Skip to main content
SpringerLink
Log in

Knockdown factor of buckling load for axially compressed cylindrical shells: state of the art and new perspectives

轴压筒壳屈曲载荷折减因子评估方法的最新进展

  • Invited Review
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

Thin-walled structures are commonly utilized in aerospace and aircraft structures, which are prone to buckling under axial compression and extremely sensitive to geometric imperfections. After decades of efforts, it still remains a challenging issue to accurately predict the lower-bound buckling load due to the impact of geometric imperfections. Up to now, the lower-bound curve in NASA SP-8007 is still widely used as the design criterion of aerospace thin-walled structures, and this series of knockdown factors (KDF) has been proven to be overly conservative with the significant promotion of the manufacturing process. In recent years, several new numerical and experimental methods for determining KDF have been established, which are systematically reviewed in this paper. The Worst Multiple Perturbation Load Approach (WMPLA) is one of the most representative methods to reduce the conservatism of traditional methods in a rational manner. Based on an extensive collection of test data from 1990 to 2020, a new lower-bound curve is approximated to produce a series of improved KDFs. It is evident that these new KDFs have an overall improvement of 0.1–0.3 compared with NASA SP-8007, and the KDF predicted by the WMPLA is very close to the front of the new curve. This may provide some insight into future design guidelines of axially compressed cylindrical shells, which is promising for the lightweight design of large-diameter aerospace structures.

摘要

薄壁筒壳结构作为航空航天的主承力构件, 在轴压载荷下易发生屈曲失稳, 并且对几何缺陷表现为强敏感性. 尽管经过数十年的研究, 精准地预测几何缺陷影响下轴压筒壳的折减因子仍是一个非常具有挑战的科学难题. 直至现在, NASA 20世纪提出航天薄壁轴压筒壳折减因子下限设计准则SP-8007仍被广泛使用, 随着制造工艺的进步和发展, SP-8007已经被证明过于保守. 近年来, 学者们基于数值方法和实验技术发展了一系列折减因子的确定方法, 本文对这些方法进行了全面综述, 其中作者提出的多点最不利扰动载荷法(WMPLA)是最具代表性的方法之一, 其以合理的方式有效地降低了传统折减因子预测方法的保守程度. 另外, 本文还基于搜集的1990∼2020年轴压筒壳屈曲实验数据, 对原始的折减因子下限准则曲线进行了改进. 可以发现, 相比于原始的SP-8007准则, 新折减因子准则曲线整体上提升了0.1∼0.3, 并且使用WMPLA预测的折减因子非常接近于新准则曲线的边界. 本文的研究工作有助于新一代轴压筒壳设计准则的建立, 并可服务于大直径航天运载器主承力薄壁结构的轻量化设计.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Lorenz, Achsensymmetrische verzerrungen in dünnwandigen hohlzylindern (in German), Z. Vereines Dtsch Ingen. 52, 1706 (1908).

    Google Scholar 

  2. S. P. Timoshenko, and J. M. Gere, Theory of Elastic Stability, 2nd ed (Dover Publications, New York, 2009).

    Google Scholar 

  3. L. H. Donnell, and C. C. Wan, Effect of imperfections on buckling of thin cylinders and columns under axial compression, J. Appl. Mech. 17, 73 (1950).

    Article  MATH  Google Scholar 

  4. T. von Kármán, and H. Tsien, The Buckling of Thin Cylindrical Shells under Axial Compression (Elsevier, 2012), pp. 165–181.

  5. W. T. Koiter, On the Stability of Elastic Equilibrium, Vol. 833 (National Aeronautics and Space Administration, 1967).

  6. J. P. Peterson, P. Seide, V. I. Weingarten, J. P. Peterson, P. Seide, and V. I. Weingarten, Buckling of thin-walled circular cylinders, NASA SP-8007 (NASA Special Publication, 1968).

  7. B. O. Almroth, A. B. Burns, and E. V. Pittner, Design criteria for axially loaded cylindrical shells, J. Spacecraft Rockets 7, 714 (1971).

    Article  Google Scholar 

  8. A. Takano, Statistical knockdown factors of buckling anisotropic cylinders under axial compression, J. Appl. Mech. 79, 051004 (2012).

    Article  Google Scholar 

  9. J. M. Rotter, and H. Schmidt, Buckling of Steel Shells: European Design Recommendations (European Convention for Constructional Steelwork (ECCS), 2014).

