A study is presented of the effect of initial deviations on the load carrying capacity of thin circular cylindrical shells under uniform axial compression. A perturbation expansion is used to reduce the nonlinear equations of von Karman and Donnell to an infinite set of linear equations, of which only the first few need be solved to obtain a reasonably accurate solution. The results for both infinite shells and shells of finite length indicate that a small imperfection can sharply reduce the maximum load that a thin-walled cylinder will sustain. In addition, for a particular set of boundary conditions, it is shown that the effect of the length of a finite shell is small as far as the load carrying capacity is concerned, but significant when the number of waves around the circumference has to be determined. A further result of the study is that axisymmetric initial deviations reduce the load carrying capacity only slightly more than deviations characterized by a product of trigonometric functions of the axial and circumferential coordinates if the wave lengths are properly chosen.
Perturbation Solutions for the Buckling Problems of Axially Compressed Thin Cylindrical Shells of Infinite or Finite Length
Dym, C. L., and Hoff, N. J. (December 1, 1968). "Perturbation Solutions for the Buckling Problems of Axially Compressed Thin Cylindrical Shells of Infinite or Finite Length." ASME. J. Appl. Mech. December 1968; 35(4): 754–762. https://doi.org/10.1115/1.3601301
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