A mixed finite element for three-dimensional nonlinear analysis of steel frames

Computer Methods in Applied Mechanics and Engineering

Volumn 193, Issue 23-26, 2004, Pages 2507-2545

  Nukala, Phani Kumar V V ^a   White, Donald W ^b  

^a OAK RIDGE NATIONAL LABORATORY   (United States)

^b Georgia Institute of Technology   (United States)

Author keywords

Mixed finite element; Steel frames; Three dimensional nonlinear analysis

Indexed keywords

BENDING (DEFORMATION); DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; KINEMATICS; MATHEMATICAL MODELS; MECHANICAL ENGINEERING; PLASTICITY; RESIDUAL STRESSES; ROTATION; SHEAR STRESS; VARIATIONAL TECHNIQUES; VIBRATIONS (MECHANICAL);

BIAXIAL BENDING; MATERIAL INELASTICITY; NONLINEAR ANALYSIS; NONLINEAR VARIATIONS;

STEEL;

FINITE ELEMENT ANALYSIS;

EID: 16544371111     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2004.01.029     Document Type: Article

References (64)

1. Argyris J.H. Balmer H. Doltsinis J.St. Dunne P.C. Haase M. Kleiber M. Malejannakis G.A. Mlejnek H.P. Scharpf D.W. Finite element method--the natural approach Comput. Methods Appl. Mech. Engrg. 17/18 1979 1-106
2. Argyris J.H. Hilpert O. Malejannakis G.A. Scharpf D.W. On the geometric stiffness of a beam in space--a consistent v.w. approach Comput. Methods Appl. Mech. Engrg. 20 1979 105-131
3. Bathe K.J. Bolourchi S. Large displacement analysis of three-dimensional beam structures Int. J. Numer. Methods Engrg. 14 1979 961-986
4. Simo J.C. A finite strain beam formulation. The three-dimensional dynamic problem. Part I Comput. Methods Appl. Mech. Engrg. 49 1985 55-70
5. Simo J.C. Vu-Quoc L. A three-dimensional finite-strain rod model. Part II: Computational aspects Comput. Methods Appl. Mech. Engrg. 58 1986 79-116
6. Cardona A. Geradin M. A beam finite element non-linear theory with finite rotations Int. J. Numer. Methods Engrg. 26 1988 2403-2438
7. Crisfield M.A. A consistent co-rotational formulation for nonlinear, three-dimensional, beam elements Comput. Methods Appl. Mech. Engrg. 81 1990 131
8. Simo J.C. Vu-Quoc L. A geometrically-exact rod model incorporating shear, torsion-warping deformation Int. J. Solids Struct. 27 3 1991 371-393
9. Salleb A.F. Gendy A.S. Shear-flexible models for spatial buckling of thin-walled curved beams Int. J. Numer. Methods Engrg. 31 1991 729-757
10. Y.L. Pi, N.S. Trahair, Nonlinear inelastic analysis of steel beam-columns--theory, Research Report, School of Civil and Mining Engineering, The University of Sydney, NSW, Australia, November 1992
11. Ibrahimbegovic A. Frey F. Kozar I. Computational aspects of vector-like parametrization of three-dimensional finite rotations Int. J. Numer. Methods Engrg. 38 1995 3653-3673
12. Ibrahimbegovic A. On finite element implementation of geometrically nonlinear Reissner's beam theory: Three-dimensional curved beam elements Comput. Methods Appl. Mech. Engrg. 122 1995 11-26
13. Jelenic G. Saje M. A kinematically exact space finite strain beam model - finite element formulation by generalized virtual work principle Comput. Methods Appl. Mech. Engrg. 120 1995 131-161
14. Yang Y.B. McGuire W. Stiffness matrix for geometric nonlinear analysis J. Struct. Engrg.-ASCE 112 4 1986 853-877
15. Yang Y.B. McGuire W. Joint rotation and geometric nonlinear analysis J. Struct. Engrg.-ASCE 112 4 1986 878-905
16. Orbison J.G. McGuire W. Abel J.F. Yield surface applications in nonlinear steel frame analysis Comput. Methods Appl. Mech. Engrg. 33 1-3 1982 557-573
