The effect of non-uniformity of axial loading on the buckling behaviour of shells with random imperfections

In the present paper, the effect of random non-uniform axial loading on the buckling behaviour of isotropic thin-walled imperfect cylindrical shells is investigated. Random initial (out-of-plane) geometric imperfections, thickness and material property variability, together with a non-uniform stochastic axial loading are incorporated into a cost-effective non-linear stochastic finite element analysis using the non-linear TRIC shell element. For this purpose, the concept of an initial ‘imperfect’ structure is introduced involving not only deviations of the shell structure from its perfect geometry but also a spatial variability of the modulus of elasticity as well as of the thickness of the shell. The initial imperfections as well as the axial loading are modeled as stochastic fields with statistical properties that are either based on an available data bank of measured initial imperfections or assumed, in cases where no experimental data is available. Based on these simulation features, a simple and realistic approach is proposed for the estimation of the variability (scatter) of the limit loads by means of a brute-force Monte Carlo Simulation procedure. In addition, ‘worst case’ buckling scenarios are identified by means of a sensitivity analysis with respect to assumed parameters used for the description of stochastic fields that are not supported by corresponding experimental measurements. In addition it is shown that in the context of such sensitivity analysis, modeling of the non-uniformity of the axial loading is, from a computational point of view, fully equivalent to modeling the geometric boundary imperfections. The numerical tests performed demonstrate the significant role that the random varying axial loading plays on the buckling behaviour of imperfection sensitive structures like the axially compressed thin-walled cylinder considered in this study.