A corotational finite element formulation for the analysis of planar beams

Communications in Numerical Methods in Engineering

Volumn 21, Issue 10, 2005, Pages 553-570

  Urthaler, Y ^a   Reddy, J N ^a  

^a Texas AandM University   (United States)

Author keywords

Beams; Corotational formulation; Finite element analysis; Locking free elements; Shear deformable beams

Indexed keywords

COMPUTATIONAL GEOMETRY; FINITE ELEMENT METHOD; INTERPOLATION; ITERATIVE METHODS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR EQUATIONS; SHEAR DEFORMATION; STIFFNESS MATRIX; STRAIN MEASUREMENT; STRUCTURAL ANALYSIS; VECTORS;

COROTATIONAL FORMULATION; EULER-BERNOULLI BEAM; LOCKING-FREE ELEMENTS; NEWTON-RAPHSON METHOD; NON-LINEAR EQUILIBRIUM EQUATION; SHEAR DEFORMABLE BEAMS;

CANTILEVER BEAMS;

FINITE ELEMENT METHOD;

EID: 26844572161     PISSN: 10698299     EISSN: None     Source Type: Journal    
DOI: 10.1002/cnm.773     Document Type: Article

References (35)

1. Martinez CE, Urthaler Y, Goncalves R. Nonlinear finite element analysis of submarine pipelines during installation. Proceedings of the ASME Pressure Vessels and Piping Conference 1999; 385:187-194.
2. Crisfield MA, Yazdchi M. Non-linear dynamic behaviour of flexible marine pipes and risers. International Journal for Numerical Methods in Engineering 2002; 54:1265-1308.
3. Felippa CA, Haugen B. A unified formulation of small-strain corotational finite elements: I. Theory. Computer Methods in Applied Mechanics and Engineering 2005; 194:2285-2335.
4. Martin HC. On the derivation of stiffness matrices for the analysis of large deflection and stability problems. Proceedings of the Conference on Matrix Methods in Structural Mechanics 1965; 697-716.
5. Ebner AM, Uciferro JJ. A theoretical and numerical comparison of elastic nonlinear finite element methods. Computers and Structures 1972; 2:1043-1061.
6. Oran C. Tangent stiffness in plane frames. Journal of the Structural Division 1973; 99:973-985.
7. Oran C, Kassimali A. Large deformation of framed structures under static and dynamic loads. Computers and Structures 1976; 6:539-547.
8. Hsiao KM, Hou FY. Nonlinear finite element analysis of elastic frames. Computers and Structures 1987; 26: 693-701.
9. Bathe K, Bolourchi S. Large displacement analysis of three-dimensional beam structures. International Journal for Numerical Methods in Engineering 1979; 14:961-986.
10. Gattass M, Abel JF. Equilibrium considerations of the updated Lagrangian formulation of beam-columns with natural concepts. International Journal for Numerical Methods in Engineering 1987; 24:2119-2141.
11. Guo Ying Q, Batoz J. Displacement fields and large deformation analysis of 3-D beams. Lecture Notes in Engineering 1987; 406-417.
12. Behdinan K, Stylianou MC, Tabarrok B. Static and dynamic analysis of flexible beams: a consistent updated Lagrangian formulation. Transactions of the Canadian Society for Mechanical Engineering 1997; 21:141-177.
13. Pai PF, Anderson TJ, Wheater EA. Large-deformation tests and total-Lagrangian finite-element analyses of flexible beams. International Journal of Solids and Structures 2000; 37:2951-2980.
14. Argyris JH. Recent advances in matrix methods of structural analysis. In Progress in Aeronautical Sciences, Ferri A, Küchemann D, Smolderen J (eds). Pergamon Press: New York, 1964.
15. Belytschko T, Hsieh BJ. Non-linear transient finite element analysis with convected co-ordinates. International Journal for Numerical Methods in Engineering 1973; 7:255-271.
16. Argyris JH, Balmer H, Doltsinis J, Dunne PC, Haase M, Mullerand M, Scharpf DW. Finite element method-the natural approach. Computer Methods in Applied Mechanics and Engineering 1979; 17/18:1-106.
17. Belytschko T, Glaurn LW. Applications of higher order corotational stretch theories to nonlinear finite element analysis. Computers and Structures 1979; 10:175-182.
18. Crisfield MA, Cole G. Co-rotational beam elements for two- and three-dimensional non-linear analysis. Proceedings of the IUTAM/IACM Symposium on Discretization Methods in Structural Mechanics 1989; 4:115-124.
19. Crisfield MA. A consistent co-rotational formulation for non-linear, three-dimensional, beam-elements. Computer Methods in Applied Mechanics and Engineering 1990; 81:131-150.
20. Iura M, Suetake Y. Accuracy of co-rotational formulation for 3-D Timoshenko's beam. Computer Modelling in Engineering and Sciences 2003; 4:249-258.
21. Martinez CE. A theoretical and numerical evaluation of nonlinear beam elements. M.Sc. Thesis, Massachusetts Institute of Technology, Boston, MA, 1997.
22. Simo JC. Finite strain beam formulation: the three-dimensional dynamic problem-Part I. Computer Methods in Applied Mechanics and Engineering 1985; 49:55-70.
23. Yang TY. Matrix displacement solution to elastica problems of beams and frames. International Journal of Solids and Structures 1973; 9:829-842.
24. Reddy JN. An Introduction to Nonlinear Finite Element Analysis. Oxford University Press: Oxford, U.K., 2004.
25. Reddy JN. An Introduction to the Finite Element Method (3rd edn). McGraw-Hill: New York, 2006.
26. Wempner G. Finite elements, finite rotations and small strains of flexible shells. International Journal of Solids and Structures 1969; 5:117-153.
27. Crisfield MA. Non-Linear Finite Element Analysis of Solids and Structures, Volume 1: Essentials. Wiley: New York, 1991.
28. Timoshenko SP. On the correction for shear of the differential equation for transverse vibrations of prismatic bars. Philosophical Magazine 1921; 41:744-746.
29. Heyliger PR, Reddy JN. A higher-order beam finite element for bending and vibration problems. Journal of Sound and Vibration 1988; 126:309-326.
30. Reddy JN. On locking free shear deformable finite elements. Computer Methods in Applied Mechanics and Engineering 1997; 149:113-132.
31. Reddy JN. Unified finite elements based on the classical and shear deformation theories of beams and axisymmetric circular plates. Communications in Numerical Methods in Engineering 1997; 13:495-510.
32. Reddy JN. Energy Principles and Variational Methods in Applied Mechanics (2nd edn). Wiley: New York, 2002.
33. Bisshop KE, Drucker DC. Large deflections of cantilever beams. Quarterly of Applied Mathematics 1945; 3:272-275.
34. Rohde FV. Large deflections of a cantilever beam with uniformly distributed load. Quarterly of Applied Mathematics 1953; 11:337-338.
35. Wang CM, Reddy JN, Lee KH. Shear Deformable Beams and Plates: Relationships with Classical Solutions. Elsevier: Oxford, U.K., 2000.