Advertisement

Bending of Circular Cylindrical Shells

  • Wilhelm Flügge

Abstract

In the preceding Chapters dealing with the membrane theory of shells, we often met questions which this theory could not answer. This indicates that in certain cases the bending stiffness of the shell, although small, cannot be disregarded and that it is necessary to develop a bending theory. In such a theory all the stress resultants defined by eqs. (I-l a-j) (pp.5–6) will appear, and, as one may easily imagine, the mathematical analysis of such stress systems is far from simple. Therefore, solutions have been obtained for only a few of the simplest types of shells. They will be presented in this Chapter and the next.

Keywords

Cylindrical Shell Shell Element Stress Resultant Middle Surface Stress System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. W. Flügge: Die Stabilität der Kreiszylinderschale, Ing.-Arch. 3 (1932), 463–506.MATHCrossRefGoogle Scholar
  2. L. H. Donnel: Stability of thin-walled tubes under torsion, NACA, Techn. Rep. 479 (1933).Google Scholar
  3. J. Kearner: Remarks on Donnel’s equations, J. Appl. Mech. 22 (1955), 117–118;Google Scholar
  4. N. J. Hoff: The accuracy of Donnel’s equations, J. Appl. Mech. 22 (1955), 329–334;MATHGoogle Scholar
  5. J. Moe: On the theory of cylindrical shells, explicit solution of the characteristic equation and discussion of the accuracy of various shell theories, Int. Assoc. Bridge Struct. Engg., Publ. 13 (1953), 283–296.Google Scholar
  6. R. Byrne: Theory of small deformations of thin elastic shells, Univ. of Calif. Publ. in Math., n. s. 2 (1944), 103–152;MathSciNetGoogle Scholar
  7. L. S. D. Morley: An improvement on DoNNEL’s approximation for thin-walled circular cylinders, Qu. J. Mech. Appl. Math. 12 (1959), 89–99.MathSciNetMATHCrossRefGoogle Scholar
  8. M. W. Johnson, E. Reissner: On the foundations of the theory of thin elastic shells, J. Math. Phys. 37 (1959), 371–392.MathSciNetMATHGoogle Scholar
  9. H. Parus: Die Grundgleichungen der allgemeinen Zylinderschale, Österr. Ing.-Arch. 6 (1951), 30–35.Google Scholar
  10. W. Flügge, D.A. Conrad: Thermal singularities for cylindrical shells, Proc. 3rd US Nat. Congr. Appl. Mech., Providence, R. I., 1958, pp. 321–328.Google Scholar
  11. H. Reissner: Formänderungen und Spannungen einer dünnwandigen, an den Rändern frei aufliegenden Zylinderschale, Z. angew. Math. Mech. 13 (1933), 133–138;MATHGoogle Scholar
  12. C B Biezeno, J. J. Koch: Some explicit formulae, of use in the calculation of arbitrarily loaded, thin-walled cylinders, Akad. Wetensch. Amsterdam, Proc. 44 (1941), 505–512;MathSciNetGoogle Scholar
  13. N. J. Hoff: Boundary value problems of the thin-walled circular cylinder, J. Appl. Mech. 21 (1954), 343–350.MathSciNetMATHGoogle Scholar
  14. E. Schwerin: Über die Spannungen in freitragenden, gefüllten Rohren, Z. angew. Math. Mech. 2 (1922), 340–353;Google Scholar
  15. K. Miesel: Über die Festigkeit von Kreiszylinderschalen mit nicht-achsensymmetrischer Belastung, Ing.-Arch. 1 (1930), 22–71.MATHCrossRefGoogle Scholar
  16. E. Gruber: Die Berechnung zylindrischer, biegungssteifer Schalen unter beliebigem Lastangriff. Int. Assoc. Bridge Struct. Engg., Publ. 2 (1934), 196–204;Google Scholar
  17. H. Wagner, H. Simon: Über die Krafteinleitung in dünnwandige Zylinderschalen, Luftf.-Forschg. 13 (1936), 293–308.Google Scholar
  18. G. Kirchhoff: Über das Gleichgewicht und die Bewegungen einer elastischen Scheibe, J. reine angew. Math. 40 (1850), 51–88.MATHCrossRefGoogle Scholar
  19. A. B. Bassett: On the extension and flexure of cylindrical and spherical thin elastic shells, Phil. Trans. Roy. Soc. London, A, 181 (1890), 433–480.CrossRefGoogle Scholar
  20. F. Disceinger: Die strenge Berechnung der Kreiszylinderschale in ihrer Anwendung auf die Zeiss-Dywidag-Schalen, Beton u. Eisen 34 (1935), 257–264, 283–294.Google Scholar
  21. A. A. JaObsen: Über das Randstörungsproblem an Kreiszylinderschalen, Bauing. 20 (1939), 394–405Google Scholar
  22. E.-R. Berger: Die Auflösung der charakteristischen Gleichung für Zylinderschalen durch Iteration, Beton u. Stahlbet. 48 (1953), 62–64Google Scholar
  23. U. Finsterwalder: Die Theorie der zylindrischen Schalengewölbe System Zeiss-Dywidag and ihre Anwendung auf die Grossmarkthalle in Budapest, Int. Assoc. Bridge Struct. Engg., Publ. 1 (1932), 127–150Google Scholar
  24. H. Schorer: Line load action in thin cylindrical shells, Proc. Am. Soc. Civ. Eng. 61 (1935), 281–316.Google Scholar
  25. N. J. Hont, J. Kempner, F. V. Pohle: Line load applied along generators of thin-walled circular cylindrical shells of finite length, Qu. Appl. Math. 11 (1954), 411–425;Google Scholar
