Eulerian Formulation for Large‐Displacement Analysis of Space Frames
Publication: Journal of Engineering Mechanics
Volume 119, Issue 3
Abstract
In this paper, a new general procedure is presented for modeling the effects of large displacements on the response of space frames subjected to conservative loading. An incremental definition of rotations is adopted based on an improved rotational transformation matrix, and a convected (Eulerian) system is employed for establishing the contribution of individual elements to the strain energy (). The Eulerian displacements are obtained by means of element‐based local vectors in which the vectors representing the principal axes of bending follow the deformed configuration of the element and are continuously updated to a position normal to the element chord. The nonlinear solution procedure is formalized in terms of transformations between the Eulerian and the global systems, and expressions for geometric stiffness and transformation matrices are explicitly derived. Verification examples utilizing an elastic quartic formulation and employing the nonlinear analysis program ADAPTIC are presented to demonstrate the accuracy and versatility of this method in the large‐displacement analysis of space frames.
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. (1978a). “On large displacement small strain analysis of structures with rotational degrees of freedom.” Comp. Meth. Appl. Mech. Engrg., Vol. 14, 401–451.
2.
Argyris, J. H., Dunne, P. C., and Scharpf, D. W. (1978b). “On large displacement small strain analysis of structures with rotational degrees of freedom.” Comp. Meth. Appl. Mech. Engrg., Vol. 15, 99–135.
3.
Bathe, K. J., and Bolourchi, S. (1979). “Large displacement analysis of three‐dimensional beam structures.” Int. J. Num. Meth. Engrg., 14(7), 961–986.
4.
Besseling, J. F. (1977). “Derivatives of deformation parameters for bar elements and their use in buckling and postbuckling analysis.” Comp. Meth. Appl. Mech. Engrg., Vol. 12, 97–124.
5.
Izzuddin, B. A., and Elnashai, A. S. (1989). “ADAPTIC: a program for the adaptive dynamic analysis of space frames.” Rep. No. ESEE‐89/7, Imperial College, London, England.
6.
Izzuddin, B. A. (1991). “Nonlinear dynamic analysis of framed structures,” PhD thesis, University of London, Imperial College, London, England.
7.
Jennings, A. (1968). “Frame analysis including change of geometry.” J. Struct. Div., ASCE, 94(3), 627–644.
8.
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.” Comp. Struct., 24(2), 253–271.
9.
Meek, J. L., and Loganathan, S. (1989). “Geometrically non‐linear behaviour of space frame structures.” Comp. Struct., 31(1), 35–45.
10.
Oran, C. (1973). “Tangent stiffness in space frames.” J. Struct. Div., ASCE, 99(6), 987–1001.
11.
Remseth, S. N. (1979). “Nonlinear static and dynamic analysis of framed structures.” Comp. Struct., 10(6), 879–897.
12.
Shi, G., and Atluri, S. N. (1988). “Elasto‐plastic large deformation analysis of space‐frames: a plastic‐hinge and stress‐based derivation of tangent stiffnesses.” Int. J. Num. Meth. Engrg., 26(3), 589–615.
13.
Surana, K. S., and Sorem, R. M. (1989). “Geometrically non‐linear formulation for three dimensional curved beam elements with large rotations.” Int. J. Num. Meth. Engrg., 28(1), 43–73.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 119 • Issue 3 • March 1993
Pages: 549 - 569
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Jun 7, 1991
Published online: Mar 1, 1993
Published in print: Mar 1993
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.