On the minimal mass design of composite membranes
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abstract
2016 Elsevier Ltd This paper will show that a simple membrane (e.g. balloon) is not always the minimal mass pressure vessel. Of course one could always add cables to support the membrane, or plate, to reduce the thickness and hence mass required of the membrane. By minimizing the sum of the mass of the membrane plus the mass of the cable network, a minimal mass solution for the pressure vessel can be found. We will show the necessary and sufficient conditions (involving material choices and cable network topology) for which a composite system, composed of a membrane and cable network, has less mass than a membrane alone. The main motivator for this study is a spin-stabilized pressurized space structure useful for artificial gravity habitats. To contain and support the membrane, we will optimize the topology of the class of prestressable structures called tensegrity. These structures are usually composed of a network of axially-loaded compressive and tensile members. In the pressurized examples of this paper, inflation provides the compressive forces, and hence the optimized tensegrity topology eliminates the compressive structures when they are not needed. The minimal mass designs herein produce easily-tunable prestressed networks, and control systems that allow deployment and stiffness tuning features. The minimal mass design of those structures, for different load combinations (pressure loads and centrifugal loads), produces a composite structure composed of membranes and cable network. Two different composite systems are analyzed and compared with simple uniform membranes: the first system is composed of a cylindrical membrane supported by circular ring cables, the second system is composed by a membrane surrounded by ring cables and longitudinal cables. The comparison of the minimal mass designs with the single continuous membrane clearly highlights the advantage of the composite systems made of high-performance materials. When the material of the membrane and cables are the same, there is no advantage to the composite system, but various requirements usually demand different properties of the membrane and cable material.
