基于Cosserat理论的广义协调元法  

A generalized conforming element based on the Cosserat theory

作　　者：邢本东[1] 张若京[1] 

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《计算力学学报》2011年第3期350-354,共5页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(10772136);教育部博士点基金(20060247016);上海市重点学科建设(B302)资助项目

摘　　要：首次将广义协调元理论与Cosserat理论相结合,构造了一个基于Cosserat理论的平面四节点广义协调等参元。依据常应力与线性应力下的广义协调条件,推导了广义协调位移,进而得到有限元列式。利用广义协调元,一方面克服了协调元过于刚硬的缺点,另一方面消除了非协调元不一定收敛的弱点。分析了带有圆孔的应力集中问题,可以看出,该单元的数值精度准确和计算效率高。A generalized conforming element is developed to deal with the problems considering the Cosserat theory in this paper.It is a 4-nodes element for the Cosserat plane problems.According to the generalized conforming condition of constant stress and linear stress,the generalized conforming displacement is deduced,and the finite element equation is obtained.The generalized conforming element can overcome the weakness of the compatible and incompatible element.The stress concentration around a central circular hole in uni-axial tension is used to check the property of the element.The results show that the element has high efficiency and good accuracy.

关 键 词：COSSERAT理论 广义协调条件 广义协调等参元 

分 类 号：O242.21[理学—计算数学]