Automatic Two-Stage Calculation of Bifurcation Path of Perfect Shallow Reticulated Domes
Publication: Journal of Structural Engineering
Volume 133, Issue 2
Abstract
In this paper an attempt is made to automatically calculate the bifurcation of the buckling path of shallow lattice domes. This calculation is performed in a two-stage analysis of the space structure without introducing any geometrical imperfections. The method is implemented in a combined materially and geometrically nonlinear finite element analysis computer program based on an incremental/iterative Newton-Raphson solution procedure. In the first stage analysis, the load factors at which critical points occur are determined and the primary path is obtained. In the second stage analysis the perfect structure is lead toward the lowest bifurcation path using the technique described in this paper. The resulting theoretical predictions are verified by existing experimental observations on two model domes.
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References
Bathe, K. J. (1982). Finite element procedures in engineering analysis, Prentice-Hall, Englewood Cliffs, N.J., Chap. 8, 439–470.
Crisfield, M. A. (1980). “A fast incremental/iterative solution that handles snap-through.” Comput. Struct., 12, 55–62.
Gioncu, V. (1995). “Buckling of reticulated shells, state-of-the-art.” Int. J. Space Struct., 10(1).
Gourlay, A. R., and Watson, G. A. (1973). Computational methods for matrix eigenproblems, Unwin Brothers Ltd.
Kani, I. M. (1986). “A theoretical and experimental investigation of collapse of shallow reticulated domes.” Ph.D. thesis, Dept. of Engineering, Cambridge Univ., Cambridge, U.K.
Kani, I. M., and McConnel, R. E. (1987). “Collapse of shallow lattice domes.” J. Struct. Eng., 113(8), 1806–1819.
Kani, I. M., and McConnel, R. E. (1988). “Single layer shallow lattice domes, general behaviour, and collapse.” Int. J. Space Struct., 3(2), 64–73.
Lock, A. C. (1971). “The application of finite elements to linear and nonlinear static and dynamic analysis of shallow structures.” Ph.D. thesis, Dept. of Civil and Structural Engineering, Univ. College, Cardiff, U.K.
Ramm, E. (1980). “Strategies for tracing nonlinear response near limit points.” Europe̱U.S. workshop: Nonlinear finite element analysis in structural mechanics, Bochum, West Germany.
Riks, E. (1984). “Some computational aspects of stability analysis of nonlinear structures.” Comput. Methods Appl. Mech. Eng., 47, 219–259.
Wright, D. T. (1965). “Membrane forces and buckling in reticulated shells.” J. Struct. Div., 91, 173–201.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 133 • Issue 2 • February 2007
Pages: 185 - 194
Copyright
© 2007 ASCE.
History
Received: Aug 23, 2005
Accepted: May 15, 2006
Published online: Feb 1, 2007
Published in print: Feb 2007
Notes
Note. Associate Editor: M. Asghar Bhatti
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