, Volume 33, Issue 1, pp 11–27 | Cite as

Static Response of Composite Circular Cylindrical Shells Studied by Different Theories

  • K. Chandrashekhara
  • D.V.T.G. Pavan Kumar


A detailed study, on the static response of cross-ply laminated composite circular cylindrical shell of revolution and shell panel with various support conditions, has been made using Levy type of solution and the classical shell theories of FlSanders, Love and Donnell in an unified form. It has been shown that while developing a Levy type of solution using aforementioned theories, certain difficulty is encountered for determining the particular integral in respect of Fl Sanders and Love theories. This difficulty has been overcome by making use of the membrane solution as a particular integral. A comparative study has been carried out using the above shell theories for different geometrical parameters, lamination schemes and support conditions. It has been shown that Donnell theory predicts inaccurate results for certain lamination schemes, support conditions and geometrical parameters of the shell. It is suggested that, for developing shear deformation shell theories, it would be better to use a more accurate shell theory like Flügge Sommario. La risposta statica di gusci cilindrici circolari di materiale composito laminato, a strati incrociati, e di pannelli con varie condizioni di supporto viene analizzata utilizzando in una forma unificata soluzioni tipo Levy e le classiche teorie dei gusci di Flügge Sanders, Love e Donnell. Si mostra che nello sviluppare una soluzione di tipo Levy si incontra una certa difficoltà nel determinare l'integrale particolare rispetto alle teorie di Flügge, Sanders e Love. Tale difficoltà viene superata usando la soluzione di membrana come integrale particolare. Viene sviluppato uno studio comparativo facendo uso delle suddette teorie dei gusci per differenti parametri geometrici, schemi di laminazione e condizioni di vincolo. Si mostra che la teoria di Donnell fornisce risultati non accurati per certi schemi di laminazione, condizioni di supporto e parametri geometrici del guscio. Si suggerisce che per sviluppare teorie dei gusci che tengano conto delle deformazioni di scorrimento sarebbe più opportuno l'uso di una teoria dei gusci più accurata come ad esempio quella di Flügge.

Static analysis Laminated shells Shells Structural mechanics 


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  1. 1.
    Simitses, G.J. and Chen, Z., 'Buckling of delaminated, long, cylindrical panels under pressure', Comput. Struct. 28(2) (1988) 173–184.Google Scholar
  2. 2.
    Librescu, L., Khdeir, A.A. and Frederick, D., 'A shear deformable theory of laminated composite shallow shell-type panels and their response analysis I: Free vibration and buckling', Acta Mech. 76 (1989) 1-33.Google Scholar
  3. 3.
    Khdeir, A.A., Librescu, L. and Frederick, D., 'A shear deformable theory of laminated composite shallow shell-type panels and their response analysis II: Static response', Acta Mech. 77 (1989) 1–12.Google Scholar
  4. 4.
    Khdeir, A.A., Reddy, J.N. and Frederick, D., 'A study of bending, vibration, and buckling of cross-ply circular cylindrical shells with various shell theories', Int. J. Eng. Sci. 27(11) (1989) 1337–1351.Google Scholar
  5. 5.
    Khdeir, A.A., Rajab, M.B. and Reddy, J.N., 'Thermal effects of the response of cross ply laminated shallow shells', Int. J. Solids Struct. 29(5) (1992) 653–667.Google Scholar
  6. 6.
    Khdeir, A.A. and Reddy, J.N., 'Influence of edge conditions on the modal characteristics of cross ply laminated shells', Comput. Struct. 34(6) (1990) 817–826.Google Scholar
  7. 7.
    Nosier, A. and Reddy, J.N., 'Vibration and stability analysis of cross-ply laminated circular cylindrical shells', J. Sound Vib. 157(1) (1992) 139–159.Google Scholar
  8. 8.
    Reddy, J.N. and Liu, C.F., 'A higher-order shear deformation theory of laminated elastic shells', Int. J. Eng. Sci. 23(3) (1985) 319–330.Google Scholar
  9. 9.
    Donnell, L.H., Stability of Thin-Walled Tubes under Torsion, NACA Report 479, 1933.Google Scholar
  10. 10.
    Chandrashekhara, K. and Pavan Kumar, D.V.T.G., 'Assessment of shell theories for the static analysis of cross-ply laminated circular cylindrical shells', Thin Walled Struct., 22(4) (1995) 291–318.Google Scholar
  11. 11.
    Flügge, W., Stresses in shells, 2nd ed., Springer Verlag, Berlin, 1973.Google Scholar
  12. 12.
    Sanders, Jr. J.L., An Improved First-Approximation Theory for Thin Shells, NASA Tech. Rep., R-24, 1959.Google Scholar
  13. 13.
    Love, A.E.H., A Treatise on the Mathematical Theory of Elasticity, 4th ed., Dover Publications, New York, 1944.Google Scholar
  14. 14.
    Soldatos, K.P., 'A comparison of some shell theories used for the dynamic analysis of cross-ply laminated circular cylindrical panels', J. Sound Vib. 97(2) (1984) 305–319.Google Scholar
  15. 15.
    Vinson, J.R. and Chou, T.W., Composite Materials and Their Use in Structures, Applied Science Publishers, London, 1975.Google Scholar
  16. 16.
    Seide, P., Small Elastic Deformation of Thin Shells, Noordhoff International Publishing, Leyden, 1975.Google Scholar
  17. 17.
    Chaudhuri, R.A., Balaraman, K. and Kunukkasseril V.X., 'Arbitrarily laminated, anisotropic cylindrical shell under internal pressure', AIAA J. 24(11) (1986) 1851–1858.Google Scholar
  18. 18.
    Kovarik V., Stresses in Layered Shells of Revolution, Elsevier, Amsterdam, 1989.Google Scholar
  19. 19.
    Chandrashekhara, K. and Kumar, B.S., 'Static analysis of a thick laminated circular cylindrical shell subjected to axisymmetric load', Compos. Struct. 23(1) (1993) 1–9.Google Scholar
  20. 20.
    Chandrashekhara, K. and Kumar, B.S., 'Static analysis of thick laminated circular cylindrical shells', J. Pressure Vessel Technol., Trans. of ASME 115(2) (1993) 193–200.Google Scholar
  21. 21.
    Ren, J.G., 'Exact solutions for laminated cylindrical shells in cylindrical bending', Comp. Sci. Technol. 29 (1987) 169–187.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • K. Chandrashekhara
    • 1
  • D.V.T.G. Pavan Kumar
    • 1
  1. 1.Department of Civil EngineeringIndian Institute of ScienceBangaloreIndia

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