Retraction notice to "Free vibrations of laminated composite doubly-curved shells and panels of revolution via the GDQ method" [Computer Methods in Applied Mechanics and Engineering 200(9-12) (2011) 931-952];Free vibrations of laminated composite doubly-curved shells and panels of revolution via the GDQ method

Computer Methods in Applied Mechanics and Engineering

Volumn 200, Issue 9-12, 2011, Pages 931-952

  Tornabene, Francesco ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Doubly curved shells of revolution; First Order Shear Deformation Theory; Free vibrations; Generalized differential quadrature method; Laminated composite shells

Indexed keywords

ABAQUS; COMPOSITE STRUCTURES; DIFFERENTIATION (CALCULUS); EIGENVALUES AND EIGENFUNCTIONS; EQUATIONS OF MOTION; KINEMATICS; LAMINATING; PLATES (STRUCTURAL COMPONENTS); SHEAR DEFORMATION; SHELLS (STRUCTURES); STRUCTURAL PANELS;

DOUBLY CURVED SHELLS; FIRST-ORDER SHEAR DEFORMATION THEORY; FREE VIBRATION; GENERALIZED DIFFERENTIAL QUADRATURE METHODS; LAMINATED COMPOSITE SHELL;

LAMINATED COMPOSITES;

EID: 78650616095     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2012.08.001     Document Type: Erratum

References (75)

