Stability and load-bearing capacity of smooth and ribbed shells with local dents

Abstract

A method for analysis of the stability and load-bearing capacity of imperfect smooth and ribbed shells is developed. This method is based on the finite-difference method and is implemented as an algorithm for fast calculation of critical forces, as opposed to the finite-element method. The theoretical results discussed include both early and recent results. The emphasis is on shells with local dents. The numerical results are successively corrected and compared with available experimental data for shells with a single dent and with other data. The method enables us to discover new features in the behavior of thin-walled structures under loading: development of precritical state, change in the dent shape, and exhaustion of load-bearing capacity. The lower local critical loads and upper stresses are determined. They correspond to general buckling and agree well with available experimental data.

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REFERENCES

  1. 1.

    I. Ya. Amiro (1960) ArticleTitleStability analysis of a ribbed cylindrical shell under longitudinal compression Prikl. Mekh. 6 IssueID3 272–281

    Google Scholar 

  2. 2.

    I. Ya. Amiro (1963) ArticleTitleStability of thin cylindrical shells, revisited Prikl. Mekh. 9 IssueID3 264–269

    Google Scholar 

  3. 3.

    I. Ya. Amiro (1966) ArticleTitleInfluence of initial deflections on the stability of ribbed cylindrical shells under axial compression Prikl. Mekh. 2 IssueID1 53–58

    Google Scholar 

  4. 4.

    I. Ya. Amiro P. S. Polyakov V. G. Palamarchuk (1971) ArticleTitleStability of imperfect cylindrical shells Prikl. Mekh. 7 IssueID8 9–15

    Google Scholar 

  5. 5.

    I. Ya. Amiro, V. A. Zarutskii, and P. S. Polyakov, Ribbed Cylindrical Shells[in Russian] Naukova Dumka, Kiev (1987).

  6. 6.

    J. Arbocz (1983) Shell stability analysis in theory and practice J. M. T. Thompson G. W. Hunt (Eds) Collapse: The Buckling of Structures in Theory and Practice Cambridge University Press Cambridge 43–74

    Google Scholar 

  7. 7.

    J. Arbocz C. D. Babcock (1969) ArticleTitleThe effect of general imperfections on the buckling of cylindrical shells J. Appl. Mech. 36 IssueID1 28–38

    Google Scholar 

  8. 8.

    V. A. Voblykh (1965) ArticleTitleInfluence of initial deviations on the critical load for circular cylindrical shells Prikl. Mekh. 1 IssueID3 17–26

    Google Scholar 

  9. 9.

    A. S. Vol’mir (1967) Stability of Deformable Systems Nauka Moscow

    Google Scholar 

  10. 10.

    G. D. Gavrilenko, “Stability of imperfect cylindrical shells,” Dokl. AN USSR, Ser. A, No. 7, 523–528 (1979).

  11. 11.

    G. D. Gavrilenko (1979) ArticleTitleStudying inhomogeneous nonlinear problems in the theory of ribbed shells Prikl. Mekh. 15 IssueID9 25–31

    Google Scholar 

  12. 12.

    G. D. Gavrilenko (1980) ArticleTitleStability of stringer shells in a nonuniform stress-strain state Prikl. Mekh. 16 IssueID11 41–46

    Google Scholar 

  13. 13.

    G. D. Gavrilenko (1981) Stability of imperfect ribbed cylindrical shells in linear and nonlinear subcritical states Stability of Plates and Shells Izd. Saratov. Univ. Saratov 20–22

    Google Scholar 

  14. 14.

    G. D. Gavrilenko A. S. Sytnik (1981) ArticleTitleStudying the upper critical loads of partial buckling modes for stringer cylindrical shells Prikl. Mekh. 17 IssueID3 68–73

    Google Scholar 

  15. 15.

    G. D. Gavrilenko (1982) ArticleTitleStudying the influence of local and regular axisymmetric deflections on the critical loads of ribbed shells Prikl. Mekh. 18 IssueID4 53–57

    Google Scholar 

  16. 16.

