Multibody System Dynamics

, Volume 29, Issue 3, pp 255–269 | Cite as

Three- and four-noded planar elements using absolute nodal coordinate formulation

  • Alexander Olshevskiy
  • Oleg Dmitrochenko
  • Changwan Kim


This paper investigates two new types of planar finite elements containing three and four nodes. These elements are the reduced forms of the spatial plate elements employing the absolute nodal coordinate approach. Elements of the first type use translations of nodes and global slopes as nodal coordinates and have 18 and 24 degrees of freedom. The slopes facilitate the prevention of the shear locking effect in bending problems. Furthermore, the slopes accurately describe the deformed shape of the elements. Triangular and quadrilateral elements of the second type use translational degrees of freedom only and, therefore, can be utilized successfully in problems without bending. These simple elements with 6 and 8 degrees of freedom are identical to the elements used in conventional formulation of the finite element method from the kinematical point of view. Similarly to the famous problem called “flying spaghetti” which is used often as a benchmark for beam elements, a kind of “flying lasagna” is simulated for the planar elements. Numerical results of simulations are presented.


Finite elements Absolute nodal coordinate formulation Flexible multibody system dynamics Large displacements 



This paper was supported by Konkuk University in 2012.


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Alexander Olshevskiy
    • 1
  • Oleg Dmitrochenko
    • 2
  • Changwan Kim
    • 1
  1. 1.School of Mechanical EngineeringKonkuk UniversitySeoulKorea
  2. 2.Department of Mechanical EngineeringLappeenranta University of TechnologyLappeenrantaFinland

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