  10. H. N. R. Wagner, C. Hühne, S. Niemann, K. Tian, B. Wang, and P. Hao, Robust knockdown factors for the design of cylindrical shells under axial compression: analysis and modeling of stiffened and unstiffened cylinders, Thin-Walled Struct. 127, 629 (2018).

    Article  Google Scholar 

  11. H. N. R. Wagner, C. Hühne, and S. Niemann, Robust knockdown factors for the design of axially loaded cylindrical and conical composite shells—development and validation, Compos. Struct. 173, 281 (2017).

    Article  Google Scholar 

  12. Z. R. Tahir, and P. Mandal, Artificial neural network prediction of buckling load of thin cylindrical shells under axial compression, Eng. Struct. 152, 843 (2017).

    Article  Google Scholar 

  13. M. Hilburger, Developing the next generation shell buckling design factors and technologies, in 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference (Honolulu, 2013).

  14. R. Degenhardt, New robust design guideline for imperfection sensitive composite launcher structures—the DESICOS project, in 3rd International Conference on Buckling and Postbuckling Behaviour of Composite Laminated Shell Structures (2015).

  15. B. Wang, P. Hao, K. Du, and K. Tian, Lightweight design theory and method of grid stiffened cylinder shell allowing for imperfection sensitivity (in Chinese), China Basic Sci. 20, 28 (2018).

    Google Scholar 

  16. J. G. Teng, Buckling of thin shells: recent advances and trends, Appl. Mech. Rev. 49, 263 (1996).

    Article  Google Scholar 

  17. J. Arbocz, and J. H. Starnes Jr., Future directions and challenges in shell stability analysis, Thin-Walled Struct. 40, 729 (2002).

    Article  Google Scholar 

  18. H. Schmidt, Stability of steel shell structures, J. Constr. Steel Res. 55, 159 (2000).

    Article  MathSciNet  Google Scholar 

  19. Q. Du, Advance and application for the morden nonlinear stability theory of the thin shell (in Chinese), Struct. Environ. Eng. 29, 41 (2002).

    Google Scholar 

  20. Y. Zhao, and J. Teng, Stability design of axially compressed thin steel cylindrical shells (in Chinese), Eng. Mech. 20, 116 (2003).

    Google Scholar 

  21. B. L. O. Edlund, Buckling of metallic shells: buckling and post-buckling behaviour of isotropic shells, especially cylinders, Struct. Control Health Monit. 14, 693 (2007).

    Article  Google Scholar 

  22. X. Bai, and R. Guo, Main branches of recent elastic stability theory (in Chinese), J. Nav. Univ. Eng. 16, 44 (2004).

    Google Scholar 

  23. P. Qiao, Y. Wang, and L. Lu, Advances in stability study of cylindrical shells (in Chinese), Chin. Q. Mech. 39, 223 (2018).

    Google Scholar 

  24. F. S. Liguori, G. Zucco, A. Madeo, D. Magisano, L. Leonetti, G. Garcea, and P. M. Weaver, Postbuckling optimisation of a variable angle tow composite wingbox using a multi-modal Koiter approach, Thin-Walled Struct. 138, 183 (2019).

    Article  Google Scholar 

  25. A. Madeo, R. M. J. Groh, G. Zucco, P. M. Weaver, G. Zagari, and R. Zinno, Post-buckling analysis of variable-angle tow composite plates using Koiter’s approach and the finite element method, Thin-Walled Struct. 110, 1 (2017).

    Article  Google Scholar 

  26. G. Garcea, F. S. Liguori, L. Leonetti, D. Magisano, and A. Madeo, Accurate and efficient a posteriori account of geometrical imperfections in Koiter finite element analysis, Int. J. Numer. Meth. Engng. 112, 1154 (2017).

    Article  MathSciNet  Google Scholar 

  27. R. J. Mania, A. Madeo, G. Zucco, and T. Kubiak, Imperfection sensitivity of post-buckling of FML channel section column, Thin-Walled Struct. 114, 32 (2017).

    Article  Google Scholar 

  28. F. S. Liguori, A. Madeo, D. Magisano, L. Leonetti, and G. Garcea, Post-buckling optimisation strategy of imperfection sensitive composite shells using Koiter method and Monte Carlo simulation, Compos. Struct. 192, 654 (2018).

    Article  Google Scholar 

  29. K. Liang, M. Ruess, and M. Abdalla, An eigenanalysis-based bifurcation indicator proposed in the framework of a reduced-order modeling technique for non-linear structural analysis, Int. J. Non-Linear Mech. 81, 129 (2016).

