Buckling of Complete Spherical Shells and Spherical Caps

  • L. Kollár

Summary

The buckling behaviour of complete spherical shells and spherical caps is explained and test results are extensively reviewed. The development of the theory up to the point where theoretical and experimental results agree is presented. The treatment is confined to completely elastic material.

References

  1. 1.
    Adam, H.P.; King, P.A. /1965/: Experimental Investigation of the Stability of Monocoque Domes Subjected to External Pressure. Experimental Mechanics 5, 313–320.CrossRefGoogle Scholar
  2. 2.
    Archer, R.P.; Famili, J. /1965/: On the Vibration and Stability of Finitely Deformed Shallow Spherical Shells. Journ. Appl. Mech. 32, 116–120.MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    Budiansky, B. /1959/: Buckling of Clamped Shallow Spherical Shells. Proc. Symp. Theory of Thin Elastic Shells /Delft/. North-Holland Publ., Amsterdam, 1960.Google Scholar
  4. 4.
    Bushnell, D. /1967a/: Nonlinear Axisymmetric Behaviour of Shells of Revolution. AIAA Journ. 5, 423–439.ADSGoogle Scholar
  5. 5.
    Bushnell, D. /1967b/: Buckling of Spherical Shells Ring-Supported at the Edges. AIAA Journ. 5, 2041–2046.ADSCrossRefGoogle Scholar
  6. 6.
    Bushnell, D. /1967c/: Symmetric and Nonsymmetric Buckling of Finitely Deformed Eccentrically Stiffened Shells of Revolution. AI.AA Journ. 5, 1455–62.ADSMATHCrossRefGoogle Scholar
  7. 7.
    Bürgermeister, G.; Steup, H.; Kretschmar, H. /1963/: Stabilitätstheorie, Teil II. Akademie-Verlag, Berlin.MATHGoogle Scholar
  8. 8.
    Carlson, R.L.; Sendelbeck, R.L.; Hoff, N.J. /1967/: Experimental Studies of the Buckling of Complete Spherical Shells. Experimental Mechanics 7, 281–288.CrossRefGoogle Scholar
  9. 9.
    Csonka, P. /1956/: The Buckling of a Spheroidal Shell Curved in Wo Directions. Acta Techn. Acad. Sci. Hung. 14, 4–25-437.Google Scholar
  10. 10.
    Dickie, J.P.; Broughton, P. /1971/: Stability Criteria for Shallow Arches. Journ. Eng. Mech. Divis. /Proc. ASCE/ 97 EM3, 951–965.Google Scholar
  11. 11.
    Dostanova, S.Kh.; Raizer, V.D. /1973/: Issledovanie ustoĭ-chivosti pologih obolochek polozhitel’noi krivizny metodom lokal’nykh variatsii. Stroit. Mekh. i. Rasch. Sooruzh. 34–39.Google Scholar
  12. 12.
    Duläcska, E. /1965/: Experimental Determination of the Critical Load of Shell Structures. Proc. Symposiimi IASS /Budapest, 1965/Epitestudomanyi Intezet, Budapest.Google Scholar
  13. 13.
    Evan-Ivanowski, R.M.; Loo, T.C. /1962/: Deformations and Stability of Spherical Shells under Action of Concentrated Loads and Uniform Pressure. Techn. Report 834 /11/, 4. Syracuse University Research Institute.Google Scholar
  14. 14.
    Famili, J.; Archer, R.R. /1965/: Finite Asymmetric Deformation of Shallow Spherical Shells. AIAA Journ. 3, 506–510.Google Scholar
  15. 15.
    Fitch, J.R. /1968/: The Buckling and Posthuckling Behavior of Spherical Caps under Concentrated Loads. Int. Journ. Solids Struct. 4, 421–446.CrossRefGoogle Scholar
  16. 16.
    Gabril’iants, A.G-.; Feodos’ev, F.I. /1961/: Obsesimmetrichnykh forrnakh ravnovesiia uprugoi sfericheskoi obolochki, nakhodi&shcheisia pod deistviem ravnomerno raszpredelennogo davleniia. Prikl. Mat. i Mekh. 25, No. 6.Google Scholar
  17. 17.
    Hergenröder, A.; Büsch, H. /l96l/: Recent Findings in the Testing of Models. Proc. Symp. Shell Research, /Delft 1961/North-Holland Publ., Amsterdam, 1961Google Scholar
