线性弹性柔性壳非协调有限元计算模型

本文基于Ciarlet-Lods-Miara定义的柔性壳模型提出一种Galerkin非协调有限元离散格式.首先,对积分区域进行Delaunay三角剖分,并在三角网格上对位移前两个分量用一次Lagrange多项式逼近,对第三个分量(即法向位移)用非协调Morley元逼近.其次,讨论了构造的Galerkin非协调有限元离散格式解的存在性、唯一性和先验误差估计.最后对特殊边界条件下的锥壳采用该方法进行数值实验,计算出不同网格下锥壳的位移,并通过分析数值实验结果证明有限元离散格式的收敛性和有效性.

A Nonconforming Finite Element Method for the Linearly Elastic Flexural Shell

In this paper, we construct a Galerkin nonconforming finite element method for the linear elastic flexural shell model proposed by Ciarlet-Lods-Miara. First, we discretize the integral domain with Delaunay triangulation. We approximate the first two component of the displacement by the first-order Lagrangian polynomial, whereas we approximate the third component of the displacement, i.e., the normal displacement, by the nonconforming Morley element. Secondly, we discuss the existence, uniqueness, and a priori error estimate of the numerical solution. Finally, we run numerical experiments for the conical shell with special boundary conditions. We derive the displacements of the conical middle surface under the different meshes. We analyze the numerical results which show that the finite element method is convergent and effective.