    Article  Google Scholar 

  30. K. Liang, C. Yang, and Q. Sun, A smeared stiffener based reduced-order modelling method for buckling analysis of isogrid-stiffened cylinder, Appl. Math. Model. 77, 756 (2020).

    Article  MathSciNet  MATH  Google Scholar 

  31. J. L. Sanders Jr., Nonlinear theories for thin shells, Q. Appl. Math. 21, 21 (1963).

    Article  MathSciNet  Google Scholar 

  32. W. T. Koiter, General equations of elastic stability for thin shells, in Symposium on the Theory of Shells to Honor Lloyd Hamilton Donnett (1967), pp. 187–230.

  33. B. Budiansky, Notes on nonlinear shell theory, J. Appl. Mech. 35, 393 (1968).

    Article  Google Scholar 

  34. M. N. Isabel Figueiredo, Local existence and regularity of the solution of the nonlinear thin shell model of Donnell-Mushtari-Vlasov, Appl. Anal. 36, 221 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  35. C. P. Ellinas, and J. G. A. Croll, Elastic-plastic buckling design of cylindrical shells subject to combined axial compression and pressure loading, Int. J. Solids Struct. 22, 1007 (1986).

    Article  Google Scholar 

  36. S. Yamada, and J. G. A. Croll, Contributions to understanding the behavior of axially compressed cylinders, J. Appl. Mech. 66, 299 (1999).

    Article  Google Scholar 

  37. J. G. A. Croll, and C. P. Ellinas, Reduced stiffness axial load buckling of cylinders, Int. J. Solids Struct. 19, 461 (1983).

    Article  Google Scholar 

  38. E. M. Sosa, L. A. Godoy, and J. G. A. Croll, Computation of lower-bound elastic buckling loads using general-purpose finite element codes, Comput. Struct. 84, 1934 (2006).

    Article  Google Scholar 

  39. S. Yamada, and J. G. A. Croll, Buckling behavior of pressure loaded cylindrical panels, J. Eng. Mech. 115, 327 (1989).

    Google Scholar 

  40. J. G. A. Croll, Towards a rationally based elastic-plastic shell buckling design methodology, Thin-Walled Struct. 23, 67 (1995).

    Article  Google Scholar 

  41. G. M. Zintilis, and J. G. A. Croll, Pressure buckling of end supported shells of revolution, Eng. Struct. 4, 222 (1982).

    Article  Google Scholar 

  42. S. Yamada, and J. G. A. Croll, Buckling and post-buckling characteristics of pressure-loaded cylinders, J. Appl. Mech. 60, 290 (1993).

    Article  MATH  Google Scholar 

  43. J. G. A. Croll, and R. C. Batista, Explicit lower bounds for the buckling of axially loaded cylinders, Int. J. Mech. Sci. 23, 331 (1981).

    Article  MATH  Google Scholar 

  44. X. Ma, P. Hao, F. Wang, and B. Wang, Incomplete reduced stiffness method for imperfection sensitivity of cylindrical shells, Thin-Walled Struct. 157, 107148 (2020).

    Article  Google Scholar 

  45. E. Chater, J. W. Hutchinson, K. W. Neale, Buckle propagation on a beam on a nonlinear elastic foundation, in Collapse: The Buckling of Structures in Theory and Practice, edited by J. M. T. Thompson, and J. W. Hunt (Cambridge University Press, Cambridge, 1983), pp. 31–41.

  46. G. W. Hunt, Reflections and symmetries in space and time, IMA J. Appl. Math. 76, 2 (2011).

    Article  MathSciNet  Google Scholar 

  47. G. W. Hunt, G. J. Lord, and M. A. Peletier, Cylindrical shell buckling: a characterization of localization and periodicity, Discret. Contin. Dyn. Syst.-B 3, 505 (2003).

    MathSciNet  MATH  Google Scholar 

  48. G. W. Hunt, M. A. Peletier, A. R. Champneys, P. D. Woods, M. Ahmer Wadee, C. J. Budd, and G. J. Lord, Cellular buckling in long structures, Nonlinear Dyn. 21, 3 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  49. G. W. Hunt, and E. L. Neto, Maxwell critical loads for axially loaded cylindrical shells, J. Appl. Mech. 60, 702 (1993).

