Development of new finite element models to predict the dynamic behavior of shells subjected to flowing fluids

壳体结构是航空航天、飞机工程、核电站和海军结构中的关键部件。上述工业通常在高流体流速下使用薄壁壳体，并且需要低的壳体厚度。在这些条件下，结构变得非常容易失稳和失效。 拟议工作的目标是开发更复杂的有限元模型，具有比现有的更大的范围。这允许建模更现实的情况下，同时确保其可靠性。这项工作是我们长期目标的一部分，包括以相对于实验方法更低的成本，基于可靠且非常准确的方法完成我们的有限元模型。 第一个主题是扩展我们现有的轴对称混合模型来研究截锥壳受到内部湍流诱导的随机边界层。这就需要获得流体的互相关谱密度和任意压力场和边界层压力下壳体位移的均方值。 板和壳在超音速流中的情况也是本研究项目中要处理的一个重要问题。这允许模拟受到超音速流的弯曲和面板，如飞行器鳍或涡轮机叶片。 第三个研究课题是关于固体壳体与流体相互作用时的超弹性行为的整合。在本研究中，应变不变本构模型将被用来描述超弹性材料的行为。后者使得我们的有限元模型能够应用于具有更真实材料特性的结构。 最后一个主题涉及的混合轴对称模型与可压缩的内部流动流体耦合的重新制定。其目的是解决有关的问题，流体边界条件施加在进口和出口的结构。 新的数值模型的开发和现有的改进的动机是，在这一领域的现有软件只涵盖非常有限的情况下，流体-结构相互作用。 此外，我们对开发环形流模型的兴趣是将我们的专业知识扩展到其他应用的重要机会。 这些研究成果对国际上研究流体与结构相互作用振动问题具有一定的参考价值。实际上，NSERC支持的大多数研究项目也已经并将得到行业的支持。例如，由NSERC创建的新联盟计划（Industry-NSERC）取代了以前的计划（RD-Coop和Engage）。申请人每三年或四年有一个RD-Coop和/或Engage项目（庞巴迪，PWC，Hydro魁北克，CAE等）。

Shell structures constitute critical components in aerospace and aircraft engineering, nuclear power plants and naval structures. The aforementioned industries generally use thin-walled shells under high rates of fluid flow and require low shell thicknesses. Under these conditions, the structure becomes very susceptible to instability and failure. The objectives of the proposed work is to develop more sophisticated finite element models that have a larger scope than the existing ones. This permits modeling of more realistic cases while ensuring their reliability. This work is a part of our long-term objective that consists to complete our finite element models based on a reliable and very accurate approach at lower cost relative to experimental method. The first topic is to extend our existing axisymmetric hybrid model to study truncated conical shells subjected to a random boundary layer induced by internal turbulent flow. This requires obtaining the cross-correlation spectral density of the fluid and the mean square value of the displacements of the shell for an arbitrary pressure field and for a boundary-layer pressure. The case of plates and shells subjected to supersonic flow is also an important issue to deal with in the present research project. This allows simulating curved and panels like aircraft fins or turbine blades subjected to supersonic flow. The third research subject concerns the integration of the hyperelastic behaviour of the solid shell when interacting with a fluid. In this research, strain-invariant constitutive models will be used to describe the behaviour of hyperelastic materials. The latter makes it possible to apply our finite element models to structures with more realistic material properties. The last theme concerns the reformulation of the hybrid axisymmetric model coupled with a compressible internal flowing fluid. The objective is to resolve the issue related to fluid boundary conditions imposed on the inlet and outlet of the structure. The development of new numerical models and the improvement of existing ones are motivated by the fact that existing software in this field covers only very limited cases of fluid-structure interaction. In addition, our interest to develop annular flow models is an important opportunity to extend our expertise to others applications. All these developments and their results will be useful to international scientific community working on vibrations of structures in interaction with flowing fluid. Practically, the majority of all the research projects supported by NSERC are also have had and will have the supports of the industry. For instance, the new ALLIANCE program (Industry-NSERC) created by NSERC and replacing the former programs (RD-Coop and Engage). The applicant has and had every three or four years a project of RD-Coop and/or Engage (Bombardier, PWC, Hydro Quebec, CAE, etc.).