Static analysis of laminated composite curved shells and panels of revolution with a posteriori shear and normal stress recovery using generalized differential quadrature method

International Journal of Mechanical Sciences

Volumn 61, Issue 1, 2012, Pages 71-87

  Tornabene, Francesco ^a   Liverani, Alfredo ^a   Caligiana, Gianni ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

First Order Shear Deformation Theory; Generalized Differential Quadrature method; Laminated composite shells; Shear and normal stress recovery

Indexed keywords

3-D FINITE ELEMENT METHOD; BOUNDARY EQUILIBRIUM; COMPOSITE SHELL; DIFFERENTIAL QUADRATURE; EQUILIBRIUM EQUATION; FIRST-ORDER SHEAR DEFORMATION THEORY; FLEXURAL STRAIN; FOURIER EXPANSION; GDQ METHOD; GENERALIZED DIFFERENTIAL QUADRATURE METHODS; GENERALIZED DISPLACEMENTS; HIGHER ORDER; INITIAL CURVATURE; KINEMATICAL MODELS; LAMINATE THICKNESS; LAMINATED COMPOSITE SHELL; MECHANICAL MODEL; MIXED FORMULATIONS; MODERATELY THICK; NORMAL STRESS; POSTERIORI; RECONSTRUCTION PROCEDURE; REGULARIZATION PROCEDURE; REISSNER-MINDLIN THEORY; SEMI-ANALYTICAL METHODS; SHELL ELEMENT; STRESS PROFILE; STRESS RESULTANTS; STRUCTURAL ELEMENTS; SYSTEM OF EQUATIONS; THREE-DIMENSIONAL THEORY; TRANSVERSE SHEAR;

DIFFERENTIATION (CALCULUS); FINITE ELEMENT METHOD; LAMINATED COMPOSITES; PLATES (STRUCTURAL COMPONENTS); RECOVERY; SHELLS (STRUCTURES); STRAIN;

THREE DIMENSIONAL;

EID: 84863300982     PISSN: 00207403     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijmecsci.2012.05.007     Document Type: Article

References (64)

