具有一致精度的薄壳方程的线性有限元方法  

A uniformly accurate linear fnite element method for thin shells

作　　者：张胜 Zhang Sheng(Wayne State University,Michigan 48201,USA)

机构地区：[1]韦恩州立大学,底特律密歇根48202

出　　处：《纯粹数学与应用数学》2022年第3期403-414,共12页Pure and Applied Mathematics

摘　　要：对Naghdi壳的弯曲问题提出一种混合有限元方法.该方法采用连续分片线性函数逼近切向延压应力张量和横向剪切应力向量,并采用间断线性函数来逼近壳的中面位移和法向纤维旋转.建立了适用于任意几何形状的壳的一般性的误差估计.分析表明如果壳中面的几何系数是分片常数,该方法对主要变量具有最优阶的,与壳的厚度无关的一致的精度.在一般情况下,在壳体几何形状快速变化的区域中适当细化有限元网格是必要的.无论如何,当有限元网格尺寸不超过壳的厚度的平方根时,最优阶的一致精度可得到保证.We propose a mixed finite element method for the bending problem of Naghdi shells. In the method we use continuous piecewise linear function to approximate the membrane stress tensor and transverse shear stress vector, and use discontinuous piecewise linear function for the primary mid-surface displacement vector and normal fiber rotation. We establish an error estimate for the most general shape of shells. It shows that when the geometrical coefficients of the shell surface are piecewise constants, the method has the optimal order of accuracy that is uniform with respect to the shell thickness. Generally, it suggests that the mesh should be refined according to the curvature of the shell surface. In any case, uniform accuravy is assured if the mesh size is bounded by the squareroot of the shell thickness.

关 键 词：壳模型 延压/剪切闭锁 混合/间断伽辽金 

分 类 号：O178[理学—数学]