Axiomatic/asymptotic PVD/RMVT-based shell theories for free vibrations of anisotropic shells using an advanced Ritz formulation and accurate curvature descriptions

Composite Structures

Volumn 108, Issue 1, 2014, Pages 91-110

  Fazzolari, F A ^a   Banerjee, J R ^a  

^a CITY UNIVERSITY   (United Kingdom)

Author keywords

Axiomatic asymptotic shell theories; Doubly curved anisotropic laminated shells; Free vibration; Lam parameters; Ritz method

Indexed keywords

ANISOTROPY; LAGRANGE MULTIPLIERS; LAMINATED COMPOSITES; PLATES (STRUCTURAL COMPONENTS); SHEAR STRESS; THREE DIMENSIONAL;

ANISOTROPIC LAMINATED SHELL; FREE VIBRATION; LAMINATED COMPOSITE SHELL; PRINCIPLE OF VIRTUAL DISPLACEMENTS; REISSNER'S MIXED VARIATIONAL THEOREMS; RITZ METHODS; SHELL THEORY; TRIGONOMETRIC RITZ FORMULATIONS;

SHELLS (STRUCTURES);

EID: 84896663461     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2013.08.037     Document Type: Article

References (88)

1. Fazzolari F.A., Carrera E. Advanced variable kinematics Ritz and Galerkin formulations for accurate buckling and vibration analysis of laminated composite plates. Compos Struct 2011, 94(1):50-67.
2. Fazzolari F.A., Carrera E. Accurate free vibration analysis of thermo-mechanically pre/post-buckled anisotropic multilayered plates and FGM plates based on a refined hierarchical trigonometric Ritz formulation. Compos Struct 2013, 95:381-402.
3. Fazzolari F.A., Carrera E. Free vibration analysis of sandwich plates with anisotropic face sheets in thermal environment by using the hierarchical trigonometric Ritz formulation. Compos Part B: Eng 2013, 50:67-81.
4. Fazzolari F.A., Carrera E. Thermo-mechanical buckling analysis of anisotropic multilayered composite and sandwich plates by using refined variable-kinematics theories. J Therm Stress 2012, 36(4):321-350.
5. Fazzolari F.A., Carrera E. Advances in the Ritz formulation for free vibration response of doubly-curved anisotropic laminated composite shallow and deep shells. Compos Struct 2013, 101:111-128.
6. Novozhilov V.V. The theory of thin elastic shells 1964, P. Noordhoff Lts, Groningen, The Netherlands.
7. Aron H. Das gleichgewicht und die bewegung einer unendlich dunnen,beliebig gekrummten elastischen schale. J für Math 1874, 136-174.
8. Love A.E.H. A treatise on the mathematical theory of elasticity 1944, Dover Pub., New York. 4th ed.
9. Love A.E.H. The small free vibrations and deformations of a thin elastic shell. Phil Trans Roy Soc (London) Ser A 1888, (179):491-549.
10. Lur'e A.I. General theory of elastic shells. Prikl Mat Mekh 1940, 4(1):7-34.
11. Gol'denveizer A.L. Theory of thin shells 1961, Pergamon Press, New York.
12. Airy G.B. On the strains in the interior of beams. Phil Trans Roy Soc 1862, 153:49-80.
13. Mushtari K.M. On the stability of cylindrical shells subjected to torsion, (in Russian). Trudy Kazanskego Aviatsionnugo Inatituta 1938, 2.
14. Mushtari K.M. Certain generalizations of the theory of thin shells, (in Russian). Izv Fiz Mat Odd pri Kazan Univ 1938, 11(8).
15. Donnell LH. Stability of thin walled tubes under torsion. Tech. rep. 479, NACA; 1933.
16. Donnell LH. A discussion of thin shell theory. In: Proceedings of the fifth international congress for applied mechanics; 1938.
17. Vlasov VZ. Osnovnye differentsialnye uravnenia obshche teorii uprugikh obolochek (english translation: NACA TM 1241. Basic differential equations in the general theory of elastic shells; 1951). Prikl Mat Mekh, vol. 8; 1944.
18. Vlasov VZ. Obshchaya teoriya obolochek; yeye prilozheniya v tekhike (english translation: NASA TTF-99. General theory of shells and its applications in engineering; 1964). Gos Izd Tekh-Teor-Lit, Moscow-Leningrad; 1949.
19. Flügge W. Statik und Dynamik der Schalen 1934, Julius Springer, Berlin, (Reprinted by Edwards Brothers Inc., Ann Arbor, Mich.; 1943).
20. Flügge W. Stresses in shells 1962, Springer-Verlag, Berlin.
21. Byrne R. Theory of small deformations of a thin elastic shell. Seminar Reports Math Univ Calif Pub Math NS 1944, 2(1):103-152.
22. Sanders JL. An improved first approximation theory of thin shells. Tech. rep. R24, NASA; 1959.
23. Whitney J.M., Sun C.T. A refined theory of laminated anisotropic, cylindrical shells. J Appl Mech 1974, 41:471-476.
24. Librescu L. Elasto-statics and kinetics of anisotropic heterogeneous shell-type structures 1975, Noordhoff International, Leyden, The Nederlands. 1st ed.
25. Gulati S.T., Essemberg F. Effect of anisotropy in axisymmetric cylindrical shells. J Appl Mech 1967, 34:659-666.