1. Timoshenko S., Woinowsky-Krieger S. Theory of Plates and Shells 1959, McGraw-Hill.
2. Flügge W. Stresses in Shells 1960, Springer-Verlag.
3. Gol'Denveizer A.L. Theory of Elastic Thin Shells 1961, Pergamon Press.
4. Novozhilov V.V. Thin Shell Theory 1964, P. Noordhoff.
5. V.Z. Vlasov, General Theory of Shells and its Application in Engineering, NASA-TT-F-99, 1964.
6. S.A. Ambartusumyan, Theory of Anisotropic Shells, NASA-TT-F-118, 1964.
7. Kraus H. Thin Elastic Shells 1967, John Wiley & Sons.
8. A.W. Leissa, Vibration of Plates, NASA-SP-160, 1969.
9. A.W. Leissa, Vibration of Shells, NASA-SP-288, 1973.
10. Markuš Š. The Mechanics of Vibrations of Cylindrical Shells 1988, Elsevier.
11. Ventsel E., Krauthammer T. Thin Plates and Shells 2001, Marcel Dekker.
12. Soedel W. Vibrations of Shells and Plates 2004, Marcel Dekker.
13. Shu C. Free vibration analysis of composite laminated conical shells by generalized differential quadrature. J. Sound Vib. 1996, 194:587-604.
14. Hua L., Lam K.Y. The generalized quadrature method for frequency analysis of a rotating conical shell with initial pressure. Int. J. Numer. Methods Engrg. 2000, 48:1703-1722.
15. Lam K.Y., Li H., Ng T.Y., Chua C.F. Generalized differential quadrature method for the free vibration of truncated conical panels. J. Sound Vib. 2002, 251:329-348.
16. Ng T.Y., Li H., Lam K.Y. Generalized differential quadrature method for the free vibration of rotating composite laminated conical shell with various boundary conditions. Int. J. Mech. Sci. 2003, 45:567-587.
17. Redekop D. Buckling analysis of an orthotropic thin shell of revolution using differential quadrature. Int. J. Press. Vessels Pip. 2005, 82:618-624.
18. Wang X.H., Xu B., Redekop D. Theoretical natural frequencies and mode shapes for thin and thick curved pipes and toroidal shells. J. Sound Vib. 2006, 292:424-434.
19. Reissner E. The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. ASME 1945, 12:66-77.
20. Gould P.L. Finite Element Analysis of Shells of Revolution 1984, Pitman Publishing.
21. Gould PL. Analysis of Plates and Shells 1999, Prentice-Hall.
22. Toorani M.H., Lakis A.A. General equations of anisotropic plates and shells including transverse shear deformations, rotary inertia and initial curvature effects. J. Sound Vib. 2000, 237:561-615.
23. Reddy J.N. Mechanics of Laminated Composites Plates and Shells 2003, CRC Press, New York.
24. Wu C.P., Tarn J.Q., Tang S.C. A refined asymptotic theory of dynamic analysis of doubly curved laminated shells. Int. J. Solid Struct. 1998, 35:1953-1979.
25. Wu C.P., Lee C.Y. Differential quadrature solution for the free vibration analysis of laminated conical shells with variable stiffness. Int. J. Mech. Sci. 2001, 43:1853-1869.
26. Messina A. Free vibrations of multilayered doubly curved shells based on a mixed variational approach and global piecewise-smooth functions. Int. J. Solid Struct. 2003, 40:3069-3088.
27. Viola E., Artioli E. The G.D.Q. method for the harmonic dynamic analysis of rotational shell structural elements. Struct. Engrg. Mech. 2004, 17:789-817.
28. Artioli E., Gould P., Viola E. A differential quadrature method solution for shear-deformable shells of revolution. Engrg. Struct. 2005, 27:1879-1892.
29. Artioli E., Viola E. Static analysis of shear-deformable shells of revolution via G.D.Q. method. Struct. Engrg. Mech. 2005, 19:459-475.
30. Artioli E., Viola E. Free vibration analysis of spherical caps using a G.D.Q. numerical solution. J. Press. Vessel-Tech. ASME 2006, 128:370-378.
31. Shu C. Differential Quadrature and its Application in Engineering 2000, Springer, Berlin.
32. Bert C., Malik M. Differential quadrature method in computational mechanics. Appl. Mech. Rev. 1996, 49:1-27.
33. Liew K.M., Han J.B., Xiao Z.M. Differential quadrature method for thick symmetric cross-ply laminates with first-order shear flexibility. Int. J. Solid Struct. 1996, 33:2647-2658.
34. Han J.B., Liew K.M. An eight-node curvilinear differential quadrature formulation for Reissner/Mindlin plates. Comput. Methods Appl. Mech. Engrg. 1997, 141:265-280.
35. Liew K.M., Han J.B. An four-node differential quadrature method for straight-sided quadrilateral Reissner/Mindlin plates. Commun. Numer. Methods Engrg. 1997, 13:73-81.
36. Hua L., Lam K.Y. Frequency characteristics of a thin rotating cylindrical shell using the generalized differential quadrature method. Int. J. Mech. Sci. 1998, 40:443-459.
37. Liew K.M., Teo T.M. Modeling via differential quadrature method: three-dimensional solutions for rectangular plates. Comput. Methods Appl. Mech. Engrg. 1998, 159:369-381.
38. Ng T.Y., Li H., Lam K.Y., Loy C.T. Parametric instability of conical shells by the generalized differential quadrature method. Int. J. Numer. Methods Engrg. 1999, 44:819-837.
39. Han J.-B., Liew K.M. Static analysis of Mindlin plates: the differential quadrature element method (DQEM). Comput. Methods Appl. Mech. Engrg. 1999, 177:51-75.
40. Liu F.-L., Liew K.M. Vibration analysis of Mindlin sector plates: numerical solution by differential quadrature method. Comput. Methods Appl. Mech. Engrg. 1999, 177:77-92.
41. Liu F.-L., Liew K.M. Differential quadrature element method: a new approach for free vibration of polar Mindlin plates having discontinuities. Comput. Methods Appl. Mech. Engrg. 1999, 179:407-423.
42. Liew K.M., Liu F.-L. Differential quadrature method for vibration analysis of shear deformable annular sector plates. J. Sound Vib. 2000, 230:335-356.
43. Hua L., Lam K.Y. Orthotropic influence on frequency characteristics of rotating composite laminated conical shell by the generalized differential quadrature method. Int. J. Solids Struct. 2001, 38:3995-4015.
