Structural Modeling of a Five-Meter Thin-Film Inflatable Antenna/Concentrator
Inflatable structures have been the subject of renewed interest in recent years for space applications such as communications antennas, solar thermal propulsion, and space solar power. A major advantage of using inflatable structures in space is their extremely light weight. An obvious second advantage is on-orbit deployability and related space savings in the launch configuration. A recent technology demonstrator flight for inflatable structures was the Inflatable Antenna Experiment (IAE) that was deployed on orbit from the Shuttle Orbiter. Although difficulty was encountered in the inflation/deployment phase, the flight was successful overall and provided valuable experience in the use of such structures. Several papers on static structural analysis of inflated cylinders have been written, describing different techniques such as linear shell theory, and nonlinear and variational methods, but very little work had been done in dynamics of inflatable structures until recent years. In 1988 Leonard indicated that elastic beam bending modes could be utilized in approximating lower-order frequencies of inflatable beams. Main, et al. wrote a very significant 1995 paper describing results of modal tests of inflated cantilever beams and the determination of effective material properties. Changes in material properties for different pressures were also discussed, and the beam model was used in a more complex structure. The paper demonstrated that conventional finite element analysis packages could be very useful in the analysis of complex inflatable structures. The purposes of this paper are to discuss the methodology for dynamically characterizing a large 5-meter thin film inflatable reflector, and to discuss the test arrangement and results. Nonlinear finite element modal results are compared to modal test data. The work is significant and of considerable interest to researchers because of 1) the large size of the structure, making it useful for scaling studies, and 2) application of commercially available finite element software for modeling pressurized thin-film structures.
Deflections of inflated cylindrical cantilever beams subjected to bending and torsion
In the aeronautical field, there has been from time to time an interest in inflatable structures, ranging from their consideration for use in space to the design and manufacture of an inflatable wing for a man-powered aircraft and their use in remotely piloted vehicles . This interest stems from the fact that such structures have relatively low weight; are suitable for reacting light loads and can be packed into a small volume. One particularly useful structural component is the inflated circular cylinder acting as a cantilever and a number of such cylinders are used in Ref. 3 to form the main load carrying structure of a wing. In Ref. 1 an expression is derived for the collapse load of a single cylinder with the assumption that the root behaves like a plastic hinge, and in Ref. 5, Comer and Levy go on to consider the beam deflections and stresses between incipient wrinkling and final collapse.
NUMBER OF TRIANGULATIONS OF A MÖBIUS STRIP
Consider a Möbius strip with n chosen points on its edge. A triangulation is a maximal collection of arcs among these points and cuts the strip into triangles. In this paper, we proved the number of all triangulations that one can obtain from a Möbius strip with n chosen points on its edge is given by 4n−1 + (2n−2 n−1 ) , then we made the connection with the number of clusters in the quasi-cluster algebra arising from the Möbius strip.