26. Zucas J.A., Vinson J.R. Laminated transversely isotropic cylindrical shells. J Appl Mech 1971, 38:400-407.
27. Ambartsumian S.A. Some main equations of the theory of thin layered shell. DAN ArmSSR 1948, 8(5).
28. Ambartsumian S.A. Symmetrically loaded anisotropic shells of rotation. DAN ArmSSR 1948, 9(5).
29. Ambartsumian S.A. Analysis of layered shells of rotation. DAN ArmSSR 1949, 11(2).
30. Ambartsumian S.A. Calculation of slow cylindrical shells made up from anisotropic layers. Izvestija ANArmSSR (FME i T nauki) 1951, 4(5).
31. Ambartsumian S.A. Long anisotropic shells of rotation. Izvestija ANArmSSR (FME i T nauki) 1951, 4(6).
32. Ambartsumian S.A. Thermal stresses in layered anisotropic shells. Izvestija ANArmSSR (FME i T nauki) 1952, 5(6).
33. Ambartsumian S.A. Toward the calculation of long shells of double curvature. Izvestija AN ArmSSR (FME i T nauki) 1953, 6(5-6).
34. Ambartsumian S.A. On the limits of applicability of some hypotheses of the theory of thin cylindrical shells. Izvestija AN SSSR, OTN 1954, (5).
35. Naghdi P.M., Berry J.G. On the equations of motion of cylindrical shells. J Appl Mech 1964, 21(2):160-166.
36. Ambartsumian SA. Theory of anisotropic shells. NASA report TT F-118; 1964.
37. Bert C.W. Analysis of shells. Composite materials 1974, vol. 7:207-258. Accademic Press, New york. C.C. Chamis, L.J. Broutman, R.K. Krock (Eds.).
38. Bert C.W. Dynamic of composite and sandwich panels - Part I. Shock Vib Dig 1976, 8(10):37-48.
39. Bert C.W. Dynamic of composite and sandwich panels - Part II. Shock Vib Dig 1976, 8(11):15-24.
40. Reddy J.N. Exact solutions of moderately thick laminated shells. J Eng Mech 1984, 110(5):794-809.
41. Hsu T.M., Wang J.T.S. A theory of laminated cylindrical shells consisting of layers of orthotropic laminae. AIAA J 1970, 8(12):2141-2146.
42. Cheung Y.K., Wu C.I. Free vibration of thick, layered cylinders having finite length with various boundary conditions. J Sound Vib 1972, 24:189-200.
43. Barbero E.J., Reddy J.N., Teply J.L. General two-dimensional theory of laminated cylindrical shells. AIAA J 1990, 28(3):544-553.
44. Carrera E. Multilayered shell theories accounting for layerwise mixed description, Part 1: Governing equations. AIAA J 1999, 37(9):1107-1116.
45. Carrera E. Multilayered shell theories accounting for layerwise mixed description, Part 2: Numerical evaluations. AIAA J 1999, 37(9):1117-1124.
46. Carrera E. A Reissner's mixed variational theorem applied to vibration analysis of multilayered shells. J Appl Mech 1999, 66:69-78.
47. Denis S.T., Palazotto A.N. Transverse shear deformation in orthotropic cylindrical pressure vessels using a higher-order shear deformation theory. AIAA J 1989, 27(10):1441-1447.
48. Di S., Ramm E. Hybrid stress formulation for higher-order theory of laminated shell analysis. Comput Methods Appl Mech Eng 1993, 109:356-359.
49. Qatu M.S., Asadi E. Vibration of doubly curved shallow shells with arbitrary boundaries. Appl Acoust 2012, 73:21-27.
50. Asadi E., Wenchao W., Qatu M.S. Static and vibration analyses of thick deep laminated cylindrical shells using 3d and various shear deformation theories. Compos Struct 2012, 94:494-500.
51. Ferreira A.J.M., Castro L.M., Bertoluzza S. A wavelet collocation approach for the analysis of laminated shells. Compos Part B: Eng 2011, 42:99-104.
52. Ferreira A.J.M., Carrera E., Cinefra M., Roque C.M.C. Analysis of laminated doubly-curved shells by a layerwise theory and radial basis functions collocation, accounting for through-the-thickness deformations. Comput Mech 2011, 48:13-25.
53. Tornabene F. 2-D GDQ solution for free vibrations of anisotropic doubly-curved shells and panels of revolution. Compos Struct 2011, 93:1854-1876.
54. Tornabene F., Viola E., Fantuzzi N. General higher order equivalent single layer therory for free vibrations of doubly-curved laminated composite shells and panels. Compos Struct 2013, 104:94-117.
55. Carrera E. C0z requirements-models for the two dimensional analysis of multilayered structures. Compos Struct 1997, 37:373-384.
56. Reissner E. On a certain mixed variational theorem and a proposed application. Int J Numer Methods Eng 1984, 20(7):1366-1368.
57. Reissner E. On a mixed variational theorem and on a shear deformable plate theory. Int J Numer Methods Eng 1986, 23:193-198.
58. Reissner E. On a certain mixed variational theorem and on laminated elastic shell theory. Int J Numer Methods Eng 1986, 219:17-27.
