04.01: Buckling of very short elastic cylinders with weld imperfections under uniform bending

The length-dependent domains of behaviour of thin elastic cylindrical shells under uniform bending have recently received significant research attention. Ovalisation is known to affect very long cylinders which undergo significant cross-sectional flattening before failing by local buckling. This effect is restrained by the end boundary condition in shorter cylinders, which fail instead by local buckling at moments close to the classical analytical prediction. In very short cylinders, however, even this local buckling is restrained by the end boundary, and failure occurs instead through the development of a destabilising meridional fold on the compressed side. Although this is a limit point instability under bending, ovalisation does not play any role at all. This ‘very short’ length domain has only recently been explored for the first time with the aid of finite element modelling. A brief overview of the nonlinear buckling behaviour of very short elastic cylinders under uniform bending is presented in this paper. Two types of edge rotational restraint are used to illustrate the influence of a varying support condition on the stability in this short length range. It is shown that short cylinders under bending do not suffer at all from local short-wave buckling. Additionally, when the meridional dimension of such cylinders becomes particularly short the resulting numerical models may predict indefinite stiffening without a limit point, even when the shell is modelled using more complete 3D solid continuum finite elements. Idealised weld depressions, which are realistic representations of a systemic manufacturing defect, are used to demonstrate only a very mild sensitivity to geometric imperfections at such short lengths owing to a pre-buckling stress state dominated by local compatibility bending. The topic should be of interest to researchers studying shell problems dominated by local bending with computational tools and designers of multi-segment shells with very close segment spacing.