    Article  Google Scholar 

  50. G. W. Hunt, H. M. Bolt, and J. M. T. Thompson, Structural localization phenomena and the dynamical phase-space analogy, Proc. R. Soc. Lond. A 425, 245 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  51. C. J. Budd, G. W. Hunt, and R. Kuske, Asymptotics of cellular buckling close to the Maxwell load, Proc. R. Soc. Lond. A 457, 2935 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  52. J. M. T. Thompson, and J. Sieber, Shock-sensitivity in shell-like structures: with simulations of spherical shell buckling, Int. J. Bifurcat. Chaos 26, 1630003 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  53. J. M. T. Thompson, and G. H. M. van der Heijden, Quantified “shock-sensitivity” above the Maxwell load, Int. J. Bifurcat. Chaos 24, 1430009 (2014).

    Article  MATH  Google Scholar 

  54. J. W. Hutchinson, and J. M. T. Thompson, Imperfections and energy barriers in shell buckling, Int. J. Solids Struct. 148–149, 157 (2018).

    Article  Google Scholar 

  55. J. W. Hutchinson, and J. M. T. Thompson, Nonlinear buckling interaction for spherical shells subject to pressure and probing forces, J. Appl. Mech. 84, 61001 (2017).

    Article  Google Scholar 

  56. W. T. Koiter, The stability of elastic equilibrium. Stab Elastic Equilib (1970).

  57. H. N. R. Wagner, C. Hühne, K. Rohwer, S. Niemann, and M. Wiedemann, Stimulating the realistic worst case buckling scenario of axially compressed unstiffened cylindrical composite shells, Compos. Struct. 160, 1095 (2017).

    Google Scholar 

  58. B. Wang, X. Ma, P. Hao, Y. Sun, K. Tian, G. Li, K. Zhang, L. Jiang, and J. Guo, Improved knockdown factors for composite cylindrical shells with delamination and geometric imperfections, Compos. Part B-Eng. 163, 314 (2019).

    Article  Google Scholar 

  59. Y. Chen, Z. X. Zhu, Y. Q. Li, and T. Tanh, On ultimate bearing capability of sandwich composite cylinders for underwater vehicle under hydrostatic external pressure, J. Nav. Univ. Eng. 2, 83 (2018).

    Google Scholar 

  60. M. W. Hilburger, and J. H. Starnes Jr., Effects of imperfections of the buckling response of composite shells, Thin-Walled Struct. 42, 369 (2004).

    Article  Google Scholar 

  61. B. Wang, K. Du, P. Hao, C. Zhou, K. Tian, S. Xu, Y. Ma, and X. Zhang, Numerically and experimentally predicted knockdown factors for stiffened shells under axial compression, Thin-Walled Struct. 109, 13 (2016).

    Article  Google Scholar 

  62. B. Wang, S. Zhu, P. Hao, X. Bi, K. Du, B. Chen, X. Ma, and Y. J. Chao, Buckling of quasi-perfect cylindrical shell under axial compression: a combined experimental and numerical investigation, Int. J. Solids Struct. 130–131, 232 (2018).

    Article  Google Scholar 

  63. J. Arbocz, The Imperfection Data Bank, a Mean to Obtain Realistic Buckling Loads (Springer, Berlin, Heidelberg, 1982).

    Book  Google Scholar 

  64. Z. Chen, H. Fan, J. Cheng, P. Jiao, F. Xu, and C. Zheng, Buckling of cylindrical shells with measured settlement under axial compression, Thin-Walled Struct. 123, 351 (2018).

    Article  Google Scholar 

  65. J. Arbocz, and H. Abramovich, The initial imperfection data bank at the Delft University of Technology: Part I, Technical Report LR-290 (Delft University of Technology, 1979).

  66. R. Dancy, and D. Jacobs, The initial imperfection data bank at the Delft University of Technology: Part II, Technical Report LR-559 (Delft University of Technology, 1988).

  67. A. W. H. Klompé, and P. C. den Reyer, The initial imperfection data bank at the Delft University of Technology: Part III, Technical Report LR-568 (Delft University of Technology, 1989).

  68. S. G. P. Castro, R. Zimmermann, M. A. Arbelo, R. Khakimova, M. W. Hilburger, and R. Degenhardt, Geometric imperfections and lower-bound methods used to calculate knock-down factors for axially compressed composite cylindrical shells, Thin-Walled Struct. 74, 118 (2014).

    Article  Google Scholar 

  69. D. B. Muggeridge, and R. C. Tennyson, Buckling of axisymmetric imperfect circular cylindrical shells underaxial compression, AIAA J. 7, 2127 (1969).

