The free vibration and static stability analyses of higher order shear deformable doubly curved laminated shell panels have been carried out in this paper. The proposed shear deformation theory takes care of the parabolic variation of the transverse shear strains through the thickness of the shell and assumes rigid body motion. An eight-noded isoparametric finite shell elements with nine degrees–of-freedom per node is used for the analysis based of Kant and Khares' higher order shear deformation theory. Full geometric nonlinearity in the Green–Lagrange sense is considered for the buckling analysis, whereas for free vibration study only linear strains are taken into account. A generic code is developed in the MATLAB platform to solve the vibration and buckling eigenvalue problems. The effect of various parameters such as thickness ratio, curvature ratio, orthotropic ratio, lamination scheme, number of plies, boundary conditions, and shell geometries on the natural frequencies and critical buckling loads of shell panels are investigated. The efficacy and accuracy of the present formulation has been validated by comparing the results with those available in literature. The fundamental frequencies and critical buckling loads are found to increase with an increase in thickness ratio, ratio of principal radii of curvatures, and orthotropic ratio, but exhibit a decreasing trend with an increase in aspect ratio and radii of curvatures.
Sanders JL. An improved first-approximation theory for thin shells. NTRS, 1959, pp.1–11.
5.
FanSCLuahMH. Free vibration analysis of arbitrary thin shell structures by using spline finite element. J Sound Vib1995; 179: 763–776.
6.
ChakravortyDBandyopadhyayJNSinhaPK. Free vibration analysis of point-supported laminated composite doubly curved shells-A finite element approach. Comput Struct1995; 54: 191–198.
7.
ChakravortyDBandyopadhyayJNSinhaPK. Finite element free vibration analysis of doubly curved laminated composite shells. J Sound Vib1996; 191: 491–504.
8.
KantTKhareR. A higher-order facet quadrilateral composite shell element. J Numer Meth Eng1997; 40: 4477–4499.
9.
TooraniMHLakisAA. General equations of anisotropic plates and shells including transverse shear deformations, rotary inertia and initial curvature effects. J Sound Vib2000; 237: 561–615.
10.
ChernYCChaoCC. Comparison of natural frequencies of laminates by 3-D theory, Part II: Curved panels. J Sound Vib2000; 230: 1009–1030.
11.
KhareRKKantTGargAK. Free vibration of composite and sandwich laminates with a higher-order facet shell element. Compos Struct2004; 65: 405–418.
12.
Nguyen-ThanhNRabczukTNguyen-XuanHet al.A smoothed finite element method for shell analysis. Comput Methods Appl Mech Eng2008; 198: 165–177.
13.
PradyumnaSBandyopadhyayJN. Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation. J Sound Vib2008; 318: 176–192.
14.
PandaSKSinghBN. Nonlinear free vibration of spherical shell panel using higher order shear deformation theory – A finite element approach. Int J Press Vessel Pip2009; 86: 373–383.
15.
AmabiliMReddyJN. A new non-linear higher-order thickness stretching and shear deformation theory for large-amplitude vibrations of laminated doubly curved shells. Int J Non Linear Mech2010; 45: 409–418.
16.
QatuMSSullivanRWWangW. Recent research advances on the dynamic analysis of composite shells: 2000–2009. Compos Struct2010; 93: 14–31.
17.
FerreiraAJMCarreraECinefraMet al.Analysis of laminated shells by a sinusoidal shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations. Compos Part B: Eng2011; 42: 1276–1284.
18.
Hosseini-HashemiSAtashipourSRFadaeeMet al.An exact closed-form procedure for free vibration analysis of laminated spherical shell panels based on Sanders theory. Arch Appl Mech2012; 82: 985–1002.
19.
AsadiEWangWQatuMS. Static and vibration analyses of thick deep laminated cylindrical shells using 3D and various shear deformation theories. Compos Struct2012; 94: 494–500.
20.
TornabeneFLiveraniACaligianaG. General anisotropic doubly-curved shell theory: A differential quadrature solution for free vibrations of shells and panels of revolution with a free-form meridian. J Sound Vib2012; 331: 4848–4869.
