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

壳结构是航空航天和飞机工程、核电站和海军结构的关键部件。上述工业通常在高流体流动速率下使用薄壁壳体，并且要求壳体厚度低。在这些条件下，结构变得非常容易失稳和破坏。提出的工作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。这允许在确保其可靠性的同时对更现实的情况进行建模。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较低的成本，以可靠和非常精确的方法完成我们的有限元模型。第一个课题是扩展现有的轴对称混合模型，以研究受内部湍流诱导的随机边界层作用的截顶锥形壳。这需要在任意压力场和边界层压力下获得流体的互相关谱密度和壳的位移的均方值。板壳在超声速流动下的情况也是本课题研究的一个重要问题。这允许模拟弯曲和面板，如飞机鳍或涡轮叶片遭受超音速流动。第三个研究课题涉及固体壳与流体相互作用时的超弹性行为的集成。在本研究中，应变不变本构模型将用于描述超弹性材料的行为。后者使得将我们的有限元模型应用于具有更真实材料特性的结构成为可能。最后一个主题涉及与可压缩内部流动流体耦合的混合轴对称模型的重新表述。目的是解决与结构入口和出口施加的流体边界条件有关的问题。这一领域的现有软件只涵盖了非常有限的流固耦合情况，这一事实促使了新的数值模型的发展和现有数值模型的改进。此外，我们对开发环空流动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。所有这些进展及其结果将对国际科学界研究流动流体作用下结构振动有一定的参考价值。实际上，NSERC支持的大部分研究项目已经或将会得到业界的支持。例如，NSERC创建了新的联盟项目（Industry-NSERC），取代了之前的项目（RD-Coop和Engage）。申请人每三到四年有一个RD-Coop和/或Engage项目（庞巴迪、普华永道、魁北克水电、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.).