    Article  Google Scholar 

  70. C. Hühne, R. Rolfes, and J. Tessmer, A new approach for robust design of composite cylindrical shells under axial compression, in Proceedings of the European Conference on Spacecraft Structures, Materials and Mechanical Testing 2005 (ESA SP-581) (Noordwijk, 2015), p. 141.

  71. H. N. R. Wagner, C. Hühne, and S. Niemann, Constant single-buckle imperfection principle to determine a lower bound for the buckling load of unstiffened composite cylinders under axial compression, Compos. Struct. 139, 120 (2016).

    Article  Google Scholar 

  72. M. A. Arbelo, R. Degenhardt, S. G. P. Castro, and R. Zimmermann, Numerical characterization of imperfection sensitive composite structures, Compos. Struct. 108, 295 (2014).

    Article  Google Scholar 

  73. B. Wang, P. Hao, G. Li, Y. Fang, X. Wang, and X. Zhang, Determination of realistic worst imperfection for cylindrical shells using surrogate model, Struct. Multidisc. Optim. 48, 777 (2013).

    Article  Google Scholar 

  74. C. Hühne, R. Rolfes, E. Breitbach, and J. Teßmer, Robust design of composite cylindrical shells under axial compression—simulation and validation, Thin-Walled Struct. 46, 947 (2008).

    Article  Google Scholar 

  75. P. Błażejewski, J. Marcinowski, and M. Rotter, 04.21: Buckling of externally pressurised spherical shells: experimental results compared with recent design recommendations, Ce/Papers 1, 1010 (2017).

    Article  Google Scholar 

  76. R. C. Batista, and J. G. A. Croll, A design approach for unstiffened cylindrical shells under external pressure, in Proceedings of the International Conference on Thin Walled Structures (Glasgow, 1979).

  77. P. Hao, B. Wang, G. Li, Z. Meng, K. Tian, D. Zeng, and X. Tang, Worst multiple perturbation load approach of stiffened shells with and without cutouts for improved knockdown factors, Thin-Walled Struct. 82, 321 (2014).

    Article  Google Scholar 

  78. K. Tian, B. Wang, P. Hao, and A. M. Waas, A high-fidelity approximate model for determining lower-bound buckling loads for stiffened shells, Int. J. Solids Struct. 148–149, 14 (2018).

    Article  Google Scholar 

  79. P. Hao, B. Wang, K. Tian, K. Du, and X. Zhang, Influence of imperfection distributions for cylindrical stiffened shells with weld lands, Thin-Walled Struct. 93, 177 (2015).

    Article  Google Scholar 

  80. P. Hao, B. Wang, K. Du, G. Li, K. Tian, Y. Sun, and Y. Ma, Imperfection-insensitive design of stiffened conical shells based on equivalent multiple perturbation load approach, Compos. Struct. 136, 405 (2016).

    Article  Google Scholar 

  81. B. Wang, K. Du, P. Hao, K. Tian, Y. J. Chao, L. Jiang, S. Xu, and X. Zhang, Experimental validation of cylindrical shells under axial compression for improved knockdown factors, Int. J. Solids Struct. 164, 37 (2019).

    Article  Google Scholar 

  82. H. N. R. Wagner, E. M. Sosa, T. Ludwig, J. G. A. Croll, and C. Hühne, Robust design of imperfection sensitive thin-walled shells under axial compression, bending or external pressure, Int. J. Mech. Sci. 156, 205 (2019).

    Article  Google Scholar 

  83. E. R. Lancaster, C. R. Calladine, and S. C. Palmer, Paradoxical buckling behaviour of a thin cylindrical shell under axial compression, Int. J. Mech. Sci. 42, 843 (2000).

    Article  MATH  Google Scholar 

  84. M. Rastgar, and H. Showkati, Buckling behavior of cylindrical steel tanks with concavity of vertical weld line imperfection, J. Constr. Steel Res. 145, 289 (2018).

    Article  Google Scholar 

  85. D. Zhang, Z. Chen, Y. Li, P. Jiao, H. Ma, P. Ge, and Y. Gu, Lower-bound axial buckling load prediction for isotropic cylindrical shells using probabilistic random perturbation load approach, Thin-Walled Struct. 155, 106925 (2020).

