Two Simple Triangular Plate Elements Based on the Absolute Nodal Coordinate Formulation

In this paper, two triangular plate elements based on the absolute nodal coordinate formulation (ANCF) are introduced. Triangular elements employ the Kirchhoff plate theory and can, accordingly, be used in thin plate problems. As usual in ANCF, the introduced elements can exactly describe arbitrary rigid body motion when their mass matrices are constant. Previous plate developments in the absolute nodal coordinate formulation have focused on rectangular elements that are difficult to use when arbitrary meshes need to be described. The elements introduced in this study have overcome this problem and represent an important addition to the absolute nodal coordinate formulation. The two elements introduced are based on Specht's and Morley's shape functions, previously used in conventional finite element formulations. The numerical solutions of these elements are compared with previously proposed rectangular finite element and analytical results.

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

[2]  J. Z. Zhu,et al.  The finite element method , 1977 .

[3]  J. W. Humberston.  Classical mechanics , 1980, Nature.

[4]  C. W. Gear,et al.  Automatic integration of Euler-Lagrange equations with constraints , 1985 .

[5]  D. A. Dunavant.  High degree efficient symmetrical Gaussian quadrature rules for the triangle , 1985 .

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

[7]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[8]  K. Bathe.  Finite Element Procedures , 1995 .

[9]  Dmitry Pogorelov,et al.  Some Developments in Computational Techniques in Modeling Advanced Mechanical Systems , 1997 .

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

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

[12]  A. Shabana.  Computer Implementation of the Absolute Nodal Coordinate Formulation for Flexible Multibody Dynamics , 1998 .

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

[14]  Modeling of Slope Discontinuities in Flexible Body Dynamics Using the Finite Element Method , 2002, DAC 2002.

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

[16]  A. Mikkola,et al.  Description of Elastic Forces in Absolute Nodal Coordinate Formulation , 2003 .

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

[18]  Johannes Gerstmayr,et al.  Analysis of higher and lower order elements for the absolute nodal coordinate formulation , 2005 .

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

[20]  Daniel García-Vallejo,et al.  Modeling of Belt-Drives Using a Large Deformation Finite Element Formulation , 2006 .

[21]  Wan-Suk Yoo,et al.  Verification of Absolute Nodal Coordinate Formulation in Flexible Multibody Dynamics via Physical Experiments of Large Deformation Problems , 2006 .

[22]  A. Mikkola,et al.  A new locking-free shear deformable finite element based on absolute nodal coordinates , 2007 .