Biomimetics: Extending nature's design of thin-wall shells with cellular cores

Abstract

Thin-walled, cylindrical structures are found extensively in both engineering and nature. Minimum weight design of such structures is essential 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 elastic buckling resistance of a cylindrical shell over that of a hollow cylinder of the same weight. We extend the linear-elastic buckling theory by coupling basic plasticity theory to provide a more comprehensive analysis of isotropic, cylindrical shells with compliant cores. The minimum weight design of a thin-walled cylinder with a compliant core, of given radius and specified materials, subjected to a prescribed load in uniaxial compression or pure bending is examined. The analysis gives the values of the shell thickness, the core thickness, and the core density that minimize the weight of the structure for both loading scenarios. The weight optimization of the structure identifies the optimum ratio of the core modulus to the shell modulus. The design of natural, thin-walled structures with cellular cores is compared to the analytical optimal, and the deviation about the theoretical optimum is explored. The analysis also discusses the selection of materials in the design of the cylinders with compliant cores, identifying the most suitable material combinations. Finally, the challenges associated with achieving the optimal design in practice are discussed, and the potential for practical implementation is explored.