1. S. Timoshenko, and S. Woinowsky-Krieger Theory of plates and shells 1959 McGraw-Hill
2. W. Flügge Stresses in shells 1960 Springer-Verlag
3. A.L. GolDenveizer Theory of elastic thin shells 1961 Pergamon Press
4. Novozhilov VV. Thin shell theory, P. Noordhoff, 1964.
5. Vlasov VZ. General theory of shells and its application in engineering. NASA-TT-F-99; 1964.
6. Ambartusumyan SA. Theory of anisotropic shells. NASA-TT-F-118; 1964.
7. H. Kraus Thin elastic shells 1967 John Wiley & Sons
8. Leissa AW. Vibration of plates. NASA-SP-160; 1969.
9. Leissa AW. Vibration of Shells. NASA-SP-288; 1973.
10. Š. Markuš The mechanics of vibrations of cylindrical shells 1988 Elsevier
11. E. Ventsel, and T. Krauthammer Thin plates and shells 2001 Marcel Dekker
12. W. Soedel Vibrations of shells and plates 2004 Marcel Dekker
13. E. Reissner The effect of transverse shear deformation on the bending of elastic plates J Appl Mech ASME 12 1945 66 77
14. P.L. Gould Finite element analysis of shells of revolution 1984 Pitman Publishing
15. P.L. Gould Analysis of plates and shells 1999 Prentice-Hall
16. M.S. Qatu Accurate stress resultants equations for laminated composite deep thick shells 302 1995 ASME Compos Pressure Vessel Ind 39-44
17. M.S. Qatu Accurate theory for laminated composite deep thick shells Int J Solids Struct 36 1999 2917 2941
18. M.S. Qatu Vibration of laminated shells and plates 2004 Elsevier
19. M.H. Toorani, and A.A. Lakis General equations of anisotropic plates and shells including transverse shear deformations, rotary inertia and initial curvature effects J Sound Vib 237 2000 561 615
20. M.H. Toorani, and A.A. Lakis Free vibration of non-uniform composite cylindrical shells Nucl Eng Des 237 2006 1748 1758
21. J.N. Reddy Mechanics of laminated composites plates and shells 2003 CRC Press New York
22. E. Carrera Historical review of zig-zag theories for multilayered plates and shells Appl Mech Rev 56 2003 287 308
23. E. Carrera A unified formulation to assess theories of multilayered plates for various bending problems Compos Struct 69 2005 271 293
24. E. Carrera, S. Brischetto, M. Cinefra, and M. Soave Effects of thickness stretching in functionally graded plates and shells Compos B Eng 42 2011 123 133
25. G. Giunta, F. Biscani, S. Belouettar, and E. Carrera Hierarchical modelling of doubly curved laminated composite shells under distributed and localised loadings Compos B Eng 42 2011 682 691
26. F. Auricchio, and E. Sacco A mixed-enhanced finite-element for the analysis of laminated composite plates Int J Numer Methods Eng 44 1999 1481 1504
27. G. Alfano, F. Auricchio, L. Rosati, and E. Sacco MITC finite elements for laminated composite plates Int J Numer Methods Eng 50 2001 707 738
28. F. Auricchio, and E. Sacco Refined first-order shear deformation theory models for composite laminates J Appl Mech 70 2003 381 390
29. 0 HSDT and a novel post-processing technique Eur J Mech A/Solids 30 2011 46 53
30. C. Shu, H. Ding, and K.S. Yeo Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations Comput Methods Appl Mech Eng 192 2003 941 954
31. L.F. Qiana, R.C. Batrab, and L.M. Chen Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local Petrov-Galerkin method Compos B Eng 35 2004 685 697
32. A.J.M. Ferreira, C.M.C. Roque, and R.M.N. Jorge Free vibration analysis of symmetric laminated composite plates by FSDT and radial basis functions Comput Methods Appl Mech Eng 194 2005 4265 4278
33. A.J.M. Ferreira, and G.E. Fasshauer Computation of natural frequencies of shear deformable beams and plates by an RBF-pseudospectral method Comput Methods Appl Mech Eng 196 2006 134 146
34. J.R. Xiao, R.C. Batra, D.F. Gilhooley, J.W. Gillespie Jr., and M.A. McCarthy Analysis of thick plates by using a higher-order shear and normal deformable plate theory and MLPG method with radial basis functions Comput Methods Appl Mech Eng 196 2007 979 987
35. C. Shu Differential quadrature and its application in engineering 2000 Springer Berlin
36. E. Viola, and F. Tornabene Vibration analysis of damaged circular arches with varying cross-section Struct Integr Durab (SID-SDHM) 1 2005 155 169
37. E. Viola, and F. Tornabene Vibration analysis of conical shell structures using GDQ method Far East J Appl Math 25 2006 23 39
38. Tornabene F. Modellazione e Soluzione di Strutture a Guscio in Materiale Anisotropo. PhD thesis. University of Bologna - DISTART Department; 2007.
39. F. Tornabene, and E. Viola Vibration analysis of spherical structural elements using the GDQ method Comput Math Appl 53 2007 1538 1560
