Optimization of cylindrical shells with compliant cores

Thin-walled, cylindrical structures are found extensively in both engineering components and in nature. The weight to load bearing ratio is a critical element of design of such structures in a variety of engineering applications, including space shuttle fuel tanks, aircraft fuselages, and offshore oil platforms. In nature, thin-walled cylindrical structures are often supported by a honeycomb- or foam-like cellular core, as for example, in plant stems, porcupine quills, or hedgehog spines. Previous studies have suggested that a compliant core increases the buckling resistance of a cylindrical shell over that of a hollow cylinder of the same weight. In this paper, we extend the linear-elastic buckling theory by coupling it with basic plasticity theory to provide a more comprehensive analysis of isotropic, cylindrical shells with compliant cores. We examine the optimal design of a thin-walled cylinder with a compliant core, of given radius and specified materials, for a prescribed load bearing capacity in axial compression. The analysis gives the values of the shell thickness, the core thickness, and the core density that maximize the load bearing capacity of the shell with a compliant core over an equivalent weight hollow shell. The analysis also identifies the optimum ratio of the core modulus to the shell modulus and is supported by a Lagrangian optimization technique. The analysis further discusses the selection of materials in the design of a cylinder with a compliant core, identifying the most suitable material combinations. The performance of a cylinder with a compliant core is compared with competing designs (optimized hat-stiffened shell and optimized sandwich-wall shell). Finally, the challenges associated with achieving the optimal design in practice are discussed, and the potential for practical implementation is explored.