简明有效的四结点多变量协调等参元

Concise and efficient four node multi variable conforming isoparametric element

应用建立多变量有限元模型的统一列式，构造了平面四结点多变量协调等参元ＭＱ４ ，其简单性与单变量位移型协调等参元Ｑ４ 类似，计算精度却有了很大提高。文中结合若干典型算例对单元性能进行了考核，数值结果表明，在各种网格情况下，多变量协调等参元ＭＱ４ 的计算精度均明显高于普通等参元Ｑ４ 的计算精度，尤其是在规则网格下应力精度达到了著名的含两个内自由度的非协调等参元Ｑ６ 、ＱＭ６ 、ＱＭＭ６ 等的计算精度，对不规则网格也能保持良好的性态。

A plane four node multi variable conforming isoparametric element MQ 4 was construc ted by the uniform formulation of multi variable finite element models. It is simple and similar as standard conforming isoparametric element Q 4. And its calculation precision is improved very much. Several numerical examples were given to examine the element′s performances. It is indicated that the calculation precision of this multi varibale conforming element MQ 4 is much higher than that of standard conforming isoparametric element Q 4 in regular or irregular mesh cases. Its precision of stress in regular mesh cases reaches the same of famous non conforming isoparametric elements such as Q 6、Q M6 、Q MM6 And good performances are also presented by element MQ 4 in irregular mesh cases.