Nonlinear Analysis of Thin‐Walled Structures Using Least Element/Member
Publication: Journal of Structural Engineering
Volume 116, Issue 1
Abstract
The paper presents the derivation of a deformation stiffness matrix for an asymmetric thin‐walled beam‐column element. This matrix is a function of element deformation and incorporates the coupling between axial stretching and the lateral and torsional deformations. The stiffness matrix derived and the solution procedure proposed may be used together with the linear and geometric stiffness matrices for thin‐walled beam‐column elements to analyze large deflection behavior of space frames comprising members in which the influence of sectorial warping in the section can be neglected. These include members with solid, tubular hollow, or angle type sections. The formulation has been applied to a variety of sample problems involving arbitrarily large deflections. Results obtained from the approach using only one element per member in most cases agree very well with independent analytical and other published finite element solutions. The proposed method is suitable for analyzing the nonlinear behavior of large space frames, such as transmission towers.
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References
1.
Argyris, J. H., and Dunne, P. C. (1975). “On the application of the natural mode technique to small strain large displacement problem.” Proc. World Congress on Finite Element in Struct. Mech., Bournemouth, U.K.
2.
Barsoum, R. S., and Gallagher, R. H. (1970). “Finite element analysis of torsional‐flexural stability problems.” Int. J. Numer. Methods Engrg., 2, 335–352.
3.
Bathe, K. J., and Bolourchi, S. (1979). “Large displacement analysis of three‐dimensional beam structures.” Int. J. Numer. Methods Engrg., 14, 961–986.
4.
Bažant, Z. P., and El‐Nimeiri, M. E. (1973). “Large deflection spatial buckling of thin‐walled beams and frames.” J. Engrg. Mech. Div., ASCE, 99(6), 1259–1281.
5.
Chan, S. L., and Kitipornchai, S. (1987). “Geometric nonlinear analysis of asymmetric thin‐walled beam‐columns.” Engrg. Struct., 9(4), 243–254.
6.
Karamanlidis, D., Honecker, A., and Knothe, K. (1981). “Large deflection finite element analysis of pre‐ and post‐critical response of thin elastic frames.” Nonlinear Finite Element Analysis in Structural Mechanics, Wunderlich, Stein and Bathe, eds., New York, N.Y., 217–235.
7.
Kitipornchai, S., and Chan, S. L. (1987). “Nonlinear finite element analysis of angle and tee beam‐columns.” J. Struct. Engrg., ASCE113(4), 721–739.
8.
Koiter, W. T. (1962). “Post‐buckling analysis of a simple two‐bar frame.” Recent progress in applied mechanics, Broberg, Hult and Niordson, eds., Stockholm, 337–354.
9.
Kondoh, K., and Atluri, S. N. (1986). “A simplified finite element method for large deformation, post‐buckling analysis of large frame structures using explicitly derived tangent stiffness matrices.” Int. J. Numer. Methods Engrg., 23, 69–90.
10.
Kondoh, K., Tanaka, K., and Atluri, S. N. (1986). “An explicit expression for the tangent‐stiffness of a finitely deformed 3‐D beam and its use in the analysis of space frames.” Comput. Struct., 24(2), 253–271.
11.
Mattiasson, K. (1981). “Numerical results from large deflection beam and frame problems analysed by means of elliptic integrals.” Int. J. Numer. Methods Engrg., 17, 145–153.
12.
Oran, C. (1973a). “Tangent stiffness in plane frames.” J. Struct. Div., ASCE, 99(6), 973–985.
13.
Oran, C. (1973b). “Tangent stiffness in space frames.” J. Struct. Div., ASCE, 99(6), 987–1001.
14.
Oran, C., and Kassamali, A. (1976). “Large deformations of framed structures under static and dynamic loads.” Comput. Struct., 6, 539–547.
15.
Papadrakakis, M., and Ghionis, P. (1986). “Conjugate gradient algorithm in nonlinear structural analysis problems.” Comput. Methods Appl. Mech. Engrg., 59, 11–27.
16.
Przemieniecki, J. S. (1968). Theory of matrix structural analysis. McGraw‐Hill, Inc., New York, N.Y.
17.
Ramm, E. (1977). “A plate/shell element for large deflections and rotations.” Formulations and Computational Algorithms in Finite Element Analysis, K. J. Bathe, J. T. Oden, and W. Wunderlich, eds., MIT Press, Cambridge, Mass.
18.
Roorda, J. (1965). “Stability of structures with small imperfections.” J. Engrg. Mech., ASCE,(1), 87–106.
19.
Saafan, S. A. (1963). “Nonlinear behaviour of structural plane frames.” J. Struct. Div., ASCE, 89(4), 557–579.
20.
Vlasov, V. Z. (1961). Thin‐walled elastic beams. 2nd Ed., Nat. Sci. Found., Washington, D.C.
21.
Williams, F. W. (1964). “An approach to the nonlinear behaviour of a rigid jointed plane framework with finite deflections.” Q. J. Mech. Appl. Math., 17, 451–469.
22.
Wood, R. D., and Zienkiewicz, O. C. (1977). “Geometrically nonlinear finite element analysis of beams, frames, arches and axisymmetric shells.” Comput. Struct., 1, 725–735.
23.
Wunderlich, W., Orbecht, H., and Schrodter, V. (1986). “Nonlinear analysis and elastic‐plastic load‐carrying behaviour of thin‐walled spatial beam structures with warping constraints.” Int. J. Numer. Methods Engrg., 22, 671–695.
24.
Yang, Y. B., and McGuire, W. (1986). “Stiffness matrix for geometric nonlinear analysis.” J. Struct. Engrg., ASCE, 112(4), 853–877.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 116 • Issue 1 • January 1990
Pages: 215 - 234
Copyright
Copyright © 1990 ASCE.
History
Published online: Jan 1, 1990
Published in print: Jan 1990
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