OVERVIEW OF FINITE DEFORMATION SINGLE DIRECTOR SHELL MODELS WITHOUT COMPLEX GEOMETRIC CONCEPTS
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摘要: 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.Abstract: Based on Simo and Fox's well-known work, this article gives a comprehensiveoverview of the single director shell model and its modern representation.It describes the mathematical foundation and the mechanicalanalysis of a fully nonlinear, geometrically exact shell theory. Thisformulation of the shell equations has the advantage that, although theexact nonlinear geometric structures of the idealized two-dimensional bodyare maintained, the complex differential geometry concepts such as covariantderivatives, Riemannian connections or Christoffel symbols are avoided.Furthermore, a weak or variational statement of the local balance equationsis developed, as is ideally suited for numerical solution techniques.
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Key words:
- single director field /
- shells models /
- finite deformation /
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