基于面积坐标的四边形杂交有限元法  

A hybrid stress quadrilateral finite element method based on area coordinates

作　　者：高何金雨 张世全[1] GAO He-Jin-Yu;ZHANG Shi-Quan(School of Mathematics,Sichuan University,Chengdu 610064,China)

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2023年第4期8-16,共9页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省自然科学基金面上项目(2023NSFSC0075)。

摘　　要：本文针对二维线弹性问题提出了一种基于面积坐标的新型杂交应力四边形有限元法AGQ-LQ 6.该方法基于广义Hellinger-Reissner变分原理,位移逼近采用含内部位移的四节点广义协调元,应力逼近则采用九参数线性应力模式.数值算例表明,本文构造的有限元既能保持面积坐标广义协调元对网格畸变不敏感及粗网格精度较高的优点,又能有效克服泊松闭锁现象.In this paper,we propose a new hybrid stress quadrilateral finite element method AGQ-LQ 6 for the two-dimensional linear elasticity problems by using the area coordinates.In this method,a 4-node generalized conforming element with internal displacements for the displacement approximation and a 9-parameter linear stress mode for the stress approximation are adopted based on the generalized Hellinger-Reissner variational principle.Numerical experiments show that the method is insensitive to mesh distortion.Meanwhile,it is also shown that this method can keep high precision even under coarse mesh and avoid the so-called Poisson-locking phenomenon effectively.

关 键 词：线弹性问题 四边形面积坐标方法 杂交应力有限元 泊松闭锁现象 

分 类 号：O241.82[理学—计算数学]