基于加权残量法的多变量等参元简明列式及其应用

根据作者提出的建立多变量有限元模型的系统化方法，应用加权残量法的基本原理，给出了建立多变量等参元模型的简明列式。然后应用该列式，构造了简明有效的平面四结点多变量等参元MQ4和MQ5前者不含内部自由度，后者含有内部自由度。文中结合若干典型算例对所构造的单元性能进行了考核，并与若干典型协调与非协调等参元的数值结果进行了比较。数值结果表明，无论是在规则网格还是在不规则网格情况下，本文构造的多变量等参元，不仅能通过分片检验的要求，而且表现出了良好的性能。

A concise formulation of multivariable isoparametric elements based on weighted residual approach and its applications

The research on isoparametric elements make significant sense in the development of finite element method. A concise formulation of multivariable isoparametric elements was present based on the rational principle of residual approach and the systematic method of constructing multivariable finite elements suggested by Shi Baojun. Then two concise and efficient plane four-node multivariable isoparametric elements MQ-4 and MQ-5 were constructed by this formulation. The former one, i.e. element MQ-4, does not contain internal degree of freedom. The later one, i.e. element MQ-5, contains one internal degree of freedom. The elements performances were examined by some typical numerical examples. Their numerical results were compared with those of other typical conforming and nonconforming isoparametric elements. The numerical results show that the multivariable isoparametric elements present in this paper can pass the patch test requirements and also possess high performance either in the case of regular mesh or that of irregular mesh.