    G. D. Gavrilenko (1983) ArticleTitleBasic nonlinear and linearized equations of the theory of imperfect ribbed shells of revolution Prikl. Mekh. 19 IssueID7 55–60

    Google Scholar 

  17. 17.

    G. D. Gavrilenko I. F. Dudnik I. F. Larionov (1984) ArticleTitleStability of ribbed cylindrical shells with nonaxisymmetric dents Prikl. Mekh. 20 IssueID2 25–31

    Google Scholar 

  18. 18.

    G. D. Gavrilenko A. S. Sytnik (1985) ArticleTitleStability of ribbed shells with local dents Prikl. Mekh. 21 IssueID11 128–130

    Google Scholar 

  19. 19.

    G. D. Gavrilenko (1986) ArticleTitleInfluence of geometric imperfections and stiffness characteristics of ribs on the stability of conic shells Prikl. Mekh. 22 IssueID11 59–64

    Google Scholar 

  20. 20.

    G. D. Gavrilenko (1989) Stability of Ribbed Cylindrical Shells in a Nonuniform Stress—Strain State Naukova Dumka Kiev

    Google Scholar 

  21. 21.

    G. D. Gavrilenko (1999) Stability of Imperfect Ribbed Shells Inst. Mat. NAN Ukrainy Kiev

    Google Scholar 

  22. 22.

    G. D. Gavrilenko, “Stability of shells with initial deflections of variable amplitude,” Dokl. AN Ukraine, No. 5, 46–51 (2004).

  23. 23.

    G. D. Gavrilenko and V. L. Krasovskii, “Stability of circular cylindrical shells with a single dent,” Probl. Prochn., No. 3, 52–64 (2004).

    Google Scholar 

  24. 24.

    G. D. Gavrilenko A. S. Pal’chevskii Yu. E. Yakubovskii (1985) ArticleTitleDetermining the critical loads of imperfect models of shells Prikl. Mekh. 21 IssueID6 68–72

    Google Scholar 

  25. 25.

    G. D. Gavrilenko, V. I. Matsner, and A. S. Sytnik, “Stability of nearly cylindrical shells,” Probl. Prochn., No. 3, 30–44 (2003).

    Google Scholar 

  26. 26.

    É. I. Grigolyuk V. V. Kabanov (1978) Stability of Shells Nauka Moscow

    Google Scholar 

  27. 27.

    V. Z. Grishchak (1980) Asymptotic formula for critical stresses in axially compressed cylindrical shells with local imperfections Strength and Life of Structures Naukova Dumka Kiev 113–120

    Google Scholar 

  28. 28.

    A. N. Guz (1984) ArticleTitleStability of elastic bodies under finite strains Prikl. Mekh. 20 IssueID1 3–13

    Google Scholar 

  29. 29.

    A. N. Guz (1986) Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies Vyshcha Shkola Kiev

    Google Scholar 

  30. 30.

    V. I. Konokh V. L. Krasovskii (1973) ArticleTitleInfluence of an isolated local dent on the stability of smooth thin-walled cylinders under longitudinal compression Sopr. Mater. Teor. Sooruzh. 21 114–121

    Google Scholar 

  31. 31.

    V. L. Krasovskii, “Behavior and stability of compressed thin-walled cylinders with local geometric imperfections,” in: Proc. 15th All-Union Conf. on the Theory of Shells and Plates[in Russian] Kazan (1990), pp. 303–308.

  32. 32.

    V. L. Krasovskii, “Bulging of cylindrical shells under homogeneous longitudinal compression,” Visn. Akad. Nauk. Inform. Byul. (Pridneprovskaya State Academy of Civil Engineering and Architecture (Dnepropetrovsk)), No. 7, 25–31 (1998).

  33. 33.

    V. L. Krasovskii (2002) ArticleTitleQuality of thin-walled cylinders and mechanisms triggering their bulging under longitudinal compression Polish-Ukrainian Trans. on Theoretical Foundations of Civil Engineering 2 696–715

    Google Scholar 

  34. 34.

    V. G. Kuznetsov and Yu. V. Lipovtsev, “Influence of local imperfections on the stability of a cylindrical shell under axial compression,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 1, 134–136 (1970).

  35. 35.

