用广义协调方法推导的平面四节点等参单元

A 4-NODE ISOPARAMETRIC ELEMENT FORMULATED WITH GENERALIZED CONFORMING CONDITIONS

对平面四节点Q4单元采用优选的广义协调条件进行推导,将广义协调理论的应用拓展到最基本的平面问题单元。基于Q6以及QM6中基于内部参数的二次附加位移场,在Q4单元基础上增加满足广义协调条件的内参位移场,从而构造了一个满足广义协调条件的平面四节点等参元GQM6。数值算例表明,虽然采用了相同次数的位移场,但GQM6单元中采用的广义协调条件较QM6中采用的数值积分方法,可以进一步放松单元边界的约束,从而使单元的性能进一步提高,尤其在抗网格畸变能力方面。研究表明,将广义协调理论与一些传统单元进行深入融合仍然有着重要价值。

By using optimized generalized conforming conditions to formulate the plane 4-node element Q4, it is proved that the generalized conforming theory can be expanded to the most fundamental isoparametric elements. Based on the second-order additional displacement field of Q6 and QM6, a new form of additional displacement field was overlaid on Q4 to develop a new element GQM6, which is still second-order and formulated with generalized conforming theory. The numerical results show that the generalized conforming conditions can present more relaxed constraints at element sides than numerical integrals used in QM6, thus the new element GQM6 can exhibit better properties especially on the resistances of mesh distortion. The research shows that it i’s still valuable to combine the generalized conforming theory with those traditional finite elements deeply.