Investigation of finite element relations

In structural mechanics, finite elements were developed from different bases. Investigation of equivalence between finite elements with different bases has been an interesting research topic for many years and the investigation is believed helpful to understand and more efficiently use various formulations. As mentioned earlier, finite element expressions are large and hard to manipulate manually, especially for higher-order elements. In [14,15], with the aid of symbolic computational software Maple, relations between different finite element formulations or techniques are closely investigated with respect to simple elements from different element classes, by adopting the strategy of comparing element stiffness matrices. Quite several equivalence diagrams are obtained.