    Article  Google Scholar 

  86. P. Hao, X. Yuan, C. Liu, B. Wang, H. Liu, G. Li, and F. Niu, An integrated framework of exact modeling, isogeometric analysis and optimization for variable-stiffness composite panels, Comput. Methods Appl. Mech. Eng. 339, 205 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  87. P. Hao, D. C. Liu, K. P. Zhang, Y. Yuan, B. Wang, G. Li, and X. Zhang, Intelligent layout design of curvilinearly stiffened panels via deep learning-based method, Mater. Des. 197, 109180 (2021).

    Article  Google Scholar 

  88. P. Hao, Y. T. Wang, R. Ma, H. L. Liu, B. Wang, and G. Li, A new reliability-based design optimization framework using isogeometric analysis, Comput. Methods Appl. Mech. Eng. 345, 476 (2019).

    Article  MathSciNet  MATH  Google Scholar 

  89. G. N. Karam, and L. J. Gibson, Elastic buckling of cylindrical shells with elastic cores—II. Experiments, Int. J. Solids Struct. 32, 1285 (1995).

    Article  MATH  Google Scholar 

  90. E. T. Hambly, and C. R. Calladine, Buckling experiments on damaged cylindrical shells, Int. J. Solids Struct. 33, 3539 (1996).

    Article  Google Scholar 

  91. C. Bisagni, and P. Cordisco, Post-buckling and collapse experiments of stiffened composite cylindrical shells subjected to axial loading and torque, Compos. Struct. 73, 138 (2006).

    Article  Google Scholar 

  92. R. Khakimova, S. G. P. Castro, D. Wilckens, K. Rohwer, and R. Degenhardt, Buckling of axially compressed CFRP cylinders with and without additional lateral load: experimental and numerical investigation, Thin-Walled Struct. 119, 178 (2017).

    Article  Google Scholar 

  93. G. Totaro, and F. De Nicola, Recent advance on design and manufacturing of composite anisogrid structures for space launchers, Acta Astronaut. 81, 570 (2012).

    Article  Google Scholar 

  94. H. Fan, D. Fang, L. Chen, Z. Dai, and W. Yang, Manufacturing and testing of a CFRC sandwich cylinder with Kagome cores, Compos. Sci. Tech. 69, 2695 (2009).

    Article  Google Scholar 

  95. L. Chen, H. Fan, F. Sun, L. Zhao, and D. Fang, Improved manufacturing method and mechanical performances of carbon fiber reinforced lattice-core sandwich cylinder, Thin-Walled Struct. 68, 75 (2013).

    Article  Google Scholar 

  96. W. Li, F. Sun, P. Wang, H. Fan, and D. Fang, A novel carbon fiber reinforced lattice truss sandwich cylinder: fabrication and experiments, Compos. Part A-Appl. Sci. Manuf. 81, 313 (2016).

    Article  Google Scholar 

  97. M. Li, F. Sun, C. Lai, H. Fan, B. Ji, X. Zhang, D. Liu, and D. Fang, Fabrication and testing of composite hierarchical isogrid stiffened cylinder, Compos. Sci. Tech. 157, 152 (2018).

    Article  Google Scholar 

  98. W. Li, Q. Zheng, H. Fan, and B. Ji, Fabrication and mechanical testing of ultralight folded lattice-core sandwich cylinders, Engineering 6, 196 (2020).

    Article  Google Scholar 

  99. M. Rouhi, H. Ghayoor, J. Fortin-Simpson, T. T. Zacchia, S. V. Hoa, and M. Hojjati, Design, manufacturing, and testing of a variable stiffness composite cylinder, Compos. Struct. 184, 146 (2018).

    Article  Google Scholar 

  100. P. Jiao, Z. Chen, H. Ma, P. Ge, Y. Gu, and H. Miao, Buckling behaviors of thin-walled cylindrical shells under localized axial compression loads, Part 1: experimental study, Thin-Walled Struct. 166, 108118 (2021).

    Article  Google Scholar 

  101. P. Jiao, Z. Chen, H. Ma, P. Ge, Y. Gu, and H. Miao, Buckling behaviors of thin-walled cylindrical shells under localized axial compression loads, Part 2: numerical study, Thin-Walled Struct. 169, 108330 (2021).

    Article  Google Scholar 

  102. M. W. Hilburger, M. C. Lindell, W. A. Waters, and N. W. Gardner, Test and analysis of buckling-critical stiffened metallic launch vehicle cylinders, in 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (Kissimmee, 2018).

