The present study investigates whether an nthorder shear deformation theory is applicable for the composite laminates in cylindrical bending. The theory satisfies the traction free conditions at top and bottom surfaces of the plate and does not require problem dependent shear correction factor which is normally associated with the first order shear deformation theory. The well-known classical plate theory at (n = 1) and higher order shear deformation theory of Reddy at (n = 3) are the perticular cases of the present theory. The governing equations of equilibrium and boundary conditions are obtained using the principle of virtual work. A simply supported laminated composite plate infinitely long in y-direction is considered for the detail numerical study. A closed form solution for simply supported boundary conditions is obtained using Navier’s technique. The displacements and stresses are obtained for different aspect ratios and modular ratios.
@article{bwmeta1.element.doi-10_1515_cls-2015-0016,
author = {A. S. Sayyad and Y. M. Ghugal},
title = {A nth-order shear deformation theory for composite laminates in cylindrical bending},
journal = {Curved and Layered Structures},
volume = {2},
year = {2015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_cls-2015-0016}
}
A. S. Sayyad; Y. M. Ghugal. A nth-order shear deformation theory for composite laminates in cylindrical bending. Curved and Layered Structures, Tome 2 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_cls-2015-0016/
[1] Mindlin R.D., Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, ASME J. Appl. Mech., 1951, 18, 31-38. | Zbl 0044.40101
[2] Reddy J.N., A simple higher order theory for laminated composite plates, ASME J. Appl. Mech., 1984, 51, 745-752. | Zbl 0549.73062
[3] Touratier M., An eflcient standard plate theory, Int. J. Eng. Sci., 1991, 29, 901-916. [Crossref] | Zbl 0825.73299
[4] Soldatos K.P., A transverse shear deformation theory for homogeneous monoclinic plates, Acta Mech., 1992, 94, 195-220. [Crossref] | Zbl 0850.73130
[5] Karama M., Afaq K.S., Mistou S., Mechanical behavior of laminated composite beam by new multi-layered laminated composite structures modelwith transverse shear stress continuity, Int. J. Solids Struct., 2003, 40, 1525-1546. | Zbl 1087.74579
[6] Akavci S.S., Buckling and free vibration analysis of symmetric and anti-symmetric laminated composite plates on an elastic foundation, J. Reinf. Plast. Compos., 2007, 26, 1907-1919. [WoS][Crossref]
[7] Pagano N.J., Exact solution for composite laminates in cylindrical bending, J. Compos. Mater., 1969, 3, 398-411. [Crossref]
[8] Reddy J.N., Mechanics of Laminated Composite Plates, CRC Press, Boca Raton 1997. | Zbl 0899.73002
[9] Soldatos K.P., Watson P., A method for improving the stress analysis performance of two-dimensional theories for composite laminates, Acta Mech., 1997, 123, 163-186. | Zbl 0908.73047
[10] Shu X.P., Soldatos K.P., Cylindrical bending of angle-ply laminates subjected to different sets of edge boundary conditions, Int. J. Solids Struct., 2000, 37, 4289-4307. [Crossref] | Zbl 0974.74017
[11] Jalali S.J., Taheri F., An analytical solution for cross-ply laminates under cylindrical bending based on through-thethickness inextensibility, Part I-static loading, Int. J. Solids Struct., 1998, 35, 1559-1574. | Zbl 0920.73289
[12] Perel V.Y., Palazotta A.N., Finite element formulation for cylindrical bending of a transversely compressible sandwich plate based on assumed transverse strain, Int. J. Solids Struct., 2001, 38, 5373-5409. [Crossref] | Zbl 1051.74046
[13] Khdeir A.A., Free and forced vibration of antisymmetric angleply laminated plate strips in cylindrical bending, J. Vib. Control, 2001, 7, 781-801. [Crossref] | Zbl 1045.74026
[14] Park J., Lee S.Y., A new exponential plate theory for laminated composites under cylindrical bending, Trans. Japan Soc. Aero. Space Sci., 2003, 46, 89-95.
