Free vibration and buckling analysis of composite laminated shells using the refined zigzag theory
Dan He 1
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Department of Aeronautics and Astronautics, Shenyang Aerospace University, Shenyang, China
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, China
Beijing Institute of Astronautical Systems Engineering, Beijing, China
Department of Mechanics, Huazhong University of Science and Technology, Wuhan, China
Wanli Yang   

Department of Mechanics, Huazhong University of Science and Technology, China
Submission date: 2022-05-20
Acceptance date: 2022-05-25
Online publication date: 2022-06-17
Publication date: 2022-07-30
Journal of Theoretical and Applied Mechanics 2022;60(3):435–448
In this study, a new composite laminated shell model is proposed for free vibration and stability analysis based on the refined zigzag theory (RZT). In contrast to the published shell models based on the first-order shear deformation theory (FSDT), piecewise-linear zigzag functions are utilized to provide a more realistic representation of deformation states of a transverse shear-flexible shell. In the present formulation, the governing equations and boundary conditions of composite laminated shells are established by d’Alembert’s principle to obtain natural frequencies and critical buckling loadings. In order to evaluate the effectiveness and performance of the present new model for composite laminated shells, examples of free vibration and buckling analysis are carried out for cylindrical and spherical shells involving different lamination schemes and design parameters. The results are compared with the three dimensional (3D) exact, first-order and some high-order solutions in the literature. Numerical results show that the present model not only has high accuracy but also has superior computational efficiency in comparison with high-order models, such that it may show a great potential in engineering applications.
Averill R.C., Yip Y.C., 1996, Development of simple, robust finite elements based on refined theories for thick laminated beams, Computers and Structures, 59, 529-546.
Bhimaraddi A., 1991, Free vibration analysis of doubly curved shallow shells on rectangular planform using three-dimensional elasticity theory, International Journal of Solids and Structures, 27, 897-913.
Chern Y., Chao C.C., 2000, Comparison of natural frequencies of laminates by 3-D theory, Part II: Curved panels, Journal of Sound and Vibration, 230, 1009-1030.
Duan H.Y., Liang G.P., 2003, Mixed and nonconforming finite element approximations of Reissner-Mindlin plates, Computer Methods in Applied Mechanics and Engineering, 192, 5265-5281.
Eijo A., Oñate E., Oller S., 2013, A four-noded quadrilateral element for composite laminated plates/shells using the refined zigzag theory, International Journal for Numerical Methods in Engineering, 95, 631-660.
Iurlaro L., Gherlone M.D., Di Sciuva M., Tessler A., 2015, Refined zigzag theory for laminated composite and sandwich plates derived from Reissner’s mixed variational theorem, Composite Structures, 133, 809-817.
Khdeir A.A., Reddy J.N., Frederick D., 1989, A study of bending, vibration and buckling of cross-ply circular cylindrical shells with various shell theories, International Journal of Engineering Science, 27, 1337-1351.
Kumar A., Chakrabarti A., Bhargava P., 2013, Vibration of laminated composites and sandwich shells based on higher order zigzag theory, Engineering Structures, 56, 880-888.
Lam K.Y., Ng T.Y., Qian W., 2000, Vibration analysis of thick laminated composite cylindrical shells, AIAA Journal, 38, 1102-1107.
Li Z.M., Wang M., 2016, Large-amplitude vibration analysis of 3D braided composite cylindrical shells in an elastic medium, Journal of Aerospace Engineering, 29, 04015029.
Lu X., Liu D., 1992, An interlaminar shear stress continuity theory for both thin and thick composite laminates, Journal of Applied Mechanics, 59, 502-509.
Magnucki K., Witkowski D., Magnucka E., 2019, Buckling and free vibrations of rectangular plates with symmetrically varying mechanical properties – Analytical and FEM studies, Composite Structures, 220, 355-361.
Malekzadeh P., Farid M., Zahedinejad P., 2008. A three-dimensional layerwise-differential quadrature free vibration analysis of laminated cylindrical shells, International Journal of Pressure Vessels and Piping, 85, 450-458.
Mantari J.L., Oktem A.S., Guedes Soares C.G., 2011, Static and dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory, Composite Structures, 94, 37-49.
Matsunaga H., 2004, A comparison between 2-D single-layer and 3-D layerwise theories for computing interlaminar stresses of laminated composite and sandwich plates subjected to thermal loadings, Composite Structures, 64, 161-177.
Mindlin R.D., 1951. Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, Journal of Applied Mechanics, 18, 31-38.
Reddy J.N., 2003, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press.
Reddy J.N., Liu C.F., 1985, A higher-order shear deformation theory of laminated elastic shells, International Journal of Engineering Science, 23, 319-330.
Reissner E., 1945, The effect of transverse shear deformation on the bending of elastic plates, Journal of Applied Mechanics, 12, 69-76.
Sciuva M.D., 1984, A refined transverse shear deformation theory for multilayered anisotropic plates, Atti Accademia Science Torino, 118, 79-95.
Tessler A., Di Sciuva M., Gherlone M., 2010, A consistent refinement of first-order shear deformation theory for laminated composite and sandwich plates using improved zigzag kinematics, Journal of Mechanics of Materials and Structures, 5, 341-367.
Thakur S.N., Ray C., Chakraborty S., 2017, A new efficient higher-order shear deformation theory for a doubly curved laminated composite shell, Acta Mechanica, 228, 69-87.
Touratier M., 1992, A refined theory of laminated shallow shells, International Journal of Solids and Structures, 29, 1401-1415.
Ye J., Soldatos K.P., 1994, Three-dimensional vibration of laminated cylinders and cylindrical panels with symmetric or antisymmetric cross-ply lay-up, Composites Engineering, 4, 429-444.
Wang C.M., Lim G.T., Reddy J.N., Lee K.H., 2001, Relationships between bending solutions of Reissner and Mindlin plate theories, Engineering Structures, 23, 838-849.