  103. M. T. Rudd, M. W. Hilburger, A. E. Lovejoy, M. C. Lindell, N. W. Gardner, and M. R. Schultz, Buckling response of a large-scale, seamless, orthogrid-stiffened metallic cylinder, in 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (Kissimmee, 2018).

  104. A. Przekop, M. R. Schultz, and M. W. Hilburger, Design of buckling-critical large-scale sandwich composite cylinder test articles, in 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (Kissimmee, 2018).

  105. J. M. T. Thompson, J. W. Hutchinson, and J. Sieber, Probing shells against buckling: a nondestructive technique for laboratory testing, Int. J. Bifurcat. Chaos 27, 1730048 (2017).

    Article  Google Scholar 

  106. F. Franzoni, F. Odermann, E. Lanbans, C. Bisagni, M. Andrés Arbelo, and R. Degenhardt, Experimental validation of the vibration correlation technique robustness to predict buckling of unstiffened composite cylindrical shells, Compos. Struct. 224, 111107 (2019).

    Article  Google Scholar 

  107. L. A. Harris, H. S. Suer, W. T. Skene, and R. J. Benjamin, The stability of thin-walled unstiffened circular cylinders under axial compression including the effects of internal pressure, J. Aeronaut. Sci. 24, 587 (1957).

    Article  Google Scholar 

  108. O. G. S. Ricardo, An experimental investigation of the radial displacements of a thin-walled cylinder, Technical Report, NASA-CR-934 (National Aeronautics and Space Administration, 1967).

  109. R. D. Caswell, D. B. Muggeridge, and R. C. Tennyson, Buckling of circular cylindrical shells having axisymmetric imperfection distributions, AIAA J. 9, 924 (1971).

    Article  Google Scholar 

  110. J. W. Hutchinson, D. B. Muggeridge, and R. C. Tennyson, Effect of a local axisymmetric imperfection on the buckling behavior of a circular cylindrical shell under axial compression, AIAA J. 9, 48 (1971).

    Article  Google Scholar 

  111. R. L. Carri, Buckling behavior of composite cylinders subjected to compressive loading, Technical Report, NASA-CR-132264 (National Aeronautics and Space Administration, 1973).

  112. D. J. Wilkins, and T. S. Love, Combined compression-torsion buckling tests of laminated composite cylindrical shells, J. Aircraft 12, 885 (1975).

    Article  Google Scholar 

  113. C. T. Herakovich, Theoretical-experimental correlation for buckling of composite cylinders under combined compression and torsion, NASA-CR-157358 (National Aeronautics and Space Administration, 1978).

  114. M. Uemura, and H. Kasuya, Coupling effect on axial compressive buckling of laminated composite cylindrical shells, Prog. Sci. Eng. Compos., 583 (1982).

  115. Y. Hirano, Optimization of laminated composite cylindrical shells for axial buckling, Jpn. Soc. Aeronaut. Space Sci. Trans. 26, 154 (1983).

    Google Scholar 

  116. R. C. Tennyson, and J. S. Hansen, Optimum design for buckling of laminated cylinders, in Collapse: The Buckling of Structures in Theory and Practice, edited by J. M. T. Thompson, and J. W. Hunt (Cambridge University Press, Cambridge, 1983).

    Google Scholar 

  117. S. Kobayashi, H. Seko, and K. Koyama, Compressive buckling of CFRP circular cylindrical shells. I—Theoretical analysis and experiment, J. Jpn. Soc. Aeronaut. Space Sci. 32, 111 (1984).

    Google Scholar 

  118. C. G. Foster, Axial compression buckling of conical and cylindrical shells, Exp. Mech. 27, 255 (1987).

    Article  Google Scholar 

  119. G. Sun, Optimization of laminated cylinders for buckling (University of Toronto, 1987).

  120. B. Geier, H. Klein, and R. Zimmermann, Buckling tests with axially compressed unstiffened cylindrical shells made from CFRP (DLR, 1991).

  121. V. Giavotto, C. Poggi, M. Chryssanthopoulos, and P. Dowling, Buckling behaviour of composite shells under combined loading, in Buckling of Shell Structures, on Land, in the Sea and in the Air, edited by J. F. Jullien (CRC Press, Boca Raton, 1991), pp. 53–60.

  122. S. Krishnakumar, and C. G. Foster, Axial load capacity of cylindrical shells with local geometric defects, Exp. Mech. 31, 104 (1991).

    Article  Google Scholar 

  123. W. A. Waters, Effects of initial geometric imperfections on the behavior of graphite-epoxy cylinders loaded in compression (1996).

