Comparisons of Conventional, SRI, EAS and Hybrid-Stress Plane Q4 and Q9 Finite Element Models in Displacement and Energy Norms

Advanced finite element models have been being pursued for several decades. For plane models, the popularly employed formulations include the selectively reduced integration, enhanced assumed strain, hybrid/mixed methods, stabilization methods, among others. The accuracies of the advanced finite element models with respect to the standard element models are often demonstrated by some popular numerical tests in which displacement and stress components at a few selected points are benchmarked. The more comprehensive but laborious means of assessing the accuracy by computing the relative errors in displacement norm (Sobolev norm of order zero) and energy norm are less popularly employed. In this paper, these norms of the standard and some advanced 4-node and 9-node quadrilateral finite element models for a number of tests are computed and reported. In contrast to the common perception, the advanced models are not always more accurate than the standard ones. The discussions in this paper can be helpful for the understanding and usage of the numerical benchmark tests.