In most finite-element-analysis codes, accuracy is achieved through the use of the hexahedron hexa-20 elements (a node at each of the 8 corners and 12 edges of a brick element). Unfortunately, without an additional node in the center of each of the element’s 6 faces, nor in the center of the hexa, the hexa-20 elements are not fully quadratic such that its truncation error remains at h(0), the same as the error of a hexa-8 element formulation.
To achieve an accuracy with a truncation error of h3(0), we need the fully-quadratic hexa-27 formulation. A competitor of the hexa-27 element in the early days was the so-called serendipity cubic hexa-32 solid elements (see Ahmad, Irons, and Zienkiewicz, Int. J. Numer. Methods in Eng., 2:419-451 (1970) ). The hexa-32 elements, unfortunately, also suffer from the same lack of accuracy syndrome as the hexa20’s.
In recent work, we have developed methods to test the errors and the rate of convergence in FEA [2,3,4].
In this paper, we propose a new metric for determining the quality of isoparametric elements a priori. Significance of the highly accurate hexa-27 formulation and a comparison of its results with similar solutions using ABAQUS hexa-20 elements, are presented and discussed. Guidelines are proposed for selection of better elements.