Buckling of Long Sandwich Cylindrical Shells Under External Pressure

An elasticity solution to the problem of buckling of sandwich long cylindrical shells subjected to external pressure is presented. In this context, the structure is considered a three-dimensional body. All constituent phases of the sandwich structure, i.e., the facings and the core, are assumed to be orthotropic. The loading is a uniform hydrostatic pressure, which means that the loading remains normal to the deflected surface during the buckling process. Results are produced for laminated facings, namely, boron/epoxy, graphite/epoxy and kevlar/epoxy laminates with $0deg$ orientation with respect to the hoop direction, and for alloy-foam core. Shell theory results are generated with and without accounting for the transverse shear effect. Two transverse shear correction approaches are compared, one based only on the core, and the other based on an effective shear modulus that includes the face sheets. The results show that the shell theory predictions without transverse shear can produce highly non-conservative results on the critical pressure, but the shell theory formulas with transverse shear correction produce reasonable results with the shear correction based on the core only being in general conservative (i.e., critical load below the elasticity value). The results are presented for four mean radius over shell thickness ratios, namely 15, 30, 60, and 120 in order to assess the effect of shell thickness (and hence that of transverse shear). For the same thickness, the differences between elasticity and shell theory predictions become larger as the mean radius over thickness ratio is decreased. A comparison is also provided for the same shell with homogeneous composite construction. It is shown that the sandwich construction shows much larger differences between elasticity and shell theory predictions than the homogeneous composite construction. The solution presented herein provides a means of a benchmark for accurately assessing the limitations of shell theories in predicting stability loss in sandwich shells.