Abstract
The optimization of a single column subject to a follower load is studied. The shape of the column that maximizes the critical load for a given amount of material is found using optimization. The objective function is nonsmooth and there are also multiple local optima. Improved solutions to the optimization problem are found and compared to previous columns suggested in the literature. The sensitivity to perturbations in shape and refined discretization is also investigated.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Andersson, E.et al. 1992:LAPACK user's guide. Philadelphia: SIAM
Bažant, Z.P.; Cedolin, L. 1991:Stability of structures. Oxford: Oxford University Press
Cox, S.J.; Overton, M.L. 1992: The optimal design of columns against buckling.SIAM J. Mathematical Analysis 23, 287–325
Gutkowski, W.; Mahrenholtz, O.; Pyrz, M. 1993: Minimum weight design of structures under nonconservative forces. In: Rozvany, G.I.N. (ed.)Optimization of large structural systems, pp. 1087–1100 (Proc. NATO/DFG ASI held in Berchtesgaden, Germany, 1991). Dordrecht: Kluwer
Haftka, R.T.; Adelman, H.M. 1993: Sensitivity of discrete systems. In: Rozvany, G.I.N. (ed.)Optimization of large structural systems, pp. 289–311 (Proc. NATO/DFG ASI held in Berchtesgaden, Germany, 1991). Dordrecht: Kluwer
Mróz, Z. 1993: Design sensitivity of critical loads and vibration frequencies of nonlinear structures. In: Rozvany, G.I.N. (ed.)Optimization of large structural systems, pp. 455–476 (Proc. NATO/DFG ASI held in Berchtesgaden, Germany, 1991). Dordrecht: Kluwer
Olhoff, N.; Taylor, J.E. 1983: On structural optimization.J. Appl. Mech. 50, 1139–1151
Seyranian, A.P. 1991: Sensitivity analysis of multiple eigenvalues.DACMM Report 431, Department of Solid Mechanics, The Technical University of Denmark
Ziegler, H. 1968:Principles of structural stability. Waltham, Mass: Blaisdell
Zyczkowski, M.; Gajewski, A. 1982: Optimal structural design under stability constraints. In: Thompson, J.M.T.; Hunt, G.W. (eds.)Collapse: the buckling of structures in theory and practice, pp. 299–332. Cambridge: Cambridge University Press
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ringertz, U.T. On the design of Beck's column. Structural Optimization 8, 120–124 (1994). https://doi.org/10.1007/BF01743307
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01743307