Optimum Design of Trusses with Buckling Constraints
Publication: Journal of Structural Engineering
Volume 111, Issue 7
Abstract
A method is developed for the optimum design of trusses including constraints on tension and compression stresses, displacements and bounds on the design variables. It is intended to solve a practical problem. The method takes into account the efficiencies achieved for simpler mathematical models where the allowable values for compression stresses are constant. In this work, these values depend on the member cross section and are prescribed in the Code AISC‐78. All the peculiarities introduced by the buckling constraints are identified and solved. They are: (1) Consideration of the radius of gyration, in addition to the cross‐sectional area, as design variable; (2) introduction of more complicated constraint functions; and (3) computation of a scale factor to the constraint surface for buckling restrictions. The problem is solved by means of a sequence of approximate problems in the dual space. The approximation is basically due to the fact that the constraint functions are replaced by their first order Taylor series expansions to improve the efficiency of the solution. The effectiveness of the method is shown through some examples.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
American Institute of Steel Construction, Manual of Steel Construction, 8th Ed., AISC Inc., New York, N.Y., 1978.
2.
Berke, L., and Khot, N. S., “Use of Optimality Criteria Methods for Large Scale Systems,” Structural Optimization, AGARD‐LS‐70, Technical Editing and Reproduction Ltd., London, Sept., 1974, pp. 1.1–1.29.
3.
Brown, D. M., and Ang, A. H. S., “Structural Optimization by Nonlinear Programming,” Journal of the Structural Division, ASCE, Vol. 92, No. ST6, Dec., 1966, pp. 319–340.
4.
Cassis, J., and Aravena, S., “Diseño Optimo de Enrejados de Acero,” Proceedings of the XX Jornadas Sudamericanas de Ingeniería Estructural, VI Simposio Panamericano de Estructuras, Vol. III, Córdoba, Argentina, July, 1979, pp. E.8‐1–E.8.22.
5.
Cassis, J., and Guzmán, J., “Diseño Automático de Pórticos de Acero Aplicando Criterios de Optimidad,” Proceedings of the XIX Jornadas Sudamericanas de Ingeniería Estructural, Vol. II, Santiago, Chile, Apr., 1978, pp. F.11.1–F.11‐22.
6.
Cassis, J., and Schmit, L., “Optimum Structural Design with Dynamic Constraints,” Journal of the Structural Division, ASCE, Vol. 102, No. ST10, Oct., 1976, pp. 2053–2071.
7.
Cassis, J. H., “Optimum Design of Structures Subjected to Dynamic Loads,” UCLA, Eng.‐7451, University of California, Los Angeles, Calif., June, 1974.
8.
Fedalto, J. A., and Casis, J., “Projeto Otimo da Geometria de Trelicças Planas,” Proceedings of the Simposio sobre Sistemas Computacionais para Engenharia Civil, Vol. 2, Río de Janeiro, Brasil, Oct., 1977, pp. 383–401.
9.
Fleury, C., “Optimisation des Structures par la Méthode des Eléments Finis,” Publ. Faculty of Applied Sciences, No. 52, University of Liege, Liege, Belgium, 1976.
10.
Gellatly, R. A., and Berke, L., “Optimal Structural Design,” AFFDL‐TR‐70‐165, USAF Report, 1971.
11.
Lapay, W., and Goble, G., “Optimum Design of Trusses for Ultimate Loads,” Journal of the Structural Division, ASCE, Vol. 97, No. 1, Jan., 1971, pp. 157–173.
12.
Schmit, L. A., and Fleury, C., “An Improved Analysis/Synthesis Capability Based on Dual Methods‐Access 3,” Proceedings of the AIAA/ASME/AHS 20th Strutures, Structural Dynamics, and Materials Conference, Vol. 1, St. Louis, Mo., Apr., 1979, pp. 23–55.
13.
Schmit, L. A., and Miura, H., “Approximation Concepts for Efficient Structural Synthesis,” NASA CR‐2552, Mar., 1976.
14.
Schmit, L. A., and Farshi, B., “Some Approximation Concepts for Structural Synthesis,” Journal of the AIAA, Vol. 12, No. 5, 1974, pp. 692–699.
15.
Schmit, L. A., “Structural Design by Systematic Synthesis,” Proceedings of the 2nd National Conference on Electronic Computation, Structural Division, ASCE, Pittsburg, Pa., Sept., 1960, pp. 105–132.
16.
Sepúlveda, A., and Cassis, J., “Aplicación de Dualidad en el Diseńo Optimo de Enrejados con Variables Discretas y Mixtas,” Publicatión SES 12/84 (191), Departamento de Ingeniería Civil, Universidad de Chile, Santiago, Chile, Jan., 1984.
17.
Taig, I. C., and Kerr, R. J., “Optimisation of Aircraft Structures with Multiple Stiffness Requirements,” Proceedings of the AGARD 2nd. Symposium on Structural Optimization, Milan, Italy, Apr., 1973, AGARD‐CP‐123, Paper 16.
18.
Toews, E., and Cassis, J., “Métodos Duais em Otimizacçao Estrutural,” Proceedings of the XXI Jornadas Sul Americanas de Engenharia Estrutural, Asociación Latinoamericana para Métodos Computacionales en Ingeniería, Vol. 3, Rio de Janeiro, Brasil, May, 1981, pp. 31–52.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 111 • Issue 7 • July 1985
Pages: 1573 - 1589
Copyright
Copyright © 1985 ASCE.
History
Published online: Jul 1, 1985
Published in print: Jul 1985
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.