The modeling and numerical analysis of wrinkled membranes
The modeling and numerical analysis of wrinkled membranes
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DOI：
10.1002/nme.832
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发表时间：
2003-11
影响因子：
2.9
通讯作者：
H. Ding;Bingen Yang
中科院分区：
文献类型：
--
作者：
H. Ding;Bingen Yang
在本文中，三个基本问题的建模和分析的褶皱膜的解决。首先，提出了一种新的膜模型与可行的杨氏模量和泊松比，它的物理特性的应力松弛现象的膜褶皱，并表示拉紧，起皱和松弛状态的膜在一个系统的方式。其次，建立了新膜模型的参数变分原理。第三，通过变分原理，将原膜问题转化为数学规划中的非线性互补问题。参数有限元离散和光滑牛顿法，然后用于数值解。所提出的膜模型和数值方法能够提供收敛的结果，膜的褶皱和松弛区域的混合物，没有迭代的膜应力。提供了三个数值例子。版权所有© 2003年约翰威利父子有限公司。
In this paper three fundamental issues regarding modeling and analysis of wrinkled membranes are addressed. First, a new membrane model with viable Young's modulus and Poisson's ratio is proposed, which physically characterizes stress relaxation phenomena in membrane wrinkling, and expresses taut, wrinkled and slack states of a membrane in a systematic manner. Second, a parametric variational principle is developed for the new membrane model. Third, by the variational principle, the original membrane problem is converted to a non‐linear complementarity problem in mathematical programming. A parametric finite element discretization and a smoothing Newton method are then used for numerical solution. The proposed membrane model and numerical method are capable of delivering convergent results for membranes with a mixture of wrinkled and slack regions, without iteration of membrane stresses. Three numerical examples are provided. Copyright © 2003 John Wiley & Sons, Ltd.