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

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.

[1]  A. Mikkola,et al.  A formal procedure and invariants of a transition from conventional finite elements to the absolute nodal coordinate formulation , 2009 .

[2]  H. Adelman,et al.  Inclusion of Transverse Shear Deformation in Finite Element Displacement Formulations , 1974 .

[3]  A. Mikkola,et al.  Two Simple Triangular Plate Elements Based on the Absolute Nodal Coordinate Formulation , 2008 .

[4]  Bernhard Specht,et al.  Modified shape functions for the three‐node plate bending element passing the patch test , 1988 .

[5]  Wan-Suk Yoo,et al.  A New Thin Spatial Beam Element Using the Absolute Nodal Coordinates: Application to a Rotating Strip , 2005 .

[6]  R. Y. Yakoub,et al.  Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory , 2001 .

[7]  W. Yoo,et al.  Helicoseir as Shape of a Rotating String (II): 3D Theory and Simulation Using ANCF , 2006 .

[8]  Aki Mikkola,et al.  Shear Correction for Thin Plate Finite Elements Based on the Absolute Nodal Coordinate Formulation , 2009 .

[9]  S. von Dombrowski,et al.  Analysis of Large Flexible Body Deformation in Multibody Systems Using Absolute Coordinates , 2002 .

[10]  A. Shabana,et al.  EFFICIENT INTEGRATION OF THE ELASTIC FORCES AND THIN THREE-DIMENSIONAL BEAM ELEMENTS IN THE ABSOLUTE NODAL COORDINATE FORMULATION , 2005 .

[11]  Ahmed A. Shabana,et al.  APPLICATION OF THE ABSOLUTE NODAL CO-ORDINATE FORMULATION TO MULTIBODY SYSTEM DYNAMICS , 1997 .

[12]  Oleg Dmitrochenko,et al.  Generalization of Plate Finite Elements for Absolute Nodal Coordinate Formulation , 2003 .

[13]  Aki Mikkola,et al.  A Linear Beam Finite Element Based on the Absolute Nodal Coordinate Formulation , 2005 .

[14]  L S D Morley,et al.  The constant-moment plate-bending element , 1971 .

[15]  A. Shabana.  An Absolute Nodal Coordinate Formulation for the Large Rotation and Deformation Analysis of Flexible Bodies , 1996 .

[16]  A. Mikkola,et al.  Inclusion of Transverse Shear Deformation in a Beam Element Based on the Absolute Nodal Coordinate Formulation , 2009 .

[17]  F. Bogner,et al.  The generation of interelement compatible stiffness and mass matrices by the use of interpolation formulae , 1965 .

[18]  A. Shabana,et al.  A new plate element based on the absolute nodal coordinate formulation , 2001 .

[19]  Ahmed A. Shabana,et al.  Analysis of Thin Plate Structures Using the Absolute Nodal Coordinate Formulation , 2005 .

[20]  Mohamed A. Omar,et al.  A TWO-DIMENSIONAL SHEAR DEFORMABLE BEAM FOR LARGE ROTATION AND DEFORMATION PROBLEMS , 2001 .

[21]  A. Shabana.  Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formulation , 1997 .