The optimisation of foam-filled cylindrical shells subject to flexural loading

Work is presented to maximise the resistance of isotropic and orthotropic cylindrical tubes to the non-linear Brazier effect, by filling them with foam cores. Analytical approaches for the mass minimisation of such structures, by optimising shell wall thickness, ply lay-up and foam core density, are presented. The optimum configurations have been shown to have significant mass benefits compared to simple hollow tubes; the sample aluminium shell, aluminium foam core, tubes have been found to be up to 50% lighter (for given Brazier failure bending moment) than their hollow equivalents. The optimisation of foam filled orthotropic tubes has found that the increased resistance to the Brazier effect, provided by the foam core, can reduce the necessity for circumferentially oriented plies. The example 20mm radius tubes, CFRP shells with polymeric foam cores, showed theoretical reductions in mass, for given failure bending moments, of the order of 30%. The optimisation can readily be modified to accommodate alternative requirements, such as cost, to better reflect actual design criteria for real structures. Whilst it is noted that real structures rarely fail by the Brazier effect (material failure or local buckling generally precede it) this analysis will be of use to those seeking a minimisation of non-linearities in the deformation of long hollow structures.