Knockdown factors for cylindrical shells caused by torsional Mode-I type geometric imperfections under axial compression

Year 2021, , 419 - 425, 15.12.2021

İbrahim Kocabaş , Haluk Yılmaz

https://doi.org/10.35860/iarej.891791

Abstract

Geometrical imperfection, which is generally a result of manufacturing process and service conditions, plays a crucial role in load-bearing capacity of shell structures. This study presents a numerical study on knockdown factors of cylindrical shells as a result of torsional Mode-I type of geometric imperfections under compressive loads. The deformation patterns obtained from liner bifurcation analysis (LBA) for torsional Mode-I shape are used as a source of geometric imperfection. Then, geometrically nonlinear buckling analysis with imperfect model (GNIA) is incorporated with LBA in ANSYS Workbench to obtain limit loads of imperfect structures. A parametric study is thus performed to investigate the influence of imperfection depth on the load-bearing capacity considering a wide range of cylindrical shell configurations. Local and global buckling characteristics of the imperfect shells are examined and knockdown factors are characterized by three distinct regions as a basis of normalized imperfection depth. For a large number of shell configurations, a scattering of knockdown factors against normalized imperfection depth is given with mathematical expressions evolving lower and upper bounds. These expressions provide the minimum and maximum values of knockdown factors for a given imperfection depth, which can be treated as a design tool to ensure safety of the shell structure.

Keywords

Axial compression, Cylindrical shell, Finite element method, Geometric imperfection, Knockdown factor

References

• 1. Buckling of Steel Shells Europen Design Recommendations, ECCS, 2008. ISBN: 978-92-9147-116-4.
• 2. de Paor, C., K. Cronin, J.P. Gleeson and D. Kelliher, Statistical characterisation and modelling of random geometric imperfections in cylindrical shells, Thin-Walled Structures, 2012. 58: p. 9-17.
• 3. Kepple, J., M. Herath, G. Pearce, G. Prusty, R. Thomson, and R. Degenhardt, Improved stochastic methods for modelling imperfections for buckling analysis of composite cylindrical shells, Engineering Structures, 2015. 100: p. 385-398.
• 4. Donnell, L.H., A new theory for the buckling of thin cylinders under axial compression and bending, ASME Transactions of the American Society of Mechanical Engineers, 1934. 56(12): p. 795-806.
• 5. Flügge, W., Die stabilität der kreiszylinderschale, Ingenieur-Archiv, 1932. 3: p. 463-506.
• 6. Koiter, W.T., A translation of the stability of elastic equilibrium. 1970, USA: Stanford University, Department of Aeronautics & Astronautics.
• 7. Teng, J.G., X. Lin, J.M. Rotter, and X.L. Ding, Analysis of geometric imperfections in full-scale welded steel silos, Engineering Structures, 2005. 27(6): p. 938-950.
• 8. Rotter, J.M., R. Coleman, X.L. Ding, and J.G. Teng, The Measurement of Imperfections in Cylindrical Silos for Buckling Strength Assessment, 4th International Conference on Bulk Materials: Storage, Handling and Transportation, 1992, Wollongong, N.S.W., p. 473-479.
• 9. Zhang, D., 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 Structures, 2020. 155: p. 106925.
• 10. Peterson, J.P., P. Seide, and V.I. Weingarten, Buckling of Thin-Walled Circular Cylinders, Technical Report, 1968. NASA SP-8007.
• 11. Evkin, A., and O. Lykhachova, Energy barrier method for estimation of design buckling load of axially compressed elasto-plastic cylindrical shells, Thin-Walled Structures, 2021. 161: p. 107454.
• 12. Kim, S.E. and C.S. Kim, Buckling strength of the cylindrical shell and tank subjected to axially compressive loads, Thin-Walled Structures, 2002. 40(4): p. 329-353.
• 13. Wagner, H. N. R., 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 Structures, 2018. 127: p. 629-645.
• 14. Wagner, H. N. R., C. Hühne, and M. Janssen, Buckling of cylindrical shells under axial compression with loading imperfections: An experimental and numerical campaign on low knockdown factors, Thin-Walled Structures, 2020. 151: p. 106764.
• 15. Wang, B., 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, Composites Part B, 2019. 163: p. 314-323.
• 16. Wang, B., Z. Shiyang, H. Peng, B. Xiangju, D. Kaifan, C. Bingquan, M. Xiangtao, and C.J. Yuh, Buckling of quasi-perfect cylindrical shell under axial compression: A combined experimental and numerical investigation, International Journal of Solids Structures, 2018. 130(131): p. 232-247.
• 17. Mahdy, W.M., L. Zhao, F. Liu, R. Pian, H. Wang, and J. Zhang, Buckling and stress-competitive failure analyses of composite laminated cylindrical shell under axial compression and torsional loads, Composite Structures, 2021. 255: p. 112977.
• 18. Zhang, X., and Q. Han, Buckling and postbuckling behaviors of imperfect cylindrical shells subjected to torsion, Thin-Walled Structures, 2007. 45(12): p. 1035-1043.