  124. M. H. Schneider Jr., Investigation of the stability of imperfect cylinders using structural models, Eng. Struct. 18, 792 (1996).

    Article  Google Scholar 

  125. C. Bisagni, Experimental buckling of thin composite cylinders in compression, AIAA J. 37, 276 (1999).

    Article  Google Scholar 

  126. T. D. Kim, Fabrication and testing of composite isogrid stiffened cylinder, Compos. Struct. 45, 1 (1999).

    Article  Google Scholar 

  127. H. R. Meyer-Piening, M. Farshad, B. Geier, and R. Zimmermann, Buckling loads of CFRP composite cylinders under combined axial and torsion loading—experiments and computations, Compos. Struct. 53, 427 (2001).

    Article  Google Scholar 

  128. C. Bisagni, and P. Cordisco, An experimental investigation into the buckling and post-buckling of CFRP shells under combined axial and torsion loading, Compos. Struct. 60, 391 (2003).

    Article  Google Scholar 

  129. M. W. Hilburger, M. P. Nemeth, and J. H. Starnes Jr., Shell buckling design criteria based on manufacturing imperfection signatures, AIAA J. 44, 654 (2006).

    Article  Google Scholar 

  130. M. W. Hilburger, W. A. Waters Jr., W. T. Haynie, Buckling test results from the 8-foot-diameter orthogrid-stiffened cylinder test article TA01 (Test Dates: 19–21 November 2008), Technical Report, NASA/TP-2015-218785 (National Aeronautics and Space Administration, 2015).

  131. R. Degenhardt, A. Kling, A. Bethge, J. Orf, L. Kärger, R. Zimmermann, K. Rohwer, and A. Calvi, Investigations on imperfection sensitivity and deduction of improved knock-down factors for unstiffened CFRP cylindrical shells, Compos. Struct. 92, 1939 (2010).

    Article  Google Scholar 

  132. W. T. Haynie, M. W. Hilburger, M. Bogge, and B. Kriegesmann, Validation of lower-bound estimates for compression-loaded cylindrical shells, in 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference (Honolulu, 2012).

  133. R. S. Priyadarsini, V. Kalyanaraman, and S. M. Srinivasan, Numerical and experimental study of buckling of advanced fiber composite cylinders under axial compression, Int. J. Str. Stab. Dyn. 12, 1250028 (2012).

    Article  MATH  Google Scholar 

  134. C. Bisagni, Composite cylindrical shells under static and dynamic axial loading: an experimental campaign, Prog. Aerosp. Sci. 78, 107 (2015).

    Article  Google Scholar 

  135. C. Schillo, D. Röstermundt, and D. Krause, Experimental and numerical study on the influence of imperfections on the buckling load of unstiffened CFRP shells, Compos. Struct. 131, 128 (2015).

    Article  Google Scholar 

  136. K. Kalnins, M. Arbelo, O. Ozolins, S. Castro, and R. Degenhard, Numerical characterization of the knock-down factor on unstiffened cylindrical shells with initial geometric imperfections, in ICCM International Conferences on Composite Materials (2015).

  137. A. Takano, Buckling experiment on anisotropic long and short cylinders, Adv. Technol. Innov. 1, 25 (2016).

    Google Scholar 

  138. H. Wu, C. Lai, F. Sun, M. Li, B. Ji, W. Wei, D. Liu, X. Zhang, and H. Fan, Carbon fiber reinforced hierarchical orthogrid stiffened cylinder: fabrication and testing, Acta Astronaut. 145, 268 (2018).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Key Laboratory of Digital Twin for Industrial Equipment, Liaoning Province, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116023, China

    Bo Wang  (王博), Peng Hao  (郝鹏), Xiangtao Ma  (马祥涛) & Kuo Tian  (田阔)

Authors
  1. Bo Wang  (王博)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peng Hao  (郝鹏)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiangtao Ma  (马祥涛)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kuo Tian  (田阔)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bo Wang  (王博).

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. U21A20429, 11772078, and 11825202), and the National Defense Basic Research Program (Grant No. JCKY2020110).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, B., Hao, P., Ma, X. et al. Knockdown factor of buckling load for axially compressed cylindrical shells: state of the art and new perspectives. Acta Mech. Sin. 38, 421440 (2022). https://doi.org/10.1007/s10409-021-09035-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10409-021-09035-x

Keywords

Search

Navigation