40. E. Viola, M. Dilena, and F. Tornabene Analytical and numerical results for vibration analysis of multi-stepped and multi-damaged circular arches J Sound Vib 299 2007 143 163
41. A. Marzani, F. Tornabene, and E. Viola Nonconservative stability problems via generalized differential quadrature method J Sound Vib 315 2008 176 196
42. F. Tornabene, and E. Viola 2-D solution for free vibrations of parabolic shells using generalized differential quadrature method Eur J Mech A/Solids 27 2008 1001 1025
43. F. Tornabene Vibration analysis of functionally graded conical, cylindrical and annular shell structures with a four-parameter power-law distribution Comput Methods Appl Mech Eng 198 2009 2911 2935
44. F. Tornabene, and E. Viola Free vibrations of four-parameter functionally graded parabolic panels and shell of revolution Eur J Mech A/Solids 28 2009 991 1013
45. F. Tornabene, and E. Viola Free vibration analysis of functionally graded panels and shells of revolution Meccanica 44 2009 255 281
46. F. Tornabene, E. Viola, and D.J. Inman 2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical and annular shell structures J Sound Vib 328 2009 259 290
47. E. Viola, and F. Tornabene Free vibrations of three parameter functionally graded parabolic panels of revolution Mech Res Commun 36 2009 587 594
48. F. Tornabene, A. Marzani, E. Viola, and I. Elishakoff Critical flow speeds of pipes conveying fluid by the generalized differential quadrature method Adv Theor Appl Mech 3 2010 121 138
49. F. Tornabene Free vibrations of laminated composite doubly-curved shells and panels of revolution via the GDQ method Comput Methods Appl Mech Eng 200 2011 931 952
50. F. Tornabene 2-D GDQ solution for free vibrations of anisotropic doubly-curved shells and panels of revolution Compos Struct 93 2011 1854 1876
51. F. Tornabene Free vibrations of anisotropic doubly-curved shells and panels of revolution with a free-form meridian resting on Winkler-Pasternak elastic foundations Compos Struct 94 2011 186 206
52. Tornabene F. Shear and normal stress recovery for anisotropic shells and panels of revolution via the GDQ method. In: Proceedings of the XX° Convegno Italiano dellAssociazione Italiana di Meccanica Teorica e Applicata (AIMETA 2011).
53. F. Tornabene, A. Liverani, and G. Caligiana FGM and laminated doubly curved shells and panels of revolution with a free-form meridian: a 2-D GDQ solution for free vibrations Int J Mech Sci 53 2011 446 470
54. F. Tornabene, A. Liverani, and G. Caligiana Laminated composite rectangular and annular plates: a GDQ solution for static analysis with a posteriori shear and normal stress recovery Compos B Eng 43 2012 1847 1872
55. K.Y. Lam, and L. Hua Influence of initial pressure on frequency characteristics of a rotating truncated circular conical shell Int J Mech Sci 42 2000 213 236
56. K.M. Liew, T.M. Teo, and J.B. Han Three-dimensional static solutions of rectangular plates by variant differential quadrature method Int J Mech Sci 43 2001 1611 1628
57. T.Y. Ng, H. Li, and K.Y. Lam Generalized differential quadrature method for the free vibration of rotating composite laminated conical shell with various boundary conditions Int J Mech Sci 45 2003 567 587
58. L. Zhang, Y. Xiang, and G.W. Wei Local adaptive differential quadrature for free vibration analysis of cylindrical shells with various boundary conditions Int J Mech Sci 48 2006 1126 1138
59. X. Wang, X. Wang, and X. Shi Accurate buckling loads of thin rectangular plates under parabolic edge compressions by the differential quadrature method Int J Mech Sci 49 2007 447 453
60. B. Sobhani Aragh, and M.H. Yas Three-dimensional analysis of thermal stresses in four-parameter continuous grading fiber reinforced cylindrical panels Int J Mech Sci 52 2010 1047 1063
61. S. Hosseimi-Hashemi, M. Fadaee, and S.R. Atashipour A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates Int J Mech Sci 53 2011 11 22
62. Asadi E, Qatu MS. Free vibration of thick laminated cylindrical shells with different boundary conditions using general differential quadrature. J Vib Contr, in press, doi:10.1177/1077546311432000.
63. X.-P. Shu A refined theory of laminated shells with higher-order transverse shear deformation Int J Solids Struct 34 1997 673 683
64. E. Asadi, W. Wang, and M.S. Qatu Static and vibration analyses of thick deep laminated cylindrical shells using 3D and various shear deformation theories Compos Struct 94 2012 494 500