Finite element analysis of an inflatable torus considering air mass structural element

Inflatable structures, also known as gossamer structures, are at high boom in the current space technology due to their low mass and compact size comparing to the traditional spacecraft designing. Internal pressure becomes the major source of strength and rigidity, essentially stiffen the structure. However, inflatable space based membrane structure are at high risk to the vibration disturbance due to their low structural stiffness and material damping. Hence, the vibration modes of the structure should be known to a high degree of accuracy in order to provide better control authority. In the past, most of the studies conducted on the vibration analysis of gossamer structures used inaccurate or approximate theories in modeling the internal pressure. The toroidal shaped structure is one of the important key element in space application, helps to support the reflector in space application. This paper discusses the finite-element analysis of an inflated torus. The eigen-frequencies are obtained via three-dimensional small-strain elasticity theory, based on extremum energy principle. The two finite-element model (model-1 and model-2) have cases have been generated using a commercial finite-element package. The structure model-1 with shell element and model-2 with the combination of the mass of enclosed fluid (air) added to the shell elements have been taken for the study. The model-1 is computed with present analytical approach to understand the convergence rate and the accuracy. The convergence study is made available for the symmetric modes and anti-symmetric modes about the centroidal-axis plane, meeting the eigen-frequencies of an inflatable torus with the circular cross section. The structural model-2 is introduced with air mass element and analyzed its eigen-frequency with different aspect ratio and mode shape response using in-plane and out-plane loading condition are studied.