    Kh. M. Mushtari K. Z. Galimov (1957) Nonlinear Theory of Elastic Shells Tatknigoizdat Kazan

    Google Scholar 

  36. 36.

    “Statistical estimation of the influence of random perturbations on the stability of ribbed shells from experimental data,” in: D. E. Lipovskii, G. M. Altukher, V. M. Kots et al., Design of Spatial Structures[in Russian] Stroiizdat, Moscow (1977), pp. 32–44.

  37. 37.

    V. I. Étokov (1977) ArticleTitleInfluence of reinforcements on the stability of an imperfect cylindrical shell Prikl. Mekh. 13 IssueID1 54–60

    Google Scholar 

  38. 38.

    V. I. Étokov (1979) ArticleTitleStability analysis of imperfect ribbed cylindrical shells Prikl. Mekh. 15 IssueID12 70–76

    Google Scholar 

  39. 39.

    G. Fischer (1963) ArticleTitleÜber den Einfluss der gelenkigen Lagerung auf die Stabilität dünnwandiger Kreiszylinderschalen under Axiallast und Innendruck Z. Flugwiss 11 IssueID3 111–119

    Google Scholar 

  40. 40.

    G. D. Gavrilenko (2000) ArticleTitleStability and load-carrying capacity of incomplete shells Int. Appl. Mech. 36 IssueID7 866–887

    Google Scholar 

  41. 41.

    G. D. Gavrilenko (2002) ArticleTitleStability of cylindrical shells with local imperfections Int. Appl. Mech. 38 IssueID12 1496–1500

    Google Scholar 

  42. 42.

    G. D. Gavrilenko (2003) ArticleTitleNumerical and analytical approaches to the stability analysis of imperfect shells Int. Appl. Mech. 39 IssueID9 1029–1045

    Google Scholar 

  43. 43.

    G. D. Gavrilenko (2003) ArticleTitleStability and load-carrying capacity of ribbed shells with imperfections of form Archives of Civil Engineering, XLIX 3 255–264

    Google Scholar 

  44. 44.

    G. D. Gavrilenko V. I. Matsner A. S. Sytnik (1999) ArticleTitleStability of ribbed cylindrical shells with a nonideal shape Int. Appl. Mech. 35 IssueID12 1222–1228

    Google Scholar 

  45. 45.

    G. D. Gavrilenko V. I. Matsner A. S. Sytnik (2000) ArticleTitleMinimum critical loads of ribbed shells with given initial deflections Int. Appl. Mech. 36 IssueID11 1482–1486

    Google Scholar 

  46. 46.

    G. D. Gavrilenko V. I. Matsner (2002) ArticleTitleStability and load-carrying capacity of cylindrical shells with axisymmetric dents Int. Appl. Mech. 38 IssueID7 861–871

    Google Scholar 

  47. 47.

    L. H. Donnell (1934) ArticleTitleA new theory for buckling of thin cylinders under axial compression and bending Trans. ASME 56 795–806

    Google Scholar 

  48. 48.

    A. N. Guz (2001) ArticleTitleConstructing the three-dimensional theory of stability of deformable bodies Int. Appl. Mech. 37 IssueID1 1–37

    Google Scholar 

  49. 49.

    W. T. Koiter (1963) ArticleTitleThe effect of axisymmetric imperfections on the buckling of cylindrical shells under axial compression Proc. Koninkl. Nederl. Akad. van Wetensch. 66 IssueID5 265–279

    Google Scholar 

  50. 50.

    I. I. Vorovich L. P. Lebedev (2002) ArticleTitleSome issues of continuum mechanics and mathematical problems in the theory of thin-walled structures Int. Appl. Mech. 38 IssueID4 387–398

    Google Scholar 

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Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 35–64, September 2004.

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Gavrilenko, G.D. Stability and load-bearing capacity of smooth and ribbed shells with local dents. Int Appl Mech 40, 970–993 (2004). https://doi.org/10.1007/s10778-005-0002-y

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Keywords

  • cylindrical and conical shells
  • local dent
  • nonlinear theory
  • experiment
  • specimen
  • stability
  • load-bearing capacity