##
**Buckling behaviour of elliptical cylindrical shells and tubes under compression.**
*(English)*
Zbl 1169.74408

Summary: This paper presents several issues that characterize the buckling behaviour of elliptical cylindrical shells and tubes under compression. First, a formulation of Generalised Beam Theory (GBT) developed to analyse the elastic buckling behaviour of non-circular hollow section (NCHS) members is presented. Since the radius varies along the cross-section mid-line, the main concepts involved in the determination of the deformation modes are adapted to account for the specific aspects related to elliptical cross-section geometry. After that, two independent sets of fully orthogonal deformation modes are determined: (i) local-shell modes satisfying the null membrane shear strain but exhibiting transverse extension and (ii) shell-type modes satisfying both assumptions of null membrane shear strain and null transverse extension. In order to illustrate the application, capabilities and versatility of the formulation, the local and global buckling behaviour of elliptical hollow section (EHS) members subjected to compression is analysed. In particular, in-depth studies concerning the influence of member length on the variation of the critical load and corresponding buckling mode shape are presented. Moreover, the GBT results are compared with estimates obtained by means of shell finite element analyses and are thoroughly discussed. The results show that short to intermediate length cylinders buckle mostly in local-shell modes, exhibiting only transverse extension, while intermediate length to long cylinders buckle mostly in shell-type modes (distortional and global modes), which are characterized by transverse bending and primary warping displacements. It is also shown that the present formulation is very efficient from the computational point of view since only three deformation modes (one local-shell, one distortional and one global) are required to evaluate the buckling behaviour of EHS cylinders for a wide range of lengths.

### Keywords:

non-circular hollow sections (NCHS); elliptical hollow sections (EHS); generalised beam theory (GBT); cylinders; tubes; local buckling; warping; compression
PDF
BibTeX
XML
Cite

\textit{N. Silvestre}, Int. J. Solids Struct. 45, No. 16, 4427--4447 (2008; Zbl 1169.74408)

Full Text:
DOI

### References:

[1] | CEN (Comité Européen de Normalisation), 2006. EN 10210-2: Hot finished structural hollow sections of non-alloy and fine grain steels – Part 2. Tolerances, dimensions, sectional properties. |

[2] | Chan, T. M.; Gardner, L.: Compressive resistance of hot-rolled elliptical hollow sections, Engineering structures 30, No. 2, 522-532 (2008) |

[3] | Donnel, L. H.; Wan, C. C.: Effect of imperfections on the buckling of thin cylinders and columns under axial compression, Journal of applied mechanics (ASME) 17, No. 1, 73-83 (1950) · Zbl 0039.20203 |

[4] | Donnell, L. H.: A new theory for the buckling of thin cylinders under axial compression and bending, Transactions of ASME 56, 795-806 (1934) |

[5] | Donnell, L. H.: Beams, plates and shells. Engineering societies monographs, (1976) · Zbl 0375.73053 |

[6] | Feinstein, G.; Chen, Y. N.; Kempner, J.: Buckling of clamped oval cylindrical shells under axial loads, AIAA journal 9, No. 9, 1733-1738 (1971) |

[7] | Feinstein, G.; Erickson, B.; Kempner, J.: Stability of oval cylindrical shells, Journal of experimental mechanics 11, No. 11, 514-520 (1971) |

[8] | Gardner, L.: Structural behaviour of oval hollow sections, International journal of advanced steel construction 1, No. 2, 26-50 (2005) |

[9] | Hutchinson, J. W.: Buckling and initial postbuckling behaviour of oval cylindrical shells under axial compression, Journal of applied mechanics (Transactions of ASME) 35, No. 1, 66-72 (1968) |

[10] | Ju, G. T.; Kyriakides, S.: Bifurcation and localization instabilities in cylindrical shells under bending. II. predictions, International journal of solids and structures 29, No. 9, 1143-1171 (1992) |

[11] | Kempner, J.; Chen, Y. N.: Large deflections of an axially compressed oval cylindrical shell, , 299-306 (1964) |

[12] | Kempner, J., Chen, Y.N., 1967. Buckling and postbuckling of an axially compressed oval cylindrical shell. In: Symposium on the Theory of Shells to Honor Lloyd H. Donnell, McCuthan Publishers Co., pp. 141 – 183. |

[13] | Koiter, W.T., 1945. Over der Stabiliteit van het Elastische Evenwicht, Ph.D. Thesis, Delft University, The Netherlands. (English: On the Stability of Elastic Equilibrium, NASA Report TT-F-10833, 1967.) |

[14] | Lorenz, R.: Achsensymmetrische verzerrungen in dünnwandingen hohlzzylindern, Zeitschrift des vereines deutscher ingenieure 52, No. 43, 1706-1713 (1908) |

[15] | Marguerre, K.: Stability of cylindrical shells of variable curvature, Naca tm, 1302 (1951) |

[16] | Meyers, C. A.; Hyer, M. W.: Response of elliptical composite cylinders to axial compression loading, Mechanics of advanced materials and structures 6, No. 2, 169-194 (1996) |

[17] | Sambandama, C. T.; Patel, B. P.; Gupta, S. S.; Munot, C. S.; Ganapathi, M.: Buckling characteristics of cross-ply elliptical cylinders under axial compression, Composite structures 62, No. 1, 7-17 (2003) |

[18] | Sanders, J. L.: Non-linear theories for thin shells, Quarterly journal of applied mathematics 21, No. 1, 21-36 (1963) |

[19] | Sheinman, I.; Firer, M.: Buckling analysis of laminated cylindrical shells with arbitrary non-circular cross-section, AIAA journal 32, No. 5, 648-654 (1994) · Zbl 0796.73022 |

[20] | Silvestre, N.: Generalised beam theory to analyse the buckling behaviour of circular cylindrical shells and tubes, Thin-walled structures 45, No. 2, 185-198 (2007) |

[21] | Silvestre, N.; Camotim, D.: GBT buckling analysis of pultruded FRP lipped channel members, Computers & structures 81, No. 18-19, 1889-1904 (2003) |

[22] | Soldatos, K. P.: Mechanics of cylindrical shells with non-circular cross-section: a survey, Applied mechanics reviews 52, 237-274 (1999) |

[23] | Sun, G.: Buckling and initial post-buckling behaviour of laminated oval cylindrical shells under axial compression, Journal of applied mechanics (Transactions of ASME) 58, 848-851 (1991) |

[24] | Suzuki, K.; Shikanai, G.; Leissa, A. W.: Free vibrations of laminated composite thin non-circular cylindrical shell, Journal of applied mechanics 61, 861-871 (1994) · Zbl 0851.73033 |

[25] | Tennyson, R. C.; Booton, M.; Caswell, R. D.: Buckling of imperfect elliptical cylindrical shells under axial compression, AIAA journal 9, No. 2, 250-255 (1971) |

[26] | Von Karman, T.; Tsien, H. S.: The buckling of thin cylindrical shells under axial compression, Journal of aeronautical science 8, No. 6, 303-312 (1941) · Zbl 0060.42403 |

[27] | WMS (Waterloo Maple Software), 2001. MAPLE V (release 7), University of Waterloo, Canada. |

[28] | Zhu, Y., Wilkinson, T., 2007. Finite element analysis of structural steel elliptical hollow sections in compression. Research Report No. R874, Centre for Advanced Structural Engineering, The University of Sydney. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.