Finite element for nonlinear mechanics

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The theme of our research is the investigation of the formulations that are the basis of mechanics and approximate solutions by the finite element method. We look into the theoretical foundations of mechanics, the modeling of mathematically difficult problems, variations and extension of finite element techniques. This gives understanding of the mechanics that can then be applied to the needs of industry. With this goal in mind, we are proposing the study of two specific problems.Tube bundles are found in many critical components such as heat exchangers, condensers, and nuclear steam generators.  Traditionally, these tubes wear made robustly and the equipment had rather modest performance demands, and flow-induced vibration problems were rare. However, designs with higher performance and efficiencies resulted in tubes being more flexible and were subjected to higher flow rates. Thus, flow-induced vibration problems became commonplace and their study became an important area of research. Our goal is to provide the analytical capacity to help in designing new generation heat exchangers and to assess operating nuclear steam generators.The other problem deals with the vibration of Satellite's antennas. The design requirements of these antennas are driving the satellite size to dimensions that can not be launched into space using current technology. This problem has dictated a revolutionary change in current satellite design. Instead of using large rigid antennas, new satellites may have inflatable ones. Inflatable satellites possess many advantageous properties such as ultra-lightweight, small stowage volume, high strength-to-mass ratio and low overall space program cost.  Typically, space structures have vibration problems due to low structural stiffness and the lack of air damping in the vacuum of space. Our goal is identify these vibrations and techniques to control them.