Digital Nomenclature Code for Topology and Kinematics of Finite Elements Based on the Absolute Nodal Co-Ordinate Formulation

Abstract

The role of the absolute nodal co-ordinate formulation (ANCF) within the finite-element method is studied. To this end, the topological and kinematic structure of an arbitrary finite element is represented by a multi-digit code that reflects the topological structure of the element. The multi-digit code of an element is based on dimension d, the number of nodes n, the number of scalar co-ordinates per node c, and a multiplier m. The multiplier is needed in the nomenclature to describe a vectorization procedure that allows transforming a conventional finite element to an ANCF element. The introduced classification procedure enables the description of previously undefined finite elements. The code allows for a systematic enumeration of finite elements and reflects interrelations and transformations between them. A universal procedure can be proposed to construct the geometrical and structural matrices of a finite element by its code dncm. The elements of such a procedure are discussed in the article.