Finite element for nonlinear mechanics

我们研究的主题是调查的配方是力学和有限元法的近似解的基础。我们研究力学的理论基础，数学难题的建模，有限元技术的变化和扩展。这使我们了解了可以应用于工业需求的机制。考虑到这一目标，我们提出了两个具体问题的研究。管束被发现在许多关键部件，如热交换器，冷凝器和核蒸汽发生器。 传统上，这些管道磨损坚固，设备的性能要求相当温和，流致振动问题很少。然而，具有更高性能和效率的设计导致管更灵活并且经受更高的流速。因此，流致振动问题变得普遍，并且它们的研究成为一个重要的研究领域。我们的目标是提供分析能力，以帮助设计新一代热交换器和评估运行的核蒸汽发生器。另一个问题涉及卫星天线的振动。这些天线的设计要求正在将卫星尺寸推到无法使用当前技术发射到太空的尺寸。这个问题要求对目前的卫星设计进行革命性的改变。新的卫星可能使用充气天线，而不是使用大型刚性天线。充气卫星具有超轻、装载体积小、高强度质量比和低成本等优点。 典型地，空间结构由于低的结构刚度和在真空空间中缺乏空气阻尼而具有振动问题。我们的目标是识别这些振动和控制它们的技术。

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.