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From Tennyson, et al.
This slide shows the dynamic emergence of buckles in a cylindrical shell of the type displayed in the previous slide.
Relevant papers:
R.C. Tennyson, (University of Toronto), “An experimental investigation of the buckling of circular cylindrical shells in axial compression using the photoelastic technique (Photoelastic analysis of circular cylinder shell buckling in axial compression)”, 1964 (no publisher given)
R. C. Tennyson (Institute for Aerospace Studies, University of Toronto, Toronto, Ontario, Canada), “Photoelastic circular cylinders in axial compression”, in Test Methods for Compression Members, ASTM STP 419, Am. Soc. Testing Mats., 1967, p. 31
ABSTRACT: A novel method for fabricating “near-perfect” circular cylinders of photoelastic plastic is presented. The spin-casting technique was found to yield circular cylinders having thickness variations as low as plus or minus 0.0006 in., and capable of maintaining this tolerance on shells with radius-tio-thickness ratios in the range of 100 < R/t < 600. The cylinders generally were found to buckle within 10 per cent of the classical computed load, and within only a few per cent of the reduced value taking into account the clamped end constraints. This represents an increase over previous experimental data. Buckling was completely elastic, and, as a result, repeatability of the buckling load and buckling process was observed for as many as 20 tests on any one shell. Experimental evidence of the unstable states occupied by the shell during the buckling process was found by photographing the change in the 45-degree isoclinics with wave shape. Shell alignment, end constraints, and the method of applying a uniform compressive end load on the cylinder are also discussed. Although no new techniques were employed, the methods used were found reliable and accurate.
R.C. Tennyson and S.W. Welles (Institute for Aerospace Studies, University of Toronto, Ontario, Canada), “Analysis of the buckling process of circular cylindrical shells under axial compression”, February 1968,
DTIC Accession Number: AD0665531
ABSTRACT: Geometrically 'near-perfect' circular cylindrical photoelastic shells having radius-to-thickness ratios of the order 100 - 440 were tested in pure axial compression. The critical buckling loads were found to agree within 10 - 14% of the classical value, or within a few percent of the reduced buckling load taking into account the clamped end constraint. High speed photographs of the buckling process were obtained using two cameras viewing the change in the 45 deg isoclinics over the entire cylinder's length and over 60% of the cylinder's perimeter. A theoretical analysis of the inception of buckling using Koiter's mode shapes demonstrated that the classical buckling mode was observed in the experiments for the first time. Further investigation of the nonlinear postbuckling mode shapes just after initial buckling predicted the wave forms observed. It was also determined that the shallow shell equations used to describe the large-deflection postbuckling behaviour do not predict isoclinic patterns which are observed in the later stages of buckling.
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