Elastic buckling of cylindrical shells with elastic cores—I. Analysis

Thin walled cylindrical shell structures are widespread in nature; examples include plant stems, porcupine quills and hedgehog spines. All have an outer shell of almost fully dense material supported by a low density, cellular core. In nature, all are loaded in some combination of axial compression and bending; failure is typically by buckling. Natural structures are often optimized. Here we have analysed the elastic buckling of a thin cylindrical shell supported by an elastic core to show that this structural configuration achieves significant weight saving over a hollow cylinder. Biomimicking of natural cylindrical shell structures may offer the potential to increase the mechanical efficiency of engineering cylindrical shells. The results of the analysis are compared with data in the following, companion paper.