44. Wu C.P., Lee C.Y. Differential quadrature solution for the free vibration analysis of laminated conical shells with variable stiffness. Int. J. Mech. Sci. 2001, 43:1853-1869.
45. Lam K.Y., Li H., Ng T.Y., Chua C.F. Generalized differential quadrature method for the free vibration of truncated conical panels. J. Sound Vib. 2002, 251:329-348.
46. Karami G., Malekzadeh P. A new differential quadrature methodology for beam analysis and the associated differential quadrature element method. Comput. Methods Appl. Mech. Engrg. 2002, 191:3509-3526.
47. Liew K.M., Ng T.Y., Zhang J.Z. Differential quadrature-layerwise modeling technique for three dimensional analysis of cross-ply laminated plates of various edge supports. Comput. Methods Appl. Mech. Engrg. 2002, 191:3811-3832.
48. Wu T.Y., Wang Y.Y., Liu G.R. Free vibration analysis of circular plates using generalized differential quadrature rule. Comput. Methods Appl. Mech. Engrg. 2002, 191:5365-5380.
49. Fung T.C. Stability and accuracy of differential quadrature method in solving dynamic problems. Comput. Methods Appl. Mech. Engrg. 2002, 191:1311-1331.
50. Wu T.Y., Wang Y.Y., Liu G.R. A generalized differential quadrature rule for bending analyses of cylindrical barrel shells. Comput. Methods Appl. Mech. Engrg. 2003, 192:1629-1647.
51. Huang Y.Q., Li Q.S. Bending and buckling analysis of antisymmetric laminates using the moving least square differential quadrature method. Comput. Methods Appl. Mech. Engrg. 2004, 193:3471-3492.
52. Wang X., Wang Y. Free vibration analyses of thin sector plates by the new version of differential quadrature method. Comput. Methods Appl. Mech. Engrg. 2004, 193:3957-3971.
53. Malekzadeh P., Karami G., Farid M. A semi-analytical DQEM for free vibration analysis of thick plates with two opposite edges simply supported. Comput. Methods Appl. Mech. Engrg. 2004, 193:4781-4796.
54. Hsu M.H. Vibration analysis of edge-cracked beam on elastic foundation with axial loading using the differential quadrature method. Comput. Methods Appl. Mech. Engrg. 2005, 194:1-17.
55. Viola E., Tornabene F. Vibration analysis of damaged circular arches with varying cross-section. Struct. Integr. Durab. (SID-SDHM) 2005, 1:155-169.
56. Ding H., Shu C., Yeo K.S., Xu D. Numerical computation of three-dimensional viscous flows in primitive variable form by local multiquadric differential quadrature. Comput. Methods Appl. Mech. Engrg. 2006, 195:516-533.
57. Viola E., Tornabene F. Vibration analysis of conical shell structures using GDQ method. Far East J. Appl. Math. 2006, 25:23-39.
58. Wang X. Nonlinear stability analysis of thin doubly curved orthotropic shallow shells by the differential quadrature method. Comput. Methods Appl. Mech. Engrg. 2007, 196:2242-2251.
59. F. Tornabene, Modellazione e Soluzione di Strutture a Guscio in Materiale Anisotropo, Ph.D. Thesis, University of Bologna - DISTART Department, 2007.
60. Tornabene F., Viola E. Vibration analysis of spherical structural elements using the GDQ method. Comput. Math. Appl. 2007, 53:1538-1560.
61. Viola E., Dilena M., Tornabene F. Analytical and numerical results for vibration analysis of multi-stepped and multi-damaged circular arches. J. Sound Vib. 2007, 299:143-163.
62. Marzani A., Tornabene F., Viola E. Nonconservative stability problems via generalized differential quadrature method. J. Sound Vib. 2008, 315:176-196.
63. Tornabene F., Viola E. 2-D solution for free vibrations of parabolic shells using generalized differential quadrature method. Eur. J. Mech. A/Solids 2008, 27:1001-1025.
64. Alibeigloo A., Modoliat R. Static analysis of cross-ply laminated plates with integrated surface piezoelectric layers using differential quadrature. Comput. Struct. 2009, 88:342-353.
65. Tornabene F. Vibration analysis of functionally graded conical, cylindrical and annular shell structures with a four-parameter power-law distribution. Comput. Methods Appl. Mech. Engrg. 2009, 198:2911-2935.
66. Tornabene F., Viola E. Free vibrations of four-parameter functionally graded parabolic panels and shell of revolution. Eur. J. Mech. A/Solids 2009, 28:991-1013.
67. Tornabene F., Viola E. Free vibration analysis of functionally graded panels and shells of revolution. Meccanica 2009, 44:255-281.
68. Tornabene F., Viola E., Inman D.J. 2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical and annular shell structures. J. Sound Vib. 2009, 328:259-290.
69. Viola E., Tornabene F. Free vibrations of three parameter functionally graded parabolic panels of revolution. Mech. Res. Commun. 2009, 36:587-594.
70. Tornabene F., Marzani A., Viola E., Elishakoff I. Critical flow speeds of pipes conveying fluid by the generalized differential quadrature method. Adv. Theor. Appl. Mech. 2010, 3:121-138.
71. Auricchio F., Sacco E. A mixed-enhanced finite-element for the analysis of laminated composite plates. Int. J. Numer. Methods Engrg. 1999, 44:1481-1504.
72. Alfano G., Auricchio F., Rosati L., Sacco E. MITC finite elements for laminated composite plates. Int. J. Numer. Methods Engrg. 2001, 50:707-738.
73. Auricchio F., Sacco E. Refined first-order shear deformation theory models for composite laminates. J. Appl. Mech. 2003, 70:381-390.
74. Liew K.M., Peng L.X., Ng T.Y. Three-dimensional vibration analysis of spherical shell panels subjected to different boundary conditions. Int. J. Mech. Sci. 2002, 44:2103-2117.
75. Hosseini-Hashemi Sh., Fadaee M., Es'haghi M. A novel approach for in-plane/out-of-plane frequency analysis of functionally graded circular/annular plates. Int. J. Mech. Sci. 2010, 52:1025-1035.