21.
TornabeneFViolaEFantuzziN. General higher order layer-wise theory for free vibrations of doubly-curved laminated composite shells and panels. Compos Struct2013; 104: 94–117.
22.
ViolaETornabeneFFantuzziN. Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories. Compos Struct2013; 101: 59–93.
23.
TornabeneFViolaE. Static analysis of functionally graded doubly-curved shells and panels of revolution. Meccanica2013; 48: 901–930.
24.
TornabeneFFantuzziNBacciocchiM. Free vibrations of free-form doubly-curved shells made of functionally graded materials using higher-order equivalent single layer theories. Compos Part B: Eng2014; 67: 490–509.
25.
TornabeneFFantuzziNBacciocchiM. The local GDQ method applied to general higher-order theories of doubly-curved laminated composite shells and panels: The free vibration analysis. Compos Struct2014; 116: 637–660.
26.
BacciocchiMEisenbergerMFantuzziNet al.Vibration analysis of variable thickness plates and shells by the Generalized Differential Quadrature method. Compos Struct2016; 156: 218–237.
27.
DeySMukhopadhyayTAdhikariS. Stochastic free vibration analyses of composite shallow doubly curved shells - A Kriging model approach. Compos Part B: Eng2015; 70: 99–112.
28.
KangJ-H. Vibration analysis of shallow spherical domes with non-uniform thickness. Int J Struct Stab Dyn2016; 16: 1750016.
29.
WattanasakulpongNPornpeerakeatSChaikittiratanaA. Chebyshev collocation solutions for vibration analysis of circular cylindrical shells with arbitrary boundary conditions. Int J Struct Stab Dyn2016; 16: 1750020.
30.
TornabeneFFantuzziNBacciocchiMet al.An equivalent layer-wise approach for the free vibration analysis of thick and thin laminated and sandwich shells. Appl Sci2016; 7: 17.
31.
ZhangXGaoRXYanRet al.Analysis of laminated plates and shells using b-spline wavelet on interval finite element. Int J Struct Stab Dyn2016; 17: 1750062.
32.
TornabeneFFantuzziNBacciocchiM. A new doubly-curved shell element for the free vibrations of arbitrarily shaped laminated structures based on Weak Formulation Isogeometric Analysis. Compos Struct2017; 171: 429–461.
33.
TornabeneFFantuzziNBacciocchiM. Linear static response of nanocomposite plates and shells reinforced by agglomerated carbon nanotubes. Compos Part B: Eng2017; 115: 449–476.
34.
LibrescuLKhdeirAAFrederickD. A shear deformable theory of laminated composite shallow shell-type panels and their response analysis I: Free vibration and buckling. Acta Mech1989; 76: 1–33.
35.
Di SciuvaMCarreraE. Static buckling of moderately thick, anisotropic, laminated and sandwich cylindrical shell panels. AIAA J1990; 28: 1782–1793.
MatsunagaH. Vibration and stability of thick simply supported shallow shells subjected to in plane stress. J Sound Vib1999; 225: 41–60.
38.
KunduCKSinhaPK. Post buckling analysis of laminated composite shells. Compos Struct2007; 78: 316–324.
39.
KunduCKMaitiDKSinhaPK. Post buckling analysis of smart laminated doubly curved shells. Compos Struct2007; 81: 314–322.
40.
KunduCKHanJ-H. Vibration and post-buckling behavior of laminated composite doubly curved shell structures. Adv Compos Mater2009; 18: 21–42.
41.
Nguyen-VanHMai-DuyNKarunasenaWet al.Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with in-plane rotations. Comput. Struct2011; 89: 612–625.
42.
ChallamelNKolvikGHelleslandJ. Plate buckling analysis using a general higher-order shear deformation theory. Int J Struct Stab Dyn2013; 13: 1350028.
43.
FazzolariFABanerjeeJRBoscoloM. Buckling of composite plate assemblies using higher order shear deformation theory—An exact method of solution. Thin-Walled Struct2013; 71: 18–34.
