Thin-wall, cylindrical structures are found extensively in both engineering components and in 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-wall 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. In this thesis, 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. This thesis examines the minimum weight design of a thin-wall cylinder with a compliant core, of given radius and specified materials, subjected to a prescribed load in uniaxial compression or pure bending. 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.
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