A simple FEM formulation for large deflection 2D frame analysis based on position description

Computer Methods in Applied Mechanics and Engineering

Volumn 193, Issue 33-35, 2004, Pages 3541-3557

  Coda, H B ^a   Greco, M ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

2D frame analysis; FEM; Position description

Indexed keywords

DEFLECTION (STRUCTURES); ENGINEERING; FIBERS; FINITE ELEMENT METHOD; MECHANICS; PROBLEM SOLVING; STRAIN MEASUREMENT;

DISPLACEMENTS; FORMULATIONS; STRAIN DETERMINATION; STRAIN ENERGY;

COMPUTER AIDED ANALYSIS;

FINITE ELEMENT METHOD;

EID: 3142768383     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2004.01.005     Document Type: Article

References (42)

1. Bisshopp K.E. Drucker D.C. On the deflection of a cantilever beam Quart. Appl. Math. 3 1945 272-275
2. Mattiasson K. Numerical results from large deflection beam and frame problems analysed by means of elliptic integrals Internat. J. Numerical Methods Engrg. 17 1981 145-153
3. Chuchkeepsakul S. Bucharoen S. Huang T. Elastica of simple variable-arc-length beam subjected to end moment J. Engrg. Mech.--ASCE 121 1995 767-772
4. Simitses G.J. Giri J. Kounadis A.N. Non-linear analysis of portal frames Internat. J. Numerical Methods Engrg. 17 1981 123-132
5. Pai P.F. Palazotto A.N. Large-deformation analysis of flexible beams Internat. J. Solids and Structures 33 1996 1335-1353
6. Goto Y. Watanabe Y. Kasugai T. Obata M. Elastic buckling phenomenon applicable to deployable rings Internat. J. Solids and Structures 29 1992 893-909
7. Elias Z.M. Theory and Methods of Structural Analysis 1986 John Wiley New York
8. Frisch-Fay R. Flexible Bars 1962 Butterwoths London
9. Barten H.J. On the deflection of a cantilever beam Quart. Appl. Math. 2 1944 168-171
10. Barten H.J. On the deflection of a cantilever beam Quart. Appl. Math. 3 1945 275-276
11. Jenkins J.A. Seitz T.B. Przemieniecki J.S. Large deflections of diamond-shaped frames Internat. J. Solids and Structures 2 1966 591-603
12. Kerr C.N. Large deflection of a square frame Quart. J. Mech. Appl. Math. 17 1964 23-38
13. James M.E. Kozik T.J. Martinez J.E. Effect of curvature on nonlinear frame analyses J. Structural Division--ASCE 100 1974 1451-1457
14. Oran C. Kassimali A. Large deformations of framed structures under static and dynamic loads Comput. - structures 6 1976 539-547
15. Mondkar D.P. Powell G.H. Finite element analysis of non-linear static and dynamic response Internat. J. Numerical Methods Engrg. 11 1977 499-520
16. Belytschko T. Schwer L. Klein M.J. Large displacement, transient analysis of space frames Internat. J. Numerical Methods Engrg. 11 1977 65-84
17. Argyris J.H. Dunne P.C. Scharpf D.W. Large displacement small strain analysis of structures with rotational degrees of freedom Comput. Methods Appl. Mech. Engrg. 14 1978 401-451
18. Bathe K.J. Bolourchi S. Large displacement analysis of 3-dimensional beam structures Internat. J. Numerical Methods Engrg. 14 1979 961-986
19. Argyris J.H. Balmer H. Doltsinis J.S. Dunne P.C. Haase M. Kleiber M. Malejannakis G.A. Mlejnek H.P. Muller M. Scharpf D.W. Finite-element method--natural approach Comput. Methods Appl. Mech. Engrg. 17 1979 1-106
20. Riks E. Incremental approach to the solution of snapping and buckling problems Internat. J. Solids and Structures 15 1979 529-551
21. Argyris J.H. Stdoltsinis J. Pimenta P.M. Wustenberg H. Natural finite element techniques for viscous-flow motion Comput. Methods Appl. Mech. Engrg. 45 1984 3-55
22. Argyris J.H. Stdoltsinis J. Pimenta P.M. Wustenberg H. Thermomechanical response of solids at high strains--natural approach Lewis R.W. Numerical Methods in Coupled Systems 1986 59-117 John Wiley
23. Peterson A. Petersson H. On finite-element analysis of geometrically nonlinear problems Comput. Methods Appl. Mech. Engrg. 51 1985 277-286
24. Bathe K.J. Ramm E. Wilson E.L. Finite element formulations for large deformation dynamic analysis Internat. J. Numerical Methods Engrg. 9 1975 353-386
25. Crisfield M.A. Non-linear Finite Element Analysis of Solids and Structures vol. 1 1991 John Wiley England
26. Gattass M. Abel J.F. Equilibrium considerations of the updated Lagrangian formulation of beam-columns with natural concepts Internat. J. Numerical Methods Engrg. 24 1987 2119-2141
27. Bathe K.J. Finite Element Procedures 1996 Prentice-Hall Englewood Cliffs, NJ
28. Crisfield M.A. A fast incremental-iterative solution procedure that handles snap-through Comput. - Structures 13 1981 55-62
29. Wriggers P. Simo J.C. A general procedure for the direct computation of turning and bifurcation points Internat. J. Numerical Methods Engrg. 30 1990 155-176
30. Kleiber M. Incremental finite element modeling in non-linear solid mechanics 1989 Ellis Horwood England
31. Wylie C.R. Barrett L.C. Advanced Engineering Mathematics sixth ed. 1995 McGraw-Hill New York
32. Petrolito J. Legge K.A. Unified nonlinear elastic frame analysis Comput. - Structures 60 1996 21-30
33. Izzuddin B.A. Elnashai A.S. Eulerian formulation for large-displacement analysis of space frames J. Engrg. Mech.--ASCE 119 1993 549-569
34. Crisfield M.A. A consistent corotational formulation for nonlinear, 3-dimensional, beam-elements Comput. Methods Appl. Mech. Engrg. 81 1990 131-150
35. Wong M.B. Tinloi F. Geometrically nonlinear analysis of elastic framed structures Comput. - Structures 34 1990 633-640
36. The L.H. Clarke M.J. Co-rotational and Lagrangian formulations for elastic three-dimensional beam finite elements J. Construct. Steel Res. 48 1998 123-144
37. Bergan P.G. Horrigmoe G. Krakeland B. Soreide T.H. Solution techniques for nonlinear finite-element problems Internat. J. Numerical Methods Engrg. 12 1978 1677-1696
38. Behdinan K. Stylianou M.C. Tabarrok B. Co-rotational dynamic analysis of flexible beams Comput. Methods Appl. Mech. Engrg. 154 1998 151-161
39. Schulz M. Filippou F.C. Non-linear spatial Timoshenko beam element with curvature interpolation Internat. J. Numerical Methods Engrg. 50 2001 761-785
40. Simo J.C. Hjelmstad K.D. Taylor R.L. Numerical formulations of elasto-viscoplastic response of beams accounting for the effect of shear Comput. Methods Appl. Mech. Engrg. 42 1984 301-330
41. Ogden R.W. Non-linear Elastic Deformation 1984 Ellis Horwood England
42. Green A.E. Naghdi P.M. A note on invariance under superposed rigid body motions J. Elasticity 9 1 1979