A High-Accuracy Approach to Finite Element Analysis Using the Hexa 27-Node Element

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 h2(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) [1]). The hexa-32 elements, unfortunately, also suffer from the same lack of accuracy syndrome as the hexa20’s. In this paper, we investigate the accuracy of various elements described in the literature including the fully quadratic hexa-27 elements to a shell problem of interest to the pressure vessels and piping community, viz. the shell-element-based analysis of a barrel vault. Significance of the highly accurate hexa-27 formulation and a comparison of its results with similar solutions using ABAQUS hexa-8, and hexa-20 elements, are presented and discussed. Guidelines are proposed for selection of better elements.