没有复杂几何概念的单方向场壳体有限变形模型综述

OVERVIEW OF FINITE DEFORMATION SINGLE DIRECTOR SHELL MODELS WITHOUT COMPLEX GEOMETRIC CONCEPTS

基于Simo和Fox的工作,介绍一种没有复杂几何概念的现代壳体有限变形理论.在推导上,使用三维连续介质理论,运用现代力学的表示方法.这个模型提供了非线性几何精确壳体理论的力学分析基础.这种模型的一个优点是虽然将壳体仍然看作二维结构,但是它没有复杂的微分几何概念,如没有协变导数、Riemannian-Christoffel记号等.另外,还介绍了壳体局部平衡的弱形式或变分表示,这种表示特别适用于数值计算.

Based on Simo and Fox's well-known work, this article gives a comprehensive overview of the single director shell model and its modern representation. It describes the mathematical foundation and the mechanical analysis of a fully nonlinear, geometrically exact shell theory. This formulation of the shell equations has the advantage that, although the exact nonlinear geometric structures of the idealized two-dimensional body are maintained, the complex differential geometry concepts such as covariant derivatives, Riemannian connections or Christoffel symbols are avoided. Furthermore, a weak or variational statement of the local balance equations is developed, as is ideally suited for numerical solution techniques.