Definition of ANCF Finite Elements

Since the absolute nodal coordinate formulation (ANCF) was introduced, a large number of fully parametrized and gradient deficient finite elements were developed. Some of the finite elements (FE) proposed do not fall into the ANCF category, and for this reason, this technical brief describes the general requirements for ANCF finite elements. As discussed in this paper, some of the conventional isoparametric finite elements can describe arbitrary rigid body displacements and can be used with a nonincremental solution procedure. Nonetheless, these isoparametric elements, particularly the ones that employ position coordinates only, are of the $C0$ type and do not ensure the continuity of the position vector gradients. It is also shown that the position vector gradient continuity conditions can be described using homogeneous algebraic equations, and such conditions are different from those conditions that govern the displacement vector gradients. The use of the displacement vector gradients as nodal coordinates does not allow for an isoparametric representation that accounts for both the initial geometry and displacements using one kinematic description, can make the element assembly more difficult, and can complicate imposing linear algebraic constraint equations at a preprocessing stage. Understanding the ANCF geometric description will allow for the development of new mechanics-based computer-aided design (CAD)/analysis systems as briefly discussed in this paper.