A direct approach to progressive buckling design considering ratcheting deformation

Fang Liu, Jian-Guo Gong, Hao feng Chen, Fu-Zhen Xuan

Research output: Contribution to journalArticlepeer-review


In this paper, the Bree diagram is extended to consider the progressive buckling failure and a direct approach for structural progressive buckling design considering ratcheting deformation is developed. Firstly, the progressive buckling mechanism of structures subjected to the combination of constant and cyclic loadings is sufficiently discussed. Then, a two-stage direct approach is developed based on the Linear Matching Method and nonlinear buckling analysis, which can generate progressive buckling design curves in the extended Bree diagram. To illustrate the application of the direct approach to progressive buckling design, a cylindrical shell model with an opening is provided as a numerical example. Furthermore, geometrical effects, e.g. the opening size and the shell thickness, on the progressive buckling limit are investigated. Formulas for progressive buckling design of cylindrical shells with various geometrical parameters are derived by fitting curves. Compared with other methods, the direct approach could predict accurate progressive buckling load.
Original languageEnglish
Number of pages36
JournalThin-Walled Structures
Publication statusAccepted/In press - 7 Mar 2021


  • bree diagram
  • direct approach
  • progressive buckling
  • ratcheting deformation
  • linear matching method

Cite this