论文标题
不可压缩的超弹性材料的精致动态有限壳壳理论：方程和二维壳虚拟工作原理
A refined dynamic finite-strain shell theory for incompressible hyperelastic materials: equations and two-dimensional shell virtual work principle
论文作者
论文摘要
基于先前针对静态问题的工作，在本文中，我们首先得出一种动态有限壳壳方程的一种形式，用于不可压缩的超弹性材料，涉及三个壳体组成关系。为了挑出弯曲效果以及减少壳本构的关系的数量，进行了进一步的细化，这导致了仅具有两个壳体构型关系（从给定的三维（3D）菌株函数中推资）的精制动态有限型壳壳理论，还会推导一些新见解。通过使用壳方程的弱公式以及3D Lagrange功能的变化，边界条件和二维（2D）壳虚拟工作原理。作为基准问题，我们考虑了动脉细分市场的扩展和通胀。基于壳方程的渐近解决方案与3D精确的渐近解决方案之间的良好一致性给出了前者的验证。精制的壳理论还应用于研究加压动脉的平面应变振动，并详细研究了轴向预拉伸，压力和纤维角对振动频率的影响。
Based on previous work for the static problem, in this paper we first derive one form of dynamic finite-strain shell equations for incompressible hyperelastic materials that involve three shell constitutive relations. In order to single out the bending effect as well as to reduce the number of shell constitutive relations, a further refinement is performed, which leads to a refined dynamic finite-strain shell theory with only two shell constitutive relations (deducible from the given three-dimensional (3D) strain energy function) and some new insights are also deduced. By using the weak formulation of the shell equations and the variation of the 3D Lagrange functional, boundary conditions and the two-dimensional (2D) shell virtual work principle are derived. As a benchmark problem, we consider the extension and inflation of an arterial segment. The good agreement between the asymptotic solution based on the shell equations and that from the 3D exact one gives verification of the former. The refined shell theory is also applied to study the plane-strain vibrations of a pressurized artery, and the effects of the axial pre-stretch, pressure and fibre angle on the vibration frequencies are investigated in detail.
