TECHNICAL PAPERS
May 1, 1983

Minimax in Structural Design

Publication: Journal of Structural Engineering
Volume 109, Issue 5

Abstract

A method for designing a trussed type structure subject to stress and displacement constraints has been developed and applied to typical examples of structural optimization. The method is based on the transformation of a constrained minimization problem with homogeneous constraints into an unconstrained minimax formulation. The latter problem is then solved using the norm optimization method. Conceptually, the technique substitutes the constrained minimization problem by a sequence of unconstrained formulations. The method is simple to implement, and does not suffer from problems inherent to the more classical penalty approach. An implementation on wellknown examples emphasizes the main features of the method.

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References

1.
Fiacco, A. V., and McCormick, G. P., Non‐linear Programming; Sequential Unconstrained Minimization Technique, John Wiley and Sons, Inc., New York, N.Y.
2.
Fox, R. L., Optimization Method in Engineering Design, Addison‐Wesley Publishing Co., Reading, Mass., 1971.
3.
Fuchs, M. B., “Structural Optimization with Linearized Homogenous Functions,” Int. J. Mech. Sc., Vol. 22, 1980, pp. 33–40.
4.
Fuchs, M. B., and Brull, M. A., “Norm Optimization Method in Structural Design,” AIAA Journal, Vol. 16, No. 1, Jan., 1970, pp. 20–28.
5.
Himmelblau, D. M., Applied Non‐Linear Programming, McGraw‐Hill Book Co., Inc., New York, N.Y., 1972.
6.
Pope, G. G., and Schmit, L. A., “Structural Design Applications of Mathematical Programming Techniques,” AGARD‐AG‐149, London, England, 1972.
7.
Reference Manual, IMSL Library, 8th ed., Vol. 3, IMSL Inc., USA, 1980.
