Thin‐Walled Space Frames. I: Large‐Deformation Analysis Theory
Publication: Journal of Structural Engineering
Volume 117, Issue 8
Abstract
A finite element formulation for the large‐deformation analysis of space‐frame structures is presented. The formulation is based on second‐order geometric nonlinear theory and Vlasov's theory for thin‐walled beams (i.e., large displacement of members with small strains, which includes the warping deformation influence). The influence of member‐distributed loading on the geometric nonlinear response of space‐frame structures also is included. An updated Lagrangian formulation is used to model large joint translations and rotations. Prismatic beams of arbitrary cross section are considered. Rodriguez's modified rotation vector is used to represent angular deformations, which avoids rotational discontinuities at the joints of deformed space‐frame structures. Numerical results and algorithmic details are presented in a companion paper.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Argyris, J. H., Dunne, P. C., and Scharpf, D. W. (1978). “On large displacement‐small strain analysis of structures with rotational degrees of freedom.” Comput. Methods Appl. Mech. Engrg., 14(3), 401–451.
2.
Barsoum, R. S., and Gallagher, R. H. (1970). “Finite element analysis of torsional‐flexural stability problems.” Int. J. Numer. Methods Engrg., 2(3), 335–352.
3.
Bathe, K. J., and Bolourchi, S. (1979). “Large displacement analysis of three‐dimensional beam structures.” Int. J. Numer. Methods Engrg., 14(7), 961–986.
4.
Cardona, A., and Geradin, M. (1988). “A beam finite element non‐linear theory with finite rotations.” Int. J. Numer. Methods Engrg., 26(11), 2403–2438.
5.
Chen, H. (1990). “Nonlinear space frame analysis including flexible connection and bifurcation behavior,” thesis submitted to the University of Kentucky, Lexington, Kentucky, in partial fulfillment for the degree of Doctor of Philosophy.
6.
Chen, H., and Blandford, G. E. (1991). “Thin‐walled space frames. II: Algorithmic details and applications.” J. Struct. Engrg., ASCE, 117(8), 2521–2539.
7.
Conci, A., and Gattass, M. (1990). “Natural approach for geometric nonlinear analysis of thin‐walled frames.” Int. J. Numer. Methods Engrg., 30(2), 207–231.
8.
Crisfield, M. A. (1990). “A consistent co‐rotational formulation for nonlinear, three‐dimensional, beam‐elements.” Comput. Methods J. Appl. Mech. Engrg., 81(2), 131–150.
9.
Elias, Z. M. (1986). Theory and methods of structural analysis. John Wiley and Sons, New York, N.Y.
10.
Hsiao, K.‐M., Horng, H.‐J., and Chen, Y.‐R. (1987). “A corotational procedure that handles large rotations of spatial beam structures.” Comput. Struct., 27(6), 769–781.
11.
Meek, J. L., and Loganathan, S. (1989). “Large displacement analysis of space‐frame structures.” Comput. Methods Appl. Mech. Engrg., 72(1), 57–75.
12.
Stemple, A. D., and Lee, S. W. (1989). “A finite element model for composite beams undergoing large deflection with arbitrary cross‐sectional warping.” Int. J. Numer. Methods Engrg., 28(9), 2143–2160.
13.
Vlasov, V. Z. (1961). Thin‐walled elastic beams. Israel Program for Scientific Translations Ltd., Jerusalem, Israel.
14.
Yang, Y. B., and McGuire, W. (1986a). “Stiffness matrix for geometric nonlinear analysis.” J. Struct. Engrg., ASCE, 112(4), 853–877.
15.
Yang, Y. B., and McGuire, W. (1986b). “Joint rotation and geometric nonlinear analysis.” J. Struct. Engrg., ASCE, 112(4), 879–905.
16.
Ziegler, H. (1968). Principles of structural stability. Blasdell Publishing, Waltham, Mass.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 117 • Issue 8 • August 1991
Pages: 2499 - 2520
Copyright
Copyright © 1991 ASCE.
History
Published online: Aug 1, 1991
Published in print: Aug 1991
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.