Extended Digital Nomenclature Code for Description of Complex Finite Elements and Generation of New Elements

Abstract

In recent research (Dmitrochenko and Mikkola, 2011), a digital nomenclature code in the form dncm was proposed for a systematic classification of topology of finite elements (given by the dimension d and the number of nodes n ) and their kinematics (described by the number of coordinates per node c and a so-called vectorization multiplier m ). The digital code allows the kinematics of simple finite elements to be enumerated by a few integers; allowing the elements to be reconstructed without the need of their graphical representations. More complicated elements possess a set of nodal coordinates X that formally correspond to some code dncm ; however, their kinematics require that an auxiliary element ( d η ς μ) to be created using different topology η and kinematics ς, μ with a different set of nodal coordinates . Then, a transformation T toward coordinates X leads to an element systematically denoted by code , which is proposed in the current paper and called the extended digital nomenclature code. Examples of such elements are planar triangles and rectangles with drilling degrees of freedom, quadrilaterals with extra shape functions, discrete Kirchhoff triangles and other elements, including rigid bodies. It is possible to construct a universal procedure, which is capable of generating the necessary structural matrices of a finite element by its extended code dncm ( d η ς μ){…}. By changing digits d , n , c , m , η, ς, μ it is possible to find new elements, some of those are proposed in the current paper.

Keywords:

• Classification
• Digital nomenclature code
• Finite elements
• Kinematics
• Topology

ACKNOWLEDGMENT

The research is supported by the Academy of Finland, project 122899.