[15] Chen W.Q., Lee K.Y., State-space approach for statics and dynamics of angle-ply laminated cylindrical panels in cylindrical bending, Int. J. Mech. Sci., 2005, 47, 374-387. [Crossref] | Zbl 1192.74235
[16] Lu C.F., Huang Z.Y., ChenW.Q., Semi-analytical solutions for free vibration of anisotropic laminated plates in cylindrical bending, J. Sound Vib., 2007, 304, 987-995. [WoS]
[17] Carrera E., Nonlinear response of asymmetrically laminated plates in cylindrical bending, AIAA J., 1992, 31(7), 1353-1357.
[18] Ghugal Y.M., Sayyad A.S., Cylindrical bending of thick orthotropic plate using trigonometric shear deformation theory, Int. J. Appl. Math. Mech., 2011, 7(5), 98-116. | Zbl 06000437
[19] Sayyad A.S., Ghugal Y.M., Naik N.S., Bending analysis of laminated composite and sandwich beams according to refined trigonometric beam theory, Curved Layer. Struct., 2015, 2, 279- 289.
[20] Natarajan S., Ferreira A.J.M., Xuan H.N., Analysis of cross-ply laminated plates using isogeometric analysis and unified formulation, Curved Layer. Struct., 2014, 1, 1-10.
[21] Sun L., Harik I.E., Analytical solution to bending of stiffened and continuous antisymmetric laminates, Curved Layer. Struct., 2015, 2, 254-270.
[22] Carpentieri G., Tornabene F., Ascione A., Fraternali F., An accurate one-dimensional theory for the dynamics of laminated composite curved beams, J. Sound Vib., 2015, 336, 96-105. [WoS]
[23] Ferreira A.J.M., Viola E., Tornabene F., Fantuzzi N., Zenkour A.M., Analysis of sandwich plates by generalized differential quadrature method, Math. Probl. Eng., 2013, Article ID 964367, 12 pages, 2013. doi:10.1155/2013/964367. [WoS][Crossref] | Zbl 1299.74113
[24] Carrera E., Filippi M., Zappino E., Free vibration analysis of laminated beam by polynomial, trigonometric, exponential and zigzag theories, J. Compos. Mater., 2014, 48(19), 2299–2316. [WoS][Crossref]
[25] Tornabene F., 2-D GDQ solution for free vibrations of anisotropic doubly-curved shells and panels of revolution, Compos. Struct., 2011, 93(7), 1854-1876. [Crossref][WoS]
[26] Tornabene F., Fantuzzi N., Viola E., Carrera E., Static analysis of doubly-curved anisotropic shells and panels using CUF approach, differential geometry and differential quadrature method, Compos. Struct., 2014, 107, 675-697. [WoS]
[27] Xiang S., Kang G.W., Xing B., A nth-order shear deformation theory for the free vibration analysis on the isotropic plates, Meccanica, 2012, 47, 1913-1921. [Crossref][WoS] | Zbl 1293.74213
[28] Xiang S., Jiang S., Bi Z., Jin Y., Yang M., A nth-order meshless generalization of Reddy’s third-order shear deformation theory for the free vibration on laminated composite plates, Compos. Struct., 2011, 93, 299-307.
[29] Xiang S., Kang G.W., A nth-order shear deformation theory for the bending analysis on the functionally graded plates, Eur. J. Mech.: A/Solids, 2013, 37, 336-343. [WoS]
[30] Xiang S., Kang G.W., Liu Y. A nth-order shear deformation theory for natural frequency of the functionally graded plates on elastic foundation, Compos. Struct., 2014, 111, 224-231. [WoS]
[31] Sayyad A.S., Ghumare S.M., Sasane S.T., Cylindrical bending of orthotropic plate strip based on nth-order plate theory, J.Mater. Eng. Struct., 2014, 1, 47-57.