerical results show that the present theory can archive accuracy comparable to the existing higher order shear deformation theories that contain more number of unknowns.
Keywords
higher-order theories;shear deformation theory of plates;laminated composite plate;
Language
English
Cited by
References
1.
Abdelhak, Z., L. Hadji, Hassaine Daouadji T. and Adda bedia E.A. (2015), "Thermal buckling of functionally graded plates using a n-order four variable refined theory", Adv. Mater. Res., 4(1), 31-44.

2.
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. Sandwich Struct. Mater., 16(3), 293-318.

3.
Aydogdu, M. (2009), "A new shear deformation theory for laminated composite plates", Compos. Struct., 89(1), 94-101.

4.
Benferhat, R., Hassaine Daouadji, T. and M. Said Mansour (2014), "A higher order shear deformation model for bending analysis of functionally graded plates", Transactions of the Indian Institute of Metals, 68(1), 7-16.

5.
Bouazza, M., K. Amara, M. Zidour, A. Tounsi and El A. Adda Bedia (2015), "Postbuckling analysis of functionally graded beams using hyperbolic shear deformation theory", Rev. Inform. Eng. Appl., 2(1), 1-14.

6.
Bouazza, M., K. Amara, M. Zidour, A. Tounsi and El A. Adda Bedia (2015), "Postbuckling analysis of nanobeams using trigonometric Shear deformation theory", Appl. Sci. Reports, 10(2), 112-121.

7.
Carrera, E. (2002), "Theories and finite elements for multilayered, anisotropic, composite plates and shells", Archiv. Comput. Meth. Eng., 9(2), 87-140.

8.
Carrera, E. and Miglioretti, F. (2012), "Selection of appropriate multilayered plate theories by using a genetic like algorithm", Compos. Struct., 94(3), 1175-1186

9.
Hassaine Daouadji, T., Tounsi, A. and Adda bedia, E.A. (2013), "Analytical solution for bending analysis of functionally graded plates", Scientia Iranica, Trans. B: Mech. Eng., 20(3), 516-523.

10.
Hebali, H., A. Tounsi, S. Houari, A. Bessaim and E.A. Adda Bedia (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., ASCE, 140(2), 374-383.

11.
Karama, M., K.S. Afaq, and S. Mistou (2003), "Mechanical behavior of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity", Int. J. Solid. Struct., 40(6), 15251546.

12.
Karama, M., Afaq, K.S. and Mistou, S. (2009), "A new theory for laminated composite plates", Proceeding of the IMechE, vol. 223 (Part L: Journal of Materials: Design and Applications).

13.
Mahi, A., E. Adda Bedia and A. Tounsi (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plate", Appl. Math. Model., Appl. Math. Model., 39(9), 2489-2508.

14.
Mantari, J.L., A.S. Oktem and C. Guedes Soares (2012), "A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates", Int. J. Solid. Struct., 49(1), 43-53.

15.
Meiche, N.E., Tounsi, A., Ziane, N., Mechab, I. and Bedia, E.A. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53(4), 237-247.

16.
Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. Mech., 18, 31-38.

17.
Nedri, K., N. El Meiche and A. Tounsi (2014), "Free vibration analysis of laminated composite plates resting on elastic foundation by using a refined hyperbolic shear deformation theory", Mech. Compos. Mater., 49(6), 629-640.

18.
Noor, A.K. (1975), "Stability of multilayered composite plate", Fibre Sci. Technol., 8(2), 81-89.

19.
Noor, K. (1973), "Free vibrations of multilayered composite plates", AIAA J., 11(7), 1038-1039.

20.
Pagano, N.J. (1970), "Exact solutions for rectangular bidirectional composites and sandwich plates", J. Compos. Mater., 4(1), 20-34.

21.
Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., ASME, 51(4), 745-752.

22.
Reddy, J.N. (1986), "A refined shear deformation theory for the analysis of laminated plates", NASA Report3955.

23.
Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., Trans., ASME, 12(2), 69-77.

24.
Ren, J.G. (1986), "A new theory of laminated plate", Compos. Sci. Technol., 26(3), 225-239.

25.
Ren, J.G. (1990), "Bending, vibration and buckling of laminated plates", Ed., Cheremisinoff, N.P., Handbook of ceramics and composites, 1, 413-450.

26.
Shimpi, R.P. and Patel, H.G. (2006), "A two variable refined plate theory for orthotropic plate analysis", Int. J. Solid. Struct., 43(22), 6783-6799.

27.
Shimpi, R.P. and Patel, H.G. (2006), "Free vibrations of plate using two variable refined plate theory", J. Sound Vib., 296(4-5), 979-999.

28.