  18. 18.
    Hoff, N.J. /1969/: Some Recent Studies of the Buckling of Thin Shells. Aeronaut, Journ. /London/ 73, 1057–70.Google Scholar
  19. 19.
    Homewood, R.H.; Brine, A.C.; Johnson, A. E. Jr. /1961/: Experimental Investigations for the Buckling Instability of Monocoque Shells. Proc. Soc. Experimental Stress Analysis 18, 88–96.Google Scholar
  20. 20.
    Huang, N.C. /1964/: Unsymmetrical Buckling of Thin Shallow Spherical Shells, Journ. Appl. Mech. 31, 447–457.ADSCrossRefGoogle Scholar
  21. 21.
    Hutchinson, J.W. /1967/: Imperfection Sensitivity of Externally Pressurized Spherical Shells. Journ. Appl. Mech. 34, 49–55.ADSMATHCrossRefGoogle Scholar
  22. 22.
    Kao, R.; Perrone, N. /1971/: Asymmetric Buckling of Spherical Caps with Asymmetrical Imperfections. Journ. Appl. Mech. 38, 172–178.ADSCrossRefGoogle Scholar
  23. 23.
    Kao, R. /1972/: A Note on Buckling of Spherical Caps with Initial Asymmetric Imperfections. Journ. Appl. Mech. 39, 842–844.ADSCrossRefGoogle Scholar
  24. 24.
    Kaplan, A.; Fung, Y.C. /1954/: A Nonlinear Theory of the Bending and Buckling of Thin Elastic Shallow Shells. NACA TN 3212.Google Scholar
  25. 25.
    Kärman, Th. von; Tsien, H.S. /1939/The Buckling of Spherical Shells by External Pressure. Journ, Aeronaut. Sci. 7, p. 43.Google Scholar
  26. 26.
    Klöppel, K.; Jungbluth, O. /1953/Beitrag zum Durchschlagproblem dünnwandiger Kugelschalen. /Versuche und Bemessungsformeln. Stahlbau 22, 121–130.Google Scholar
  27. 27.
    Klöppel, K.; Roos, E. /1956/: Beitrag zum Durchschlagproblem dünnwandiger, versteifter und ünversteifter Kugelschalen für voll- und halbseitige Belastung. Stahlbau 25, 49–60.Google Scholar
  28. 28.
    Koga, T.; Hoff, N.J. /1969/The Axisymmetric Buckling of Initially Imperfect Complete Spherical Shells. Int. Journ. Solids Struct. 5, 679–697.MATHCrossRefGoogle Scholar
  29. 29.
    Koiter, W.T. /1945/Over de stabiliteit van het elastisch evenwicht. /On the stability of the elastic equilibrium./Thesis, Delft. H.J. Paris, Amsterdam. English translation: NASA, Techn. Transl. F 10, 833, 1967.Google Scholar
  30. 30.
    Koiter, W.T. /1969/: The nonlinear Buckling Problem of a Complete Spherical Shell under Uniform External Pressure. I, II, III and IV. Proc. Kon. Nederl. Akad. Wet. Series B. 72, 40–123.ADSMATHGoogle Scholar
  31. 31.
    Koten, H. van; Haas, A.M. /1970–71/The Stability of Doubly Curved Surfaces Having a Positive Gaussian Curvature Index. Heron, 17, No. 4.Google Scholar
  32. 32.
    Krenzke, M.A.; Kiernan, T.J. /1963/Elastic Stability of Near-Perfect Shallow Spherical Shells. AIAA Jorun. 1, 2855–57.CrossRefGoogle Scholar
  33. 33.
    Litle, W.A. /1964/Reliability of Shell Buckling Predictions. Research Monograph No. 25. Cambridge, Mass., M.I.T. PressGoogle Scholar
  34. 34.
    Mushtari, Kh.M. /1955/: K teorii ustoichivosti sfericheskoi obolochki pod deistviem vneshnego davleniia. Prikl. Mat. i Mekh. 19, No. 2.Google Scholar
  35. 35.
    Neut, A. van der /1932/: De elastische stabiliteit van de dunwandige bol. /The elastic stability of the thin-walled sphere./ Thesis. Delft.Google Scholar
  36. 36.
    Parmerter, R.R. /1963/: The Buckling of Clamped Shallow Spherical Shells under Uniform Pressure. Thesis. California Institute of Technology.Google Scholar
  37. 37.
