拉格朗日皱曲方程
Lagrangian Crumpling Equations
摘要：
本文介绍了一种用拉格朗日坐标跟踪运动曲面几何演化的简明方法。所有的计算都可以在初始表面的固定几何形状中完成，尽管移动表面的复杂性不断变化。该方法被应用到三个问题的非线性弹性：在压力下的薄板（Foeppl-von Karman理论的原始动机），在压力下的球壳的屈曲，和毛细皱纹的现象引起的表面张力在薄膜。在这最后一个问题中，总能量中包含了引力势能项，从而改进了与实验的一致性。
英文摘要：
A concise method for following the evolving geometry of a moving surface using Lagrangian coordinates is described. All computations can be done in the fixed geometry of the initial surface despite the evolving complexity of the moving surface. The method is applied to three problems in nonlinear elasticity: the bulging of a thin plate under pressure (the original motivation for Foeppl-von Karman theory), the buckling of a spherical shell under pressure, and the phenomenon of capillary wrinkles induced by surface tension in a thin film. In this last problem the inclusion of a gravitational potential energy term in the total energy improves the agreement with experiment.
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