Geometric imperfections and lower-bound methods used to calculate knock-down factors for axially compressed composite cylindrical shells

• A comparison among different geometric imperfection patterns is presented: eigenmodes, dimples, single perturbation load, axisymmetric and real measurements.
• Finite element non-linear analyses were performed to obtain the knock-down curves and load-shortening curves for each pattern.
• The lower-bound methods NASA SP-8007 and the Reduced Stiffness Method were compared to the non-linear results.
• The results show that the worst eigenmode imperfection does not necessarily come from the first mode.
• Axisymmetric imperfections seem to give the lowest knock-down-factor, as shown by the circumferentially oriented eigenmodes and axisymmetric imperfections.

The important role of geometric imperfections on the decrease of the buckling load for thin-walled cylinders had been recognized already by the first authors investigating the theoretical approaches on this topic. However, there are currently no closed-form solutions to take imperfections into account already during the early design phases, forcing the analysts to use lower-bound methods to calculate the required knock-down factors (KDF). Lower-bound methods such as the empirical NASA SP-8007 guideline are commonly used in the aerospace and space industries, while the approaches based on the Reduced Stiffness Method (RSM) have been used mostly in the civil engineering field. Since 1970s a considerable number of experimental and numerical investigations have been conducted to develop new stochastic and deterministic methods for calculating less conservative KDFs. Among the deterministic approaches, the single perturbation load approach (SPLA), proposed by Hühne, will be further investigated for axially compressed fiber composite cylindrical shells and compared with four other methods commonly used to create geometric imperfections: linear buckling mode-shaped, geometric dimples, axisymmetric imperfections and measured geometric imperfections from test articles. The finite element method using static analysis with artificial damping is used to simulate the displacement controlled compression tests up to the post-buckled range of loading. The implementation of each method is explained in details and the different KDFs obtained are compared. The study is part of the European Union (EU) project DESICOS, whose aim is to combine stochastic and deterministic approaches to develop less conservative guidelines for the design of imperfection sensitive structures.