17. Y. Zhao, Modelling of inelastic cyclic behavior of members, connections, joint panels of steel frames, Ph.D. thesis, Cornell University, 1993
18. Attalla M. Deierlein G. McGuire W. Spread of plasticity: Quasi-plastic-hinge approach J. Struct. Engrg. 120 8 1994 2451-2473
19. Park M.S. Lee B.C. Geometrically nonlinear and elastoplastic three-dimensional shear flexible beam element of von-Mises-type hardening material Int. J. Numer. Methods Engrg. 39 1996 383-408
20. F. Taucer, E. Spacone, F.C. Filippou, A fiber beam-column element for seismic response analysis of reinforced concrete structures, Ucb/eerc-91/17, University of California, Berkeley, December 1991
21. Battini J.-M. Pacoste C. Co-rotational beam elements with warping effects in instability problems Comput. Methods Appl. Mech. Engrg. 191 2002 1755-1789
22. Battini J.-M. Pacoste C. Plastic instability of beam structures using co-rotational elements Comput. Methods Appl. Mech. Engrg. 191 2002 5811-5831
23. Izzuddin B.A. Smith D.L. Large-displacement analysis of elastoplastic thin-walled frames. I. Formulation, implementation J. Struct. Engrg.-ASCE 122 8 1996 905-914
24. Izzuddin B.A. Smith D.L. Large-displacement analysis of elastoplastic thin-walled frames. II. Verification and application J. Struct. Engrg.-ASCE 122 8 1996 915-925
25. Teh L.H. Clarke M.J. Plastic-zone analysis of 3d steel frames using beam elements J. Struct. Engrg.-ASCE 125 11 1999 1328-1337
26. P.K.V.V. Nukala, D.W. White, Variationally consistent state determination algorithms for nonlinear analysis using mixed finite element formulations, Comput. Methods Appl. Mech. Engrg., in press
27. V.Z. Vlasov, Thin walled elastic bars, Israel Program for Scientific Translation, Jerusalem, 1961
28. Timoshenko S.P. Gere J.M. Theory of Elastic Stability 1961 McGraw-Hill New York
29. Gjelsvik A. The Theory of Thin Walled Bars 1981 John Wiley and Sons New York
30. Billinghurst A. Williams J.R.L. Chen G. Trahair N.S. Inelastic uniform torsion of steel members J. Struct. Mech. 8 January 1991 61-92
31. G. Chen, N.S. Trahair, Inelastic nonuniform torsion of steel i-beams, Research Report, r647, School of Civil and Mining Engineering, The University of Sydney, NSW, Australia, December 1991
32. Spring K.W. Euler parameters and the use of quaternion algebra in the manipulation of finite rotations: a review Mech. Mach. Theory 21 1986 365-373
33. Yang Y.B. Kuo S.R. Cheng Y.D. Curved beam element for nonlinear analysis J. Struct. Engrg.-ASCE 115 1989 840-855
34. Dvorkin E.N. Celentano D. Cuitino A. Gioai G. A vlasov beam element Comput. Struct. 33 1 1989 187-196
35. Gruttmann F. Sauer R. Wagner W. A geometrical nonlinear eccentric 3d-beam element with arbitrary cross-sections Comput. Methods Appl. Mech. Engrg. 160 1998 383-400
36. Li M. The finite deformation theory for beam, plate and shell. Part I: The two-dimensional beam theory Comput. Methods Appl. Mech. Engrg. 146 1997 53-63
37. Li M. The finite deformation theory for beam, plate and shell structures. Part II: The kinematic model and the Green-Lagrange strains Comput. Methods Appl. Mech. Engrg. 156 1998 247-257
38. Li M. The finite deformation theory for beam, plate and shell structures. Part III: The three-dimensional beam theory and Fe formulation Comput. Methods Appl. Mech. Engrg. 162 1998 287-300
39. Malvern L.E. Introduction to the Mechanics of a Continuous Medium 1969 Prentice-Hall
40. Chen W.F. Atsuta T. Theory of Beam-Columns vol. 2 1977 McGraw Hill
