Finite Element Analysis of a Pipe Elbow Weldment Creep-Fracture Problem Using an Extremely Accurate 27-Node Tri-Quadratic Shell and Solid Element Formulation

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)^2, the same as the error of a hexa-8 element formulation. The symbol (^) denotes raising the preceding quantity to a power of the subsequent quantity. To achieve an accuracy with a truncation error of h(0)^3, 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 this paper, we investigate the applicability of the fully quadratic hexa-27 elements to three problems of interest to the pressure vessels and piping community: (1) The shell-element-based analysis of a barrel vault. (2) The solid-element-based analysis of a welded pipe elbow with a longitudinal surface crack in one of its weldments. (3) The solid-element-based analysis of the elastic bending of a simple cantilever beam. 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.