  26. R. Rabicu: Die Statik der Schalenträger, Bauplanung u. Bautechn. 9 (1955), 115–125, 162–167Google Scholar
  27. W. T. Marshall: A method of determining the secondary stresses in cylindrical shell roofs, J. Inst. Civ. Eng. 33 (1949), 126–140Google Scholar
  28. L. Issennrann F LarskiCalcul des voiles minces en béton armé, Paris 1935; R. S. Jenxins. Theory and Design of Cylindrical Shell Structures (Modern Building Techniques, Bull. 1), London 1947;Google Scholar
  29. H. Lundgren: Cylindrical Shells, vol. 1: Cylindrical Roofs, Copenhagen 1951;Google Scholar
  30. A. R. Spiinato: Teoria y cälculo de las bóvedas cascaras cilfndricas, Buenos Aires 1953;Google Scholar
  31. J. E. Gibson, D. W. Cooper: The Design of Cylindrical Shell Roofs, New York 1954; and a book: Design of Cylindrical Concrete Shell Roofs, New York 1952Google Scholar
  32. A. Galli: Sul calcolo delle dighe a semplice curvatura, Energ. Elettr. 19 (1942), 405–412.Google Scholar
  33. A. A. Jakobsen: Zylinderschalen mit veränderlichem Krümmungshalbmesser and veränderlicher Schalenstärke, Bauing. 18 (1937), 418–422, 436–444.Google Scholar
  34. H. Reissner: Über die Spannungsverteilung in zylindrischen Behälterwänden, Beton u. Eisen 7 (1908), 150–155. THOMSON functions were used by E. MFissNER: Beanspruchung and Formänderung zylindrischer Gefäße mit linear veränderlicherGoogle Scholar
  35. Wandstärke, Vj.-Schr. Naturf. Ges. Zürich 62 (1917), 153–168; see also the author’s earlier book, 2nd ed., p. 169, andGoogle Scholar
  36. M. Hetényi: Beams on Elastic Foundation, Ann. Arbor 1946, pp. 114–119.Google Scholar
  37. A. Cattin: Serbatoio cilindrico a sezione meridiana di spessore variabile, Ric. Ing. 7 (1939), 80–87.Google Scholar
  38. K. Federhofer: Berechnung der kreiszylindrischen Flüssigkeitsbehälter mit quadratisch veränderlicher Wandstärke, Österr. Ing.-Arch. 6 (1951), 43–64.MathSciNetMATHGoogle Scholar
  39. K. Federhofer: Spannungen in schwach ausgebauchten Behältern, Österr. Bau-Z. 6 (1951), 149–153;MathSciNetGoogle Scholar
  40. R. A. Clark, E. Reissner: On axially symmetric bending of nearly cylindrical shells of revolution, J. Appl. Mech. 21 (1956), 59–67.MathSciNetGoogle Scholar
  41. B. R. Baker: A large-deformation bending theory for thin cylindrical shells, Diss. Stanford 1959.Google Scholar
  42. D. C. Drucker: Limit analysis of cylindrical shells under axially-symmetric loading, Proc. 1st Midwest. Conf. Solid Mech., Urbana 1953, pp. 158–163;Google Scholar
  43. E. T. Onat: The plastic collapse of cylindrical shells under axially symmetric loading, Qu. Appl. Math. 13 (1955), 63–72;MathSciNetMATHGoogle Scholar
  44. P. G. Hodge: The rigid-plastic analysis of symmetrically loaded cylindrical shells, J. Appl. Mech. 21 (1954), 336–342;MathSciNetMATHGoogle Scholar
  45. E. T. Onat, W. Prager: Limits of economy of material in shells, De Ingenieur 67, 0 (1955), 46–49;Google Scholar
  46. W. Freiberger: Minimum weight design of cylindrical shells, J. Appl. Mech. 23 (1956) 576–580;MathSciNetMATHGoogle Scholar
  47. P. G. Hodge, S. V. Nardo: Carrying capacity of an elastic-plastic cylindrical shell with linear strain hardening, J. Appl. Mech. 25 (1958), 79–85.MATHGoogle Scholar
  48. P. G. Hodge: Plastic Analysis of Structures, New York 1959, pp. 270–309.Google Scholar
  49. W. Flügge: Ing.-Arch. 3 (see section 5.1). They have been applied to barrel vaults by F. Discringer, Beton u. Eisen 34 (see section 5. 4 ).Google Scholar
  50. H. Wagner, H. Simon, Luftf.-Forschg. 13 (see section 5.2); W. SCHNELL: Krafteinleitung in versteifte Kreiszylinderschalen, Z. Flugwiss. 3 (1955), 385–399.Google Scholar
  51. J. Born: Faltwerke, Stuttgart 1954; and D. Yitzhaki: The Design of Prismatic and Cylindrical Shell Roofs, Haifa 1958; and in the following papers: G. GRÜNING: Die Nebenspannungen in prismatischen Faltwerken, Ing.-Arch. 3 (1932), 319–337;CrossRefGoogle Scholar
  52. E. Gruber: Berechnung prismatischer Scheibenwerke, Int. Assoc. Bridge Struct. Engg., Publ. 1 (1932), 225–246;Google Scholar
  53. E. Gru-Ber: Die BerechnungäusserlichstatischunbestimmterprismatischerScheibenwerke, Int. Assoc. Bridge Struct. Engg., Publ. 3 (1935), 134–158;Google Scholar
  54. R. H Mg.: Beitrag zur Theorie der prismatischen Faltwerke, Ing.-Arch. 6 (1935), 346–354; R. OHM: Mehrfache prismatische Faltwerke, Ing.-Arch. 12 (1941), 254–258.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1960

Authors and Affiliations

  • Wilhelm Flügge
    • 1
  1. 1.Stanford UniversityLos AltosUSA

Personalised recommendations