Computer Algebra Investigation of Equivalence in 4-node Plane Stress/Strain Finite Elements

In this investigation, with the aid of computer algebra, a diagram showing equivalences between finite element formulations or techniques, among which including two newly formulated hybrid mixed field principles, in a 4-node plane stress/strain element was obtained. In the investigation, some known equivalence relations were confirmed; some new equivalence relations, mainly between the hybrid mixed field formulations and the others, were detected. The investigation shows that with computer algebra it is much easier to conduct parameter study in simple elements and it might provide a powerful tool for exploring more complex equivalence relations in higher order elements. It is observed from the investigation that if a finite element technique is hard to fit in a conventional variational principle, it might have a counterpart in a properly modified variational principle. The obtained equivalence diagram might provide information for establishing a more generally valid mathematical principle or theorem.