0
REVIEW ARTICLES

Recent developments in geometrically nonlinear and postbuckling analysis of framed structures

[+] Author and Article Information
Yeong-Bin Yang

Department of Civil Engineering, National Taiwan University, Taipei, Taiwan, Republic of China; ybyang@ntu.edu.tw

Jong-Dar Yau

Department of Architectural and Building Technology, Tamkang University, Taipei, Taiwan, Republic of China

Liang-Jenq Leu

Department of Civil Engineering, National Taiwan University, Taipei, Taiwan, Republic of China

Appl. Mech. Rev 56(4), 431-449 (Jul 22, 2003) (19 pages) doi:10.1115/1.1578498 History: Online July 22, 2003
Copyright © 2003 by ASME
Your Session has timed out. Please sign back in to continue.

References

AISC (1993), Load and Resistance Factor Design, American Institute of Steel Construction, Chicago.
Steel Structures (1990), AS4100-1990, Standards Australia (SA), Sydney, Australia.
Vlasov VZ (1961), Thin-Walled Elastic Beams, 2nd Edition, Israel Program for Scientific Translation, Jerusalem, Israel.
Timoshenko SP and Gere JM (1961), Theory of Elastic Stability, 2nd Edition, McGraw-Hill, New York.
Chajes A (1974), Principles of Structural Stability Theory, Prentice-Hall, Englewood Cliffs NJ.
Simitses GJ (1976), An Introduction to the Elastic Stability of Structures, Prentice-Hall, Englewood Cliffs NJ.
Ziegler H (1977), Principles of Structural Stability, 2nd Edition, Birkhäuser, Stuttgart, Germany.
Chen WF and Lui EM (1987), Structural Stability—Theory and Implementation, Elsevier, New York NY.
Bazant ZP and Cedolin L (1989), Stability of Structures—Elastic, Inelastic, Fracture, and Damage Theories, Oxford Univ Press, New York NY.
Kounadis  AN and Ioannidis  GI (1994), Lateral postbuckling analysis of beam columns, J. Eng. Mech. Div. 120(4), 695–706.
Goto  Y, Li  XS, and Kasugai  T (1996), Buckling analysis of elastic space rods under torsional moment, J. Eng. Mech. Div. 122(9), 826–833.
Chucheepsakul  S, Bunchareon  S, and Wang  CM (1994), Large deflection of beams under moment gradient, J. Eng. Mech. Div. 120(9), 1848–1860.
Chucheepsakul  S, Bunchareon  S, and Huang  T (1995), Elastica of a simple variable-arc-length beam subjected to an end moment, J. Eng. Mech. Div. 121(7), 767–772.
Chucheepsakul  S, Wang  CM, He  XQ, and Monprapussorn  T (1999), Double curvature bending of variable-arc-length elasticas, ASME J. Appl. Mech. 66(1), 87–94.
Wang  CM, Lam  KY, He  XQ, and Chucheepsakul  S (1997), Large deflections of an end supported beam subjected to a point load, Int. J. Non-Linear Mech. 32(1), 63–72.
Chucheepsakul  S and Monprapussorn  T (2001), Nonlinear buckling of marine elastica pipes transporting fluid, Int. J. Struct. Stability Dyn. 1(3), 333–365.
Williams  FW (1964), An approach to the non-linear behavior of the members of a rigid jointed plane framework with finite deflections, Q. J. Mech. Appl. Math. XVII, Part 4, 451–469.
Mattiasson  K (1981), Numerical results from large deflection beam and frame problems analyzed by means of elliptic integrals, Int. J. Numer. Methods Eng. 17, 145–153.
Yang  YB and Kuo  SR (1991), Out-of-plane buckling of angled frames, Int. J. Mech. Sci. 33(1), 55–67.
Yang  YB and Kuo  SR (1991), Buckling of frames under various torsional loadings, J. Eng. Mech. Div. 117(8), 1681–1697.
Pecknold  DA, Ghaboussi  J, and Healey  TJ (1985), Snap-through and bifurcation in a simple structure, J. Eng. Mech. Div. 111(7), 909–922.
Harrison  HB (1978), Post-buckling behavior of elastic circular arches, Proc. Instn. Civil Engrs. 65, Part 2, 283–298.
Cescotto S, Frey F, and Fonder G (1979), Total and updated Lagrangian descriptions in nonlinear structural analysis: A unified approach, Energy Meth. Finite Element Analysis, R Glowinski, EY Rodin, and OC Zienkiewicz (eds), John Wiley, New York NY, 283–296.
Bathe  KJ and Bolourchi  S (1979), Large displacement analysis of three-dimensional beam structures, Int. J. Numer. Methods Eng. 14, 961–986.
Yang YB and Kuo SR (1994), Theory and Analysis of Nonlinear Framed Structures, Prentice Hall, Singapore.
Yang  YB and Kuo  SR (1992), Frame buckling analysis with full consideration of joint compatibilities, J. Eng. Mech. Div. 118(5), 871–889.
Yang  YB and Kuo  SR (1991), Consistent frame buckling analysis by finite element method, J. Struct. Eng. 117(4), 1053–1069.
