There has recently been great interest in the use of three-dimensional finite elements to study local stresses in the weld areas of complex (reinforced, overlapped) tubular joints. This paper examines displacement and stress solutions obtained for selected tubular joint configurations modeled with two such thick shell and brick elements. These solutions are compared, with the aid of an a-posteriori convergence (error) criteria, to those from a well known arid widely used thin shell element. It is concluded that the three-dimensional elements examined can behave very well in typical tubular joint problems. They, however, appear to suffer more instability in irregular mesh situations than do thin shell. The proposed error criteria seems to indicate well those areas where the thin shell approximation is most suspect.


For many years thin shell theory has served as a basis for studying stress concentration factors of tubular joints. With various thin shell finite element types, detailed parametric studies have been performed in the hope of obtaining information consistent enough to establish design curves. It is not the purpose here to review this great volume of past work, but instead to compare in the tubular joint context the behavior of one well established thin shell element with two versions of publicly available three-dimensional elements.

The approach selected is to first discuss the three-dimensional element formulations outlining their salient features. The results of a small test problem are then examined and observations made. An overview of an element residua}C basis for comparing solutions of predominately thin shell problems is presented in the section ERROR ANALYSIS. A short discussion on its potential for application to of three problems solved with both thick (compatible and incompatible) and thin shell elements are compared from the displacement, stress and residual error standpoints.


In this study, two types of three-dimensional isoparametric solid elements are used. One is an eight noded "brick" element. The other is a sixteen noded "thick-shell" element. As described in the following section, various "incompatible" modes are introduced into the stiffness formulations of these elements to improve their flexural behavior. Both the basic (compatible) and the incompatible versons of these elements are utilized in this study.

Element Formulations

The 8 and 16 noded isoparametric elements under consideration are shown in Figure 1. The global Cartesian coordinates are denoted as (X1, X2, X3) and the element local coordinates as (available in full paper), both right handed systems. The local coordinates range from -1 to +1 with (0,0,0) located at the centroid of the element. In the isoparametric family of elements, the local and global coordinates are related as follows (see for example Reference [1]):

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