摘要
基于Ciarlet-Lods定义的广义膜壳,首次提出了该模型的一种Galerkin协调有限元离散格式。首先,对积分区域进行三角剖分,并在三角网格上对位移前两个分量用带泡一次Lagrange插值多项式逼近,而对第三个分量,即法向位移,用一次Lagrange插值多项式逼近。其次,讨论了广义膜壳弱解的存在性、唯一性和数值解的存在性、唯一性以及弱解与数值解的误差估计。最后,本文对生物材料的双曲膜壳采用该方法进行数值模拟,得到不同网格下双曲壳中性面上的位移,并通过分析数值模拟结果证明了有限元离散格式的收敛性和有效性。
In this paper, it's the first time that a new Galerkin conforming finite element method for the generalized membrane shell model proposed by Ciarlet-Lods is conducted. Firstly, the integral domain with triangulation is discretized. The first two components of the displacement are approximated by the 1st-order Lagrangian polynomials with bubble, whereas the third component of the displacement, i.e., the normal displacement, is approximated by the 1st-order Lagrangian polynomial. Secondly, the existence and uniqueness of the weak solution and numerical solution are discussed, respectively. At the same time, the prior error estimate is provided. Finally, the numerical experiments for biological materials with the hyperbolic middle surface are done. The displacements of the hyperbolic middle surface under the different meshes are derived and the numerical results are analyzed which show that the finite element method is stable and effective.
出处
《应用力学学报》
CSCD
北大核心
2017年第5期995-1000,共6页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金(11571275
11572244)
陕西省工业科技攻关资助项目(2015GY021
2015JQ1001)
关键词
广义膜壳
伽辽金法
双曲壳
generalized membrane shell
Galerkin method
hyperbolic shell
