标题： 柯西-纳维方程的微分几何表述 显示英文标题

标题： Differential geometric formulation of the Cauchy Navier equations

摘要： 本文用现代微分几何的语言——微分形式和李导数——重新表述了线性弹性理论中一些最基本的量和方程——应力张量与应变张量、柯西-纳维平衡方程、线性各向同性体的材料方程。类似的方法在广义相对论、量子物理和电动力学中已成功实现，并且在这些领域中非常有用。然而，在弹性理论中，这种现代微分几何方法的应用远不如其他领域普遍。此外，现有的重新表述需要大量的微分几何知识，包括非标准实体（如矢量值微分形式等）。本文提出了一种比迄今为止发表的更少通用但更容易理解的方法，用于在弹性理论中使用现代微分几何。 显示英文摘要

摘要： The paper presents a reformulation of some of the most basic entities and equations of linear elasticity - the stress and strain tensor, the Cauchy Navier equilibrium equations, material equations for linear isotropic bodies - in a modern differential geometric language using differential forms and lie derivatives. Similar steps have been done successfully in general relativity, quantum physics and electrodynamics and are of great use in those fields. In Elasticity Theory, however, such a modern differential geometric approach is much less common. Furthermore, existing reformulations demand a vast knowledge of differential geometry, including nonstandard entities such as vector valued differential forms and the like. This paper presents a less general but more easily accessible approach to using modern differential geometry in elasticity theory than those published up to now.