    Pozo Prutos, P. del; Pozo Yindel, P. del /1979/ Elastic Buckling of Non-perfect Spherical Shells of Constant Thickness. Proc. IASS World Congress, Madrid, 1, 1.173–1.179.Google Scholar
  38. 38.
    Rauch, H.E.; Jacobs, N.H; Marz, J.L. /1978/: Buckling of a Complete Spherical Shell Under Uniform External Pressure. Studies in Appl. Math. 58, 141–158.MathSciNetGoogle Scholar
  39. 39.
    Schmidt, H. /1961/: Ergebnisse von Beulversuchen mit doppelt gekrümmten Schalenmodellen aus Aluminium. Proc. Symp. Shell Research /Delft, 1961/, North-Holland Publ. Amsterdam.Google Scholar
  40. 40.
    Schubiger, E. /1950/: Die Schalenkuppel im vorgespannten Beton der Kirche Pelix und Regula in Zürich. Schweizerische Bauzeitung, 68, 223–228.Google Scholar
  41. 41.
    Seaman, L. /l96l/: The Nature of Buckling in Thin Spherical Shells. Thesis. Cambridge, Mass. Department of Civil Engineering, M.I.T.Google Scholar
  42. 42.
    Simitses, G.J.; Cole, R.T. /1968/: Effect of load Behavior on the Buckling of Thin Spherical Shells under Pressure. Journ. Appl. lech. 35, 420–422.ADSCrossRefGoogle Scholar
  43. 43.
    Stenker, H. /1961/: Gesamtbericht von Gross versuchen an doppelt gekrümmten Montageschalen für raumabschliessende Geschossdecken. Wissensch. Zeitschr. Hochschule für Architektur und Bauwesen Weimar, 8, 181–202.Google Scholar
  44. 44.
    Thompson, J.M.T. /1962/: The Elastic Instability of a Complete Spherical Shell. Aeronaut. Quart. 13, 189–201.Google Scholar
  45. 45.
    Thompson, J.M.T.; Hunt, G.W. /1973/: A General Theory of Elastic Stability. John Wiley & Sons, London - New York - Sydney - Toronto.MATHGoogle Scholar
  46. 46.
    Thurston, G.A. /1961/: A Numerical Solution of the Nonlinear Equations for Axisymmetric Bending of Shallow Spherical Shells. Journ. Appl. Mech. 28, 557–568.MathSciNetADSMATHCrossRefGoogle Scholar
  47. 47.
    Thurston, G.A. /1971/ A New Method for Computing Axisymmetric Buckling of SDherical Caps. Journ. Appl. Mech. 38, 179–184.ADSCrossRefGoogle Scholar
  48. 48.
    Thurston, G.A.; Penning, P.A. /1966/: Effect of Axisymmetric Imperfections on the Buckling of Spherical Caps under Uniform Pressure. AIAA Journ. 4, 319–327.CrossRefGoogle Scholar
  49. 49.
    Tsien, H.S. /1941/: A Theory for the Buckling of Thin Shells. Journ. Aeronaut. Sci. 9, 373–384.Google Scholar
  50. 50.
    Wang, L.R.L. /1967/: Discrepancy of Experimental Buckling Pressures of Spherical Shells. AIM Journ. 5, 357–359.ADSGoogle Scholar
  51. 51.
    Wang, L.R.L.; Rodriquez-Agrait, L. /1966/; Litle, W.A.: Effect of Boundary Conditions on Shell Buckling. Journ. Eng. Mech. Divis. /Proc. ASCE/ 92 EM6, 101–116.Google Scholar
  52. 52.
    Wedellsborg, B.W. /1962/: Critical Buckling Load on Large Spherical Shells. Journ. Struct. Divis. /Proc. ASCE/ 88 Stl, 111–121.Google Scholar
  53. 53.
    Weinitschke, H.J. /1965/: On Asymmetric Buckling of Shallow Spherical Shells. Journ. Math. Phys. 44, 141–163.MathSciNetGoogle Scholar
  54. 54.
    Wolmir, A.S. /1956/: Biegsame Platten und Schalen. Verlag für Bauwesen, Berlin, 1962.Google Scholar
  55. Vol’mir, A.S.: G-ibkie plastinki i obolochki. G-ostekhizdat, Moskva.Google Scholar
  56. 55.
    Zoelly, R. /1915/: Über ein Knickproblem an der Kugelschale. Thesis. Zürich.Google Scholar

Copyright information

© Springer, Berlin Heidelberg New York 1982

Authors and Affiliations

  • L. Kollár
    • 1
  1. 1.BudapestHungary

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