摘要
四边形面积坐标克服了等参坐标的一些缺点，如一般等参坐标不能用直角坐标的有限项来表示，单元刚度矩阵通常得不到积分显式等.同时四边形的面积坐标体系也可以与三角形面积坐标相互沟通，为四边形和三角形两类不同单元局部坐标格式的统一，提供了有效手段.本文采用四边形面积坐标体系，应用广义的协调方法，在文献［1］的基础上构造出一个四结点四边形平面问题单元MAGQ4.算例表明，该单元是收敛、可靠而且具有较好精度的平面问题四边形单元.
The quadrilateral area coorrdinates have solved some problems occurred in the is oparametric coordinates. In general, the isoparametric coordinates can not be exp ressed by polynomial in fin ite terms of Cartesian coordinates and the stiffness matrix of quadrilateral ele ment constructed by isoparametric coordinates has to be evaluated by numerical i ntegration instead of exact integration. In this paper, based reference ［1］ and combined with the generalized compatibility conditions, the area coordina tes in quadrilateral were used to construct a new fournode quadrilateral eleme nt for plane problem. The numerical results of two examples show that the present element named MAGQ4 can pass patch test and is a convergent, reliable, and accurate quadrilateral plane element.
出处
《中国矿业大学学报》
EI
CAS
CSCD
北大核心
2000年第3期310-313,共4页
Journal of China University of Mining & Technology
基金
国家自然科学基金!(59878022)
关键词
有限单元
四边形面积坐标系
广义协调
膜单元
finite element
quadrilateral area coordinates
generalized c ompatibility
membrane element
