Large-Displacement Analysis of Elastoplastic Thin-Walled Frames. I: Formulation and Implementation
Publication: Journal of Structural Engineering
Volume 122, Issue 8
Abstract
This paper presents a new formulation for the large-displacement analysis of thin-walled frames taking into account the effects of elastoplastic material behavior. The proposed formulation is derived in an Eulerian (convected) local system which allows relatively simple strain-displacement relationships to be used. Furthermore, the formulation uses the fiber approach for representing the spread of plasticity over a general open cross section, and is capable of modeling initial imperfections, residual stresses, and the Wagner effect. In accounting for material plasticity effects, consideration is given to the interaction between normal stresses and shear stresses due to twisting. Since the shear strain is directly related to the rate of twist, the shear stress in the yield function is replaced by an equivalent contribution to the cross-sectional torque, which leads to considerable computational advantages. This paper describes the formulation details and the implementation of material plasticity effects for kinematic and isotropic strain hardening, whereas the companion paper provides a number of verification and application examples.
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References
1.
Allen, H. G., and Bulson, P. S. (1980). Backgrond to buckling. McGraw-Hill Book Co., Ltd., London, England.
2.
Barsoum, R. S., and Gallagher, R. H.(1970). “Finite element analysis of torsional and torsional-flexural stability problems.”Int. J. Numer. Methods in Engrg., 2, 335–352.
3.
Bazant, Z. P., and El Nimeiri, M.(1973). “Large-deflection spatial buckling of thin-walled beams and frames.”J. Engrg. Mech. Div., ASCE, 99(6), 1259–1281.
4.
Bleich, F. (1952). Buckling strength of metal structures. McGraw-Hill Book Co., Inc., New York, N.Y.
5.
Chan, S. L., and Kitipornchai, S.(1987). “Geometric nonlinear analysis of asymmetric thin-walled beam-columns.”Engrg. Struct., 9, 243–254.
6.
Chen, H., and Blandford, G. E.(1991). “Thin-walled space frames. I: Large-deformation analysis theory.”J. Struct. Engrg., ASCE, 117(8), 2499–2520.
7.
Conci, A., and Gattass, M.(1990a). “Natural approach for geometric non-linear analysis of thin-walled frames.”Int. J. Numer. Methods in Engrg., 30, 207–231.
8.
Conci, A., and Gattass, M.(1990b). “Natural approach for thin-walled beam-columns with elastic-plasticity.”Int. J. Numer. Methods in Engrg., 29, 1653–1679.
9.
Crisfield, M. A. (1991). Non-linear finite element analysis of solids and structures, Vol. 1 . John Wiley & Sons, Inc., Chichester, England.
10.
El-Zanaty, M. H., and Murray, D. W.(1983). “Nonlinear finite element analysis of steel frames.”J. Struct. Engrg., ASCE, 109(2), 353–368.
11.
Epstein, M., Nixon, D., and Murray, W.(1978). “Large displacement inelastic analysis of beam-columns.”J. Struct. Div., ASCE, 104(5), 841–853.
12.
Goto, Y., and Chen, W. F.(1989). “On the validity of Wagner hypothesis.”Int. J. Solids and Struct., 25(6), 621–634.
13.
Hasegawa, A., Liyanage, K. K., Noda, M., and Nishino, F.(1987). “An inelastic finite displacement formulation of thin-walled members.”Struct. Engrg./Earthquake Engrg., 4(2), 269–276.
14.
Izzuddin, B. A. (1991). “Nonlinear dynamic analysis of framed structures,” PhD thesis, Dept. of Civ. Engrg., Imperial Coll., Univ. of London, England.
15.
Izzuddin, B. A.(1995). “An Eulerian approach to the large displacement analysis of thin-walled frames.”Proc., Instn. of Civ. Engrs., Struct. and Build., London, England, 110(1), 50–65.
16.
Izzuddin, B. A., and Elnashai, A. S.(1993a). “Eulerian formulation for large displacement analysis of space frames.”J. Engrg. Mech., ASCE, 119(3), 549–569.
17.
Izzuddin, B. A., and Elnashai, A. S.(1993b). “Adaptive space frame analysis. II: A distributed plasticity approach.”Proc., Instn. of Civ. Engrs., Struct. and Build., London, England, 99(3), 317–326.
18.
Izzuddin, B. A., and Lloyd Smith, D.(1996). “Large-displacement analysis of elastoplastic thin-walled frames. II: Verification and application.”J. Struct. Engrg., ASCE, 122(8), 915–925.
19.
Mallet, R. H., and Marcal, P. V.(1968). “Finite element analysis of nonlinear structures.”J. Struct. Div., ASCE, 94(9), 2081–2105.
20.
Meek, J. L., and Lin, W. J.(1990). “Geometric and material non-linear analysis of thin-walled beam-columns.”J. Struct. Engrg., ASCE, 116(6), 1473–1490.
21.
Meek, J. L., and Loganathan, S.(1990). “Geometric and material non-linear behaviour of beam-columns.”Comp. and Struct., 34(1), 87–100.
22.
Nethercot, D. A.(1975). “Inelastic buckling of steel beams under non-uniform moment.”The Struct. Engr., London, England, 53(2), 73–78.
23.
Oran, C.(1973). “Tangent stiffness in space frames.”J. Struct. Div., ASCE, 99(6), 987–1001.
24.
Pi, Y. L., and Trahair, N. S.(1992). “Prebuckling deflections and lateral buckling. I: Theory.”J. Struct. Engrg., ASCE, 118(11), 2949–2985.
25.
Pi, Y. L., and Trahair, N. S.(1994). “Nonlinear inelastic analysis of steel beam-columns. I: Theory.”J. Struct. Engrg., ASCE, 120(7), 2041–2061.
26.
Trahair, N. S., and Kitipornchai, S.(1972). “Buckling of inelastic I-beams under uniform moment.”J. Struct. Div., ASCE, 98(11), 2551–2566.
27.
Wen, R. K., and Rahimzadeh, J.(1983). “Nonlinear elastic frame analysis by finite element.”J. Struct. Engrg., ASCE, 109(8), 1952–1971.
28.
Ziegler, H.(1959). “A modification of Prager's hardening rule.”Quarterly Appl. Math., 17(1), 55–65.
Information & Authors
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Published In
Journal of Structural Engineering
Volume 122 • Issue 8 • August 1996
Pages: 905 - 914
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Aug 1, 1996
Published in print: Aug 1996
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