59. Carrera E. Developments, ideas, and evaluation based upon Reissner's mixed variational theorem in the modeling of multilayered plates and shells. Appl Mech Rev 2001, 54:301-329.
60. Ferreira A.J.M., Carrera E., Cinefra M., Roque C.M.C. Radial basis functions collocation for the bending and free vibration analysis of laminated plates using the Reissner-mixed variational theorem. Eur J Mech - A/Solid 2013, 39:104-112.
61. Grigolyuk E.I., Kulicov G.M. General direction of the development of the theory of shells. Mekhanica kompozitnykh Materialov 1988, 24(2):287-298.
62. Fettahlioglu O.A., Steele C.R. Asympthotic solutions for orthotropic non-homogeneous shells of revolution. J Appl Mech 1974, 41:753-758.
63. Widera G.E.O., Logan D.L. Refined theories for non-homogeneous anisotropic, cylindrical shells: Part I - Derivation. J Eng Mech Div ACSE 1980, 106:1053-1057.
64. Widera G.E.O., Fan H. On the derivation of a refined theory for non-homogeneous anisotropic shells of revolution. J Appl Mech 1988, 110:102-105.
65. Spencer AJM, Watson P, Rogers TG. Stress analysis of laminated circular cylindrical shells. In: Recent developments in composite materials structures; proceedings of the symposium, ASME winter annual meeting, Dallas, TX, November 25-30; 1990. p. 57-60.
66. Cicala P. Systematic approach to linear shell theory 1965, Levrotto & Bella, Turin, Italy.
67. Kapania R.K. A review on the analysis of laminated shells. J Pressure Vessels Technol 1989, 111:88-96.
68. Noor A.K., Burton W.S. Assessment of computational models for multilayered composite shells. Appl Mech Rev 1990, 43:2141-2146.
69. Carrera E. A class of two-dimensional theories for anisotropic multilayered plates analysis, Atti Accademia delle scienze Torino. Memorie Scienze Fisiche 1995, 19-20:49-87.
70. Carrera E. Theories and finite elements for multilayered anisotropic composite plates and shells. Arch Comput Methods Eng 2002, 9(2):87-140.
71. Carrera E. Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking. Arch Comput Methods Eng 2003, 10(3):216-296.
72. Tsai S.W. Composites design 1988, Dayton, Think Composites. 4th ed.
73. Reddy J.N. Mechanics of laminated composite plates and shells. Theory and analysis 2004, CRC Press. 2nd ed.
74. Jones R.M. Mechanics of composite materials 1998, Taylor & Francis, United States. 2nd ed.
75. Kirchhoff G.R. überber das gleichgewicht und diw bewegung einer elasticien (About the equilibrium and motion of elastic bodies). J für Reine Angewandte Math 1850, 40:51-88.
76. Mindlin R. Influence of rotary inertia and shear on flexural motions of isotropic elastic plates. J Appl Mech 1951, 18(10):31-38.
77. Reissner E. The effect of transverse shear deformation on the bending of elastic plates. J Appl Mech 1945, 67:A67-A77.
78. Washizu K. Variational methods in elasticity and plasticity 1968, Pergamon, Headington Hill Hall, Oxford. 1st ed.
79. Robaldo A., Carrera E., Benjeddou A. A unified formulation for finite element analysis of piezoelectric adaptive plates. Comput Struct 2006, 84(22-23):1494-1505.
80. Carrera E. On the use of Murakami's zig zag function in the modeling of layered plates and shells. Compos Struct 2004, 82:541-554.
81. Demasi L. Refined multilayered plate elements based on Murakami zig-zag functions. Compos Struct 2005, 70:308-316.
82. Carrera E., Petrolo M. Guidelines and recommendations to construct theories for metallic and composite plates. AIAA J 2010, 48:2852-2866.
83. Mashat D.S., Carrera E., Zenkour A.M., Al Khateeba S.A. Axiomatic/asymptotic evaluation of multilayered plate theories by using single and multi-points error criteria. Compos Struct 2013, 106:393-406.
84. Carrera E., Miglioretti F. Selection of appropriate multilayered plate theories by using a genetic like algorithm. Compos Struct 2013, 94(3):1175-1186.
85. Reddy J.N. Energy princiles and variational methods in applied mechanics 2002, John Wiley & Sons Inc., Hoboken, New Jersey. 2nd ed.
86. Fazzolari FA, Carrera E. Coupled thermoelastic effect in free vibration analysis of anisotropic multilayered plates and FGM plates by using an advanced variable-kinematics Ritz formulation. Eur J Mech Solid/A, in press.
87. 6 Mixed plate theories based on the generalized unified formulation. Part V: Results. Compos Struct 2009, 88(1):1-16.
88. Chern Y.C., Chao C.C. Comparison of natural frequencies of laminates by 3d theory, Part II: Curved panles. J Sound Vib 2000, 230(5):1009-1030.