41. Gendy A.S. Saleeb A.F. Chang T.Y.P. Generalized thin-walled beam models for flexural-torsional analysis Comput. Struct. 42 4 1992 531-550
42. Antman S.S. The theory of rods Handbuch der Physik vol. VIa/2 1972 Springer Berlin
43. Hughes T.J.R. The Finite Element Method 1987 Prentice-Hall
44. Simo J.C. Taylor R.L. A return mapping algorithm for plane stress elastoplasticity Int. J. Numer. Methods Engrg. 22 1986 649-670
45. Stolarski H. Belytschko T. Limitation principles for mixed finite elements based on the Hu-Washizu variational formulation Comput. Methods Appl. Mech. Engrg. 60 1987 195-216
46. Arnold D.N. Mixed finite element methods for elliptic problems Comput. Methods Appl. Mech. Engrg. 82 1990 281-300
47. Alfano G. Marotti de Sciarra F. Mixed finite element formulations and related limitation principles: A general treatment Comput. Methods Appl. Mech. Engrg. 138 1996 105-130
48. Simo J.C. Rifai M.S. A class of mixed assumed strain methods and the method of incompatible modes Int. J. Numer. Methods Engrg. 29 1990 1595-1638
49. A. Aalberg, An experimental study of beam-columns subjected to combined torsion, bending and axial actions, Ph.D. thesis, The Norwegian Institute of Technology, July 1995
50. P.K.V.V. Nukala, Three-dimensional second-order inelastic analysis of steel frames, Ph.D. thesis, Purdue University, West Lafayette, IN 47907, May 1997
51. Clarke M.J. Hancock G.J. A study of incremental-iterative strategies for non-linear analyses Int. J. Numer. Methods Engrg. 29 1990 1365-1391
52. Crisfield M.A. Non-linear Finite Element Analysis for Solids and Structures 1991 John Wiley and Sons
53. Argyris J.H. Symeonidis Sp. Nonlinear finite element analysis of elastic systems under nonconservative loading-natural formulation. Part I. Quasistatic problems Comput. Methods Appl. Mech. Engrg. 26 1981 75-123
54. Argyris J.H. Symeonidis Sp. A sequel to: Nonlinear finite element analysis of elastic systems under nonconservative loading-natural formulation. Part I. Quasistatic problems Comput. Methods Appl. Mech. Engrg. 26 1981 377-383
55. Noor A.K. Peters J.M. Mixed models, selective/reduced integration displacement models for nonlinear analysis of curved beams Int. J. Numer. Methods Engrg. 17 1981 615-631
56. DaDeppo D.A. Schmidt R. Instability of clamped-hinged circular arches subjected to a point load Trans. ASME 27 1975 894-896
57. Wood R.D. Zienkiewicz O.C. Geometrically nonlinear finite element analysis of beams, frames, arches and axisymmetric shells Comput. Struct. 7 1977 725-735
58. Borri M. Bottasso C. An intrinsic beam model based on a helicoidal approximation--Part I: Formulation Int. J. Numer. Methods Engrg. 37 1994 2267-2290
59. Borri M. Bottasso C. An intrinsic beam model based on a helicoidal approximation--Part II: Linearization and finite element implementation Int. J. Numer. Methods Engrg. 37 1994 2291-2310
60. Franchi C.G. Montelaghi F. A weak-weak formulation for large displacements beam statics: \A finite volumes approximation Int. J. Numer. Methods Engrg. 39 1996 584-604
61. Avello A. Garcia de Jalon J. Bayo E. Dynamics of flexible multibody systems using Cartesian co-ordinates and large displacement theory Int. J. Numer. Methods Engrg. 32 1991 1543-1563
62. Galambos T. Ketter R. Columns under combined bending and thrust J. Engrg. Mech.-ASCE 85 EM2 1959 1-30
63. Australian Institute of Steel Construction, Standards Australia, AS4100-1990 Steel Structures, 1990
64. S. Morino, Analysis of space frames, Ph.D. thesis, Lehigh University, 1970