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.
ShabanaA.A.Definition of the slopes and the finite element absolute nodal coordinate formulation. Multibody Syst. Dyn., 1997, 1(3), 339–348.
2.
EscalonaJ.L.HussienH.ShabanaA.A.Application of the absolute nodal coordinate formulation to multibody system dynamics. J. Sound Vibr., 1998, 214, 833–851.
3.
ShabanaA.A.YakoubR.Y.Three dimensional absolute nodal coordinate formulation for beam elements: Theory. J. Mech. Des., 2001, 123, 606–621.
4.
DmitrochenkO.N.PogorelovD.Yu., Generalization of plate finite elements for absolute nodal coordinate formulation. Multibody Syst. Dyn., 10(1), 2003, 17–43.
5.
OmarM.A.ShabanaA.A.A two-dimensional shear deformation beam for large rotation and deformation. J. Sound Vibr., 2001, 243(3), 565–576.
6.
DmitrochenkoO.MikkolaA.A formal procedure and invariants of a transition from conventional finite elements to the absolute nodal coordinate formulation. Multibody Syst. Dyn., 2009, 22, 323–339.
7.
MorleyL.S.D.The constant-moment plate-bending element. J. Strain Anal., 1971, 6(1), 2024.
8.
GerstmayrJ.ShabanaA.A.Efficient integration of the elastic forces and thin three-dimensional beam elements in the absolute nodal coordinate formulation. In Proceedings of the Multibody Dynamics 2005 ECCOMAS Conference, Madrid, Spain, 21–24 June 2005.
9.
ShabanaA.A.An absolute nodal coordinate formulation for the large rotation and large deformation analysis of flexible bodies. Report MBS96-1-UIC, Department of Mechanical Engineering, University of Illinois at Chicago, 1996.
10.
SpechtB.Modified shape functions for the three node plate bending element passing the patch test. Int. J. Numer. Methods Engng.1988, 26, 705–715.
11.
DmitrochenkoO.MikkolaA.Two simple triangular plate elements based on the absolute nodal coordinate formulation. J. Comput. Nonlinear Dyn., 2008, 3(4), 041012-1-8.
12.
MeloshR.J.Structural analysis of solids. ASCE Struct. J.1963, 4, 205–223.
13.
DufvaK.ShabanaA.A.Use of the absolute nodal coordinate formulation in the analysis of thin plate structures. Technical Report # MBS05-1-UIC, Department of Mechanical Engineering, University of Illinois at Chicago, 2005.
14.
DmitrochenkoO.MikkolaA.New finite elements in absolute nodal coordinate formulation based on an analysis of a geometric classification. In Proceedings of the EUROMECH Colloquium 515 on Advanced applications and perspectives of multibody system dynamics, Blagoevgrad, Bulgaria, 13–16 July 2010, 2 pp.
15.
OlshevskiyA.A.DmitrochenkoO.KimC.Three- and four-noded planar elements using absolute nodal coordinate formulation. In Proceedings of the 1st Joint International Conference on Multibody system dynamics, Lappeenranta, Finland, 25–27 May 2010, 9 pp.
16.
MikkolaA.M.ShabanaA.A.A new plate element based on the absolute nodal coordinate formulation. J.Mech.Des., 2005, 127(4), 621–630.
17.
KerkkänenK.S.SopanenJ.T.MikkolaA.M.A linear beam finite element based on the absolute nodal coordinate formulation. J. Mech. Des., 2005, 127(4), 621–630.
18.
MatikainenM.DmitrochenkoO.MikkolaA.Thick ANCF elements of m-dimensional beams m2cm with different complexity c = 2…7 per node. In Proceedings of the 8th International Conference of Numerical analysis and applications of mathematics (ICNAAM-10), Rhodes, Greece, 19–25 September 2010, 8 pp.
19.
DmitrochenkoO.YooW.-S.PogorelovD.Helicoseir as shape of a rotating chain (II): 3D theory and simulation using ANCF. Multibody Syst. Dyn.2006, 15(2), Springer, 181–200.
20.
von DombrowskiS., Analysis of large flexible body deformation in multibody systems using absolute coordinates. Multibody Syst. Dyn.2002, 8, 409–432.
21.
YooW.-S.DmitrochenkoO.ParkS.-J.LimO.-K.A new thin spatial beam element using the absolute nodal coordinates: Application to a rotating strip. Mech. Based Des. Struct. Mach., 2005, 33(3-4), 399–422.
22.
NarayanaswamiR.AdelmanH.M.Inclusion of transverse shear deformation in finite element displacement formulations. AIAA J.1974, 12(11), 1613–1614.
23.
MikkolaA.DmitrochenkoO.MatikainenM.Inclusion of transverse shear deformation in a beam element based on the absolute nodal coordinate formulation. J. Comput. Nonlinear Dyn., 2009, 4(1), 011004-1-9.
24.
DmitrochenkoO.MikkolaA., Shear correction of a thin plate element in absolute nodal coordinates. In Proceedings of the 8th World Congress on Computational Mechanics (WCCM8) and 5th European Congress on Computitional methods in applications of science and engineering (ECCOMAS 2008), Venice, Italy, 30–4 June 2008, p. 127.
25.
DmitrochenkoO.MikkolaA.Shear correction for thin plate finite elements based on the absolute nodal coordinate formulation. In Proceedings of the ASME 2009 IDETC/CIE 2009, San Diego, California, USA, 30–02 August 2009, pp. 1–9.
26.
BognerF.K.FoxR.L.SchmitL.A.The generation of interelement-compatible stiffness and mass matrices by the use of interpolation formulae. In Proceedings of the 1st Conference on Matrix methods in structural mechanics, Wright Patterson Air Force Base, Ohio, October 1966, vol. AFFDITR-66-80, pp. 397–443.
27.
NachbagauerK.GerstmayrJ.SinwelA.S.IrschikH.A linear and quadratic planar finite element based on the absolute nodal coordinate formulation. In Proceedings of the 1st Joint International Conference on Multibody system dynamics, Lappeenranta, Finland, 25–27 May 2010, p.10.