Argyris  JH, Dunne  PC, Malejannakis  GA, and Scharpf  DW (1978), On large displacement-small strain analysis of structures with rotational degrees of freedom, Comput. Methods Appl. Mech. Eng. 14, 401–451; 15, 99–135.
Argyris  JH, Hilbert  O, Malejannakis  GA, and Scharpf  DW (1979), On the geometrical stiffness of a beam in space—a consistent v.w. approach, Comput. Methods Appl. Mech. Eng. 20, 105–131.
Hasegawa  A, Liyanage  K, Ikeda  T, and Nishino  F (1985), A concise and explicit formulation of out-of-plane instability of thin-walled members, Proc. JSCE Struct. Engrg./Earthquake Engrg. 2(1), 57–65.
Yang  YB and McGuire  W (1986), Stiffness matrix for geometric nonlinear analysis, J. Struct. Eng. 112(4), 853–877.
Yang  YB and McGuire  W (1986), Joint rotation and geometric nonlinear analysis, J. Struct. Eng. 112(4), 1986, 879–905.
Elias ZM (1986), Theory and Methods of Structural Analysis, John Wiley, New York NY.
Conci  A and Gattass  M (1990), Natural approach for geometric non-linear analysis of thin-walled frames, Int. J. Numer. Methods Eng. 30, 207–231.
Chen  H and Blandford  GE (1991), Thin-walled space frames. I: large-deformation analysis theory, J. Struct. Eng. 117(8), 2499–2520.
Chen  H and Blandford  GE (1991), Thin-walled space frames. II: algorithmic details and applications, J. Struct. Eng. 117(8), 2521–2539.
Simo  JC and Vu-Quoc  L (1991), A geometrically-exact rod model incorporating shear and torsion-warping deformation, Int. J. Solids Struct. 27(3), 371–393.
Reissner E (1973), On one-dimensional large-displacement finite-strain beam theory, Studies in Appl. Math., LII (2), MIT, Cambridge MA.
Teh  LH and Clarke  MJ (1999), Symmetry of tangent stiffness matrices of 3D elastic frame, J. Eng. Mech. Div. 125(2), 248–251.
Izzuddin  BA (2001), Conceptual issues in geometrically nonlinear analysis of 3D framed structures, Comput. Methods Appl. Mech. Eng. 191, 1029–1053.
Zienkiewicz, OC and Taylor RL (2000), The Finite Element Method, Volume 1: The Basis, 5th Edition, Butterworth-Heinemann, Oxford.
Irons B and Ahmad S (1980), Techniques of Finite Elements, John Wiley, New York NY.
Cook, RD, Malkus, DS, Plesha, ME, and Witt, RJ (2001), Concepts and Applications of Finite Element Analysis, 4th Edition, John Wiley, New York NY.
Yang  YB and  Yang  YB (1987), Rigid body motion test for nonlinear analysis with beam elements, J. Eng. Mech. Div. 113(9), 1404–1419.
Gattass  M and Abel  JF (1987), Equilibrium considerations of the updated Lagrangian formulation of beam columns with natural concepts, Int. J. Numer. Methods Eng. 24, 2119–2143.
Yang  YB, Chou  JH, and Leu  LJ (1992), Rigid body considerations for nonlinear finite element analysis, Int. J. Numer. Methods Eng. 33(8), 1597–1610.
Leu  LJ and Yang  YB (1990), Effects of rigid body and stretching on nonlinear analysis of trusses, J. Struct. Eng. 116(10), 2582–2598.
Yang  YB and Leu  LJ (1994), Non-linear stiffnesses in analysis of planar frames, Comput. Methods Appl. Mech. Eng. 117, 233–247.
Yang  YB and Leu  LJ (1991), Force recovery procedures in nonlinear analysis, Comput. Struct. 41(6), 1255–1261.
Kuo  SR, Yang  YB, and Chou  JH (1993), Nonlinear analysis of space frames with finite rotations, J. Struct. Eng. 119(1), 1–15.
Sandhu  JS, Stevens  KA, and Davies  GAO (1990), A 3-D, co-rotational, curved and twisted beam element, Comput. Struct. 35(1), 69–79.
Yang  YB, Kuo  SR, and Wu  YS (2002), Incrementally small-deformation theory for nonlinear analysis of structural frames, Eng. Struct. 24, 783–798.
Argyris JH (1965), Continua and discontinua, Proc of 1st Matrix Methods in Structural Mechanics, Wright-Patterson Air Force Base, Ohio, 11–89.
Pian THH and Tong P (1971), Variational formulation of finite displacement analysis, Proc of IUTAM Symp on High Speed Computing of Elastic Structures, de Veubeke BF (ed), Univ of Liege, Liege, Belgium, 43–63.
Zienkiewicz  OC (1971), Incremental displacement in non-linear analysis, Int. J. Numer. Methods Fluids 3, 587–588.
Wempner  GA (1971), Discrete approximation related to nonlinear theories of solids, Int. J. Solids Struct. 7, 1581–1599.
Riks  E (1972), The application of Newton’s method to the problem of elastic stability, ASME J. Appl. Mech. 39, 1060–1066.
Ramm E (1981), Strategies for tracing the nonlinear response near limit point, Nonlinear Finite Element Analysis in Struct. Mech., W Wunderlich, E Stein, and KJ Bathe (eds), Springer-Verlag, Berlin, 63–89.
