广义协调六结点平面曲边单元研究

THE STUDY ON GENERALIZED CONFORMING 6-NODE CURVED QUADRILATERAL ELEMENT

主要运用广义协调原理,针对计算平面曲边单元的有限元算法进行了研究,并且利用点、周混合协调条件构造了三种高性能六结点曲边单元。第一、二种单元在平面直角坐标内分别采用解析试函数和完全三次多项式构造,第三种单元在六结点等参单元Q6的基础上附加广义协调泡状位移而成。这三种单元均能通过强式分片试验,并且显示了良好的计算精度和抗畸变能力。

Three 6-node curved quadrilateral elements, ATFM6, M6 and Q6λ10, are obtained based on generalized conforming principle. Displacement field in plane Cartesian coordinate system of elements ATFM6 and M6 are constructed from analytical trial functions （ATF） and complete cubic polynomial, respectively. Element Q6λ10 is obtained by adding ten generalized bubble displacement terms to compatible isoparametric element Q6. All the three elements can pass patch test under arbitrary curved quadrilateral mesh. Numerical experiments show that they have excellent accuracy and insensitivity to geometric distortion.