A rational finite element method based on the absolute nodal coordinate formulation

Nonlinear Dynamics

Volumn 58, Issue 3, 2009, Pages 565-572

  Sanborn, Graham G ^a   Shabana, Ahmed A ^a  

^a University of Illinois at Chicago   (United States)

Author keywords

Absolute nodal coordinate formulation; B spline; Isogeometric analysis; NURBS; Rational finite element method

Indexed keywords

ABSOLUTE NODAL COORDINATE FORMULATION; B-SPLINE; B-SPLINE REPRESENTATION; CO-ORDINATE TRANSFORMATION; COMPLEX GEOMETRIES; COMPLEX SHAPES; CUBIC BEZIER CURVE; END POINTS; FINITE ELEMENT; FINITE ELEMENT FORMULATIONS; GRADIENT VECTORS; NODAL POINTS; NODAL POSITIONS; NONLINEAR DYNAMIC EQUATIONS; NURBS CURVES; PARAMETERIZED; RATIONAL POLYNOMIAL; SHAPE FUNCTIONS;

COMPUTATIONAL GEOMETRY; COMPUTATIONAL METHODS; COMPUTER AIDED ANALYSIS; COMPUTER AIDED DESIGN; COMPUTER AIDED SOFTWARE ENGINEERING; COMPUTER CONTROL; COMPUTER CRIME; EQUATIONS OF MOTION; FUNCTION EVALUATION; GRAPH THEORY; NONLINEAR EQUATIONS; SPLINES;

FINITE ELEMENT METHOD;

EID: 70450241066     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-009-9501-4     Document Type: Article

References (16)

1. Piegl, L., Tiller, W.: The NURBS Book, 2nd edn. Springer, New York (1997)
2. Dierckx, P.: Curve and Surface Fitting with Splines. Oxford University Press, New York (1993)
3. Farin, G.: Curves and Surfaces for CAGD, A Practical Guide, 5th edn. Morgan Kaufmann, San Francisco (1999)
4. Crisfield, M.A.: Nonlinear Finite Element Analysis of Solids and Structures, vol. 1: Essentials. Wiley, New York (1991)
5. Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method for Solid and Structural Mechanics, 6th edn. Butterworth Heinemann, London (2005)
6. Bazilevs, Y., Calo, V.M., Cottrell, J.A., Evans, J., Hughes, T.J.R., Lipton, S., Scott, M.A., Sederberg, T.W.: Isogeometric analysis: toward unification of computer aided design and finite element analysis. In: Papadrakakis, M., Topping, B.H.V. (eds.) Trends in Engineering Computational Technology. Saxe-Coburg, Stirlingshire (2008)
7. J.A. Cottrell T.J.R. Hughes A. Reali 2007 Studies of refinement and continuity in the isogeometric analysis Comput. Methods Appl. Mech. Eng. 196 4160 4183 10.1016/j.cma.2007.04.007 2361475 (Pubitemid 47201738)
8. Sanborn, G.G., Shabana, A.A.: Relationship between B-splines, NURBS, and the finite element absolute nodal coordinate formulation in our document. Technical report #MBS08-5-UIC, UIC, Department of Mechanical Engineering, University of Illinois at Chicago (2008)
9. Shabana, A.A.: An absolute nodal coordinate formulation for the large rotation and deformation analysis of flexible bodies. Technical report #MBS96-1-UIC, Department of Mechanical Engineering, University of Illinois at Chicago (1996)
10. Shabana, A.A.: Dynamics of Multibody Systems, 3rd edn. Cambridge University Press, Cambridge (2005)
11. Shabana, A.A.: Computational Continuum Mechanics. Cambridge University Press, Cambridge (2008)
12. O.N. Dmitrochenko D.Y. Pogorelov 2003 Generalization of plate finite elements for absolute nodal coordinate formulation Multibody Syst. Dyn. 10 1 17 43 1137.74435 10.1023/A:1024553708730
13. D. Garcia-Vallejo J. Mayo J.L. Escalona J. Dominguez 2004 Efficient evaluation of the elastic forces and the Jacobian in the absolute nodal coordinate formulation Nonlinear Dyn. 35 4 313 329 1068.74517 10.1023/B:NODY.0000027747.41604.20
14. J. Gerstmayr A.A. Shabana 2006 Analysis of thin beams and cables using the absolute nodal coordinate formulation Nonlinear Dyn. 45 109 130 1138.74391 10.1007/s11071-006-1856-1 (Pubitemid 44048452)
15. A.A. Shabana A.M. Mikkola 2003 Use of the finite element absolute nodal coordinate formulation in modeling slope discontinuity ASME J. Mech. Des. 125 2 342 350 10.1115/1.1564569
16. W.S. Yoo J.H. Lee S.J. Park J.H. Sohn D. Pogorelov O. Dimitrochenko 2004 Large deflection analysis of a thin plate: computer simulation and experiment Multibody Syst. Dyn. 11 2 185 208 1143.74339 10.1023/B:MUBO.0000025415.73019.bb