Crisfield  MA (1981), A fast incremental/iterative solution procedure that handles snap-through, Comput. Struct. 13, 55–62.
Powell  G and Simons  J (1981), Improved iteration strategy for nonlinear structures, Int. J. Numer. Methods Eng. 17, 1455–1467.
Yang YB and McGuire W (1985), A work control method for geometrically nonlinear analysis, Proc of Int Conf on Numer Methods in Engineering: Theory & Appl, J Middleton and GN Pande (eds), Univ College Swansea, Wales, UK, 913–921.
Yang  YB and Shieh  MS (1990), Solution method for nonlinear problems with multiple critical points, AIAA J. 28(12), 2110–2116.
Bergan  PG (1978), Solution technique for non-linear finite element problems, Int. J. Numer. Methods Eng. 12, 1677–1696.
Huang  BZ and Atluri  SN (1995), A simple method to follow post-buckling paths in finite element analysis, Comput. Struct. 57(3), 477–489.
Kuo  SR and Yang  YB (1995), Tracing postbuckling paths of structures containing multi loops, Int. J. Numer. Methods Eng. 38(23), 4053–4075.
Yang  YB, Chang  JT, and Yau  JD (1999), A simple nonlinear triangular plate element and strategies of computation for nonlinear analysis, Comput. Methods Appl. Mech. Eng. 178, 307–321.
Cook  RD (1987), A plate hybrid element with rotational d.o.f. and adjustable stiffness, Int. J. Numer. Methods Eng. 24, 1499–1508.
Batoz  JL, Bathe  KJ, and Ho  LW (1980), A study of three-node triangular plate bending element, Int. J. Numer. Methods Eng. 15, 1771–1812.
Yang  YB (1993), Recent researches on buckling of framed structures and curved beams, J. Constr. Steel Res. 26, 193–210.
Yoo  CH (1982), Flexural-torsional stability of curved beams, J. Eng. Mech. Div. 108(6), 1351–1369.
Yang  YB and Kuo  SR (1986), Static stability of curved thin-walled beams, J. Eng. Mech. Div. 112(8), 821–841.
Yang  YB and Kuo  SR (1987), Effect of curvature on stability of curved beams, J. Struct. Eng. 113(6), 1185–1202.
Yang  YB, Kuo  SR, and Cherng  YD (1989), Curved beam elements for nonlinear analysis, J. Eng. Mech. Div. 115(4), 840–855.
Bazant  ZP and El Nimeiri  M (1973), Large-deflection spatial buckling of thin-walled beams and frames, J. Eng. Mech. Div. 99(6), 1259–1281.
Rajasekaran  S and Ramm  E (1984), Discussion of “Flexural-torsional stability of curved beams” by Yoo CH, J. Eng. Mech. Div. 110(1), 144–148.
Palani  GS and Rajasekaran  S (1992), Finite element analysis of thin-walled curved beams made of composites, J. Struct. Eng. 118(8), 2039–2062.
Yang  YB and Kuo  SR (1994), Discussion of “Finite element analysis of thin-walled curved beams made of composites” by GS Palani and S Rajasekaran, J. Struct. Eng. 120(2), 671–673.
Yang  YB, Kuo  SR, and Yau  JD (1991), Use of straight-beam approach to study buckling of curved beams, J. Struct. Eng. 117(7), 1963–1978.
Kuo  SR and Yang  YB (1995), New theory on buckling of curved beams, J. Eng. Mech. Div. 117(8), 1698–1717.
Papangelis  JP and Trahair  NS (1987), Flexural-torsional buckling of arches, J. Struct. Eng. 113(4), 889–906.
Trahair  NS and Papangelis  JP (1987), Flexural-torsional buckling of monosymmetric arches, J. Struct. Eng. 113(10), 2271–2288.
Papangelis  JP and Trahair  NS (1987), Flexural-torsional buckling tests on arches, J. Struct. Eng. 113(7), 1433–1443.
Rajasekaran  S and Padmanabhan  S (1989), Equations of curved beams, J. Eng. Mech. Div. 115(5), 1094–1111.
Yang  YB and Kuo  SR (1991), Discussion of “Equations of curved beams” by Rajasekaran S and Padmanabhan S, J. Eng. Mech. Div. 117(3), 717–718.
Kang  YJ and Yoo  CH (1993), Thin-walled curved beams. I: formulation of nonlinear equations, J. Eng. Mech. Div. 120(10), 2072–2101.
Kang  YJ and Yoo  CH (1993), Thin-walled curved beams. II: analytical solutions for buckling of arches, J. Eng. Mech. Div. 120(10), 2102–2125.
Yang  YB and Kuo  SR (1996), Discussion of “Thin-walled curved beams, I: formulation of nonlinear equations” by YJ Kang and CH Yoo, J. Eng. Mech. Div. 122(5), 482–483.
Yang  YB and Kuo  SR (1996), Discussion of “Thin-walled curved beams, II: analytical solutions for buckling of arches” by YJ Kang and CH Yoo, J. Eng. Mech. Div. 122(5), 484–485.
Kang  JK and Yoo  CH (1996), Closure to “Thin-walled curved beams, I: formulation of nonlinear equations,” J. Eng. Mech. Div. 122(5), 483–484.
Kang  JK and Yoo  CH (1996), Closure to “Thin-walled curved beams, II: analytical solutions for buckling of arches,” J. Eng. Mech. Div. 122(5), 486.
Elias  ZM and Chen  KL (1988), Nonlinear shallow curved-beam finite element, J. Eng. Mech. Div. 114(6), 1076–1087.
Wen  RK and Suhendro  B (1991), Nonlinear curved-beam element for arch structures, J. Struct. Eng. 117(11), 3496–3515.
Pak  RYS and Stauffer  EJ (1994), Nonlinear finite deformation analysis of beams and columns, J. Eng. Mech. Div. 120(10), 2136–2153.
Pi  YL, Papangelis  JP, and Trahair  NS (1995), Prebuckling deformations and flexural-torsional buckling of arches, J. Struct. Eng. 121(9), 1313–1322.
Pi  YL and Trahair  NS (1996), Three-dimensional nonlinear analysis of elastic arches, Eng. Struct. 18(1), 46–63.
Pi  YL and Trahair  NS (1997), Nonlinear elastic behavior of I-beam curved in plan, J. Struct. Eng. 123(9), 1201–1209.
Pi  YL and Trahair  NS (1998), Non-linear buckling and postbuckling of elastic arches, Eng. Struct. 20(7), 571–579.
Mirmiran  A, Amde  AM, and Xu  Z (2001), Effect of geometric and loading conditions on stability of prestressed arches, Int. J. Struct. Stability Dyn. 1(4), 509–526.
Yang  YB and Leu  LJ (1990), Postbuckling analysis of trusses with various Lagrangian formulation, AIAA J. 28(5), 946–948.
Yang  YB and Leu  LJ (1991), Constitutive laws and force recovery procedures in nonlinear analysis of trusses, Comput. Methods Appl. Mech. Eng. 92, 121–131.
Murtha-Smith  E (1994), Nonlinear analysis of space trusses, J. Struct. Eng. 120(9), 2717–2736.
Blandford  GE (1996), Progressive failure analysis of inelastic space truss structures, Comput. Struct. 58(5), 981–990.
Yang  YB, Yang  CT, Chang  TP, and Chang  PK (1997), Effects of member buckling and yielding on ultimate strength of space trusses, Eng. Struct. 19(2), 179–191.
Ander  MKA and Samuelsson  AG (1999), Finite element analysis of geometrically non-linear structures using translational variables, Int. J. Numer. Methods Eng. 46, 1367–1383.
Chan  SL and Zhou  ZH (1994), Pointwise equilibrating polynomial element for nonlinear analysis of frames, J. Struct. Eng. 120(6), 1703–1717.
Chan  SL and Zhou  ZH (1995), Second-order elastic analysis of frames using single imperfect element per member, J. Struct. Eng. 121(6), 939–945.
Zhou  ZH and Chan  SL (1996), Refined second-order analysis of frames with members under lateral and axial loads, J. Struct. Eng. 122(5), 548–554.
Zhou  ZH and Chan  SL (1997), Second-order analysis of slender steel frames under distributed axial and member loads, J. Struct. Eng. 123(9), 1187–1193.
Chan  SL and Gu  JX (2000), Exact tangent stiffness for imperfect beam-column members, J. Struct. Eng. 126(9), 1094–1102.
Clarke  MJ and Hancock  GJ (1995), Tests and nonlinear analyses of small-scale stressed-arch frames, J. Struct. Eng. 121(2), 187–200.
Clarke  MJ and Hancock  GJ (1995), Design of top chord of stressed-arch frames, J. Struct. Eng. 121(2), 201–213.
Simitses  GJ, Swisshelm  JD, and Vlahinos  AS (1984), Flexibly-jointed unbraced portal frames, J. Constr. Steel Res. 4, 27–44.
Mohamed  SE and Simitses  GJ (1993), Stability and strength of rigid and semirigid plane frameworks, ASCE, J. Aerosp. Eng. 6(12), 186–198.
Narayanan R (ed.) (1985), Steel Framed Structures—Stability and Strength, Elsevier, New York NY.
Council on Tall Buildings and Urban Habitat (1992), Semi-Rigid Connections in Steel Frames, McGraw Hill, New York NY.
Aristizabal-Ochoa  JD (1997), First- and second-order stiffness matrices and load vector of beam-columns with semirigid connections, J. Struct. Eng. 123(5), 669–678.
Neuenhofer  A and Filippou  FC (1998), Geometrically nonlinear flexibility-based frame finite element, J. Struct. Eng. 124(6), 704–711.
Leu  LJ and Huang  CW (1998), A reduced basis method for geometric nonlinear analysis of structures, J. Int. Assoc. Shell & Spatial Struct. 39, 71–76.
Makode  PV, Corotis  RB, and Ramirez  MR (1999), Nonlinear analysis of frame structures by pseudodistortions, J. Struct. Eng. 125(11), 1309–1317.
Makode  PV, Corotis  RB, and Ramirez  MR (1999), Geometric nonlinear analysis of frame structures by pseudodistortions, J. Struct. Eng. 125(11), 1318–1327.
Pi  YL and Bradford  M (2001), Effects of approximations in analyses of beams of open thin-walled cross section, Part I: Flexural-torsional stability, Int. J. Numer. Methods Eng. 51, 757–772.
Pi  YL and Bradford  MA (2001), Effects of approximations in analyses of beams of open thin-walled cross section, Part II: 3-D Nonlinear behavior, Int. J. Numer. Methods Eng. 51, 773–790.

Figures

Grahic Jump Location
Typical configurations of nonlinear analysis
Grahic Jump Location
Various moment mechanisms: a) QT-1, b) QT-2, and c) ST
Grahic Jump Location
Quasitangential bending moments: a) My and b) Mz
Grahic Jump Location
Semitangential torque Mx
Grahic Jump Location
Angle frame undergoing buckling rotations: a) angle frame, b) QT moments, and c) ST moments
Grahic Jump Location
Angle frame subjected to various moments: a) QT-1, b) QT-2, and c) ST
Grahic Jump Location
Compressed bar: a) before and b) after rigid body rotation
Grahic Jump Location
Plane element: a) before and b) after rigid body rotation
Grahic Jump Location
Characteristics of a typical nonlinear system
Grahic Jump Location
Divergence near limit point
Grahic Jump Location
Displacement control method
Grahic Jump Location
Rigid body rotation and natural deformation
Grahic Jump Location
Nodal forces of the 3D beam
Grahic Jump Location
Curved beam in uniform bending: a) positive and b) negative
Grahic Jump Location
Curved beam under radial loads: a) tension and b) compression
Grahic Jump Location
Curved beam: a) original and b) straight beam approximation
Grahic Jump Location
Displacements of nodes A and B vs load p
Grahic Jump Location
Internal force of bar AB vs load p
Grahic Jump Location
Deformed shapes of the structure in different stages

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In