Probabilistic approach for improved buckling knock-down factors of CFRP cylindrical shells

Abstract

Aerospace industry demands for significantly reduced development and operating costs. Reduction of structural weight at safe design is one avenue to achieve this objective. The running ESA (European Space Agency) study Probabilistic Aspects of Buckling Knock Down Factor acts on this route. It concentrates on thin-walled circular cylindrical CFRP shells subjected to axial compression. It is well known that such structures exhibit not only a high load carrying capacity but also are prone to buckling which is highly imperfection sensitive. Imperfections are defined as deviations from perfect parameters like shape, thickness, material properties and loading distributions, they can reduce the buckling load drastically compared to a perfect shell. In order to account for these imperfections the theoretical buckling load of a perfect cylinder must be multiplied, and therefore reduced, by a knock-down factor (the ratio of buckling loads of imperfect and perfect cylindrical shell). Thus the closer the knock-down factor reflects the effect of imperfections the better is the prediction of the real buckling load. In the still used NASA SP-8007 design guideline from 1968 a lower bound curve for the knock-down factor is proposed. The factor depends on the slenderness (the ratio of radius and wall thickness) and decreases with increasing slenderness. This factor is rather conservative and the structural behaviour of composite material is not considered adequately. Advanced thin-walled cylindrical shell structures under compression are therefore penalized if the knock-down factor based on this early NASA report must be applied. The current ESA study started in May 2006 and will run for 18 months. Its main objective is to achieve a better buckling knock-down factor for unstiffened CFRP cylindrical shells and to validate the linear and non-linear buckling simulations by test results. The main results will comprise an experimental data base (material properties, measured thicknesses, full scale shape imperfections, load-shortening curves, strains, and deformations) obtained by testing of 10 nominally identical axially compressed CFRP cylindrical shells, sensitivity analyses using Monte-Carlo simulation, validation with tests and a design guideline for that type of structure with a less conservative knock-down factor than taken from NASA SP-8007. All tasks of the ESA study are performed at the Institute of Composite Structures and Adaptive Systems of DLR Braunschweig, which has a rich body of experience in design, manufacturing, testing and analysis of shells prone to buckling. The paper outlines the objectives and expected results of the running ESA study and presents the results achieved so far.