Paradoxical buckling behaviour of a thin cylindrical shell under axial compression

• Published in: International journal of mechanical sciences Vol. 42; no. 5; pp. 843 - 865
• Main Authors: Lancaster, E.R., Calladine, C.R., Palmer, S.C.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-05-2000; Elsevier
• Subjects: Axial load; Boundary conditions; Buckling; Compressive stress; Cylindrical shell; Defects; Exact sciences and technology; Experiments; Fundamental areas of phenomenology (including applications); Imperfections; Physics; Self-stress imperfections; Solid mechanics; Static buckling and instability; Statically determinate boundary conditions; Stress concentration; Structural analysis; Structural and continuum mechanics; Structural loads; Imperfections; Statically determinate boundary conditions; Axial load; Cylindrical shell; Self-stress imperfections; Buckling; Experiments; Vertical cylinder; Uniaxial compression; Geometrical shape; Thin shell; Testing equipment; Form defect; Critical load; Revolution shell; Experimental study
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/S0020-7403(99)00030-2

The widely accepted theory of buckling of thin cylindrical shells under axial compressive loading emphasises the sensitivity of the buckling load to the presence of initial imperfections. These imperfections are conventionally taken to be minor geometric perturbations of a shell which is initially stress-free. The original aim of the present study was to investigate the effect on the buckling load of imperfections in the form of
local initial stress, which are probably more typical of practice than purely geometric ones. Experiments were performed on a vertical “melinex” cylinder of diameter
∼0.9 m and height
∼0.7 m, with radius
/thickness ratio
∼1800. The upper and lower edges of the cylinder were clamped to end discs by means of circumferential belts — an arrangement that allowed states of self-stress to be introduced to the shell readily by means of local “uplift” at the base. The upper disc was made sufficiently heavy to buckle the shell, and it was supported by a vertical central rod under screw control. Many buckling tests were performed. Surprisingly, the buckling loads were generally at the upper end of the range of fractions of the classical buckling load that have been found in many previous experimental studies. Even when the local uplift at the base caused a local “dimple” to be formed before the shell was loaded, the buckling load was relatively high. A surface-scanning apparatus allowed the geometric form of the shell to be monitored, and the progress of such a dimple to be followed; and it was found that a dimple generally grew in size and migrated in a stable fashion up the shell as the load increased, until a point was reached when unstable buckling occurred. These unexpected and paradoxical features of the behaviour of the experimental shell may be attributed to the particular boundary conditions of the shell, which provide in effect
statically determinate support conditions. This study raises some new issues in the field of shell buckling, both for the understanding of buckling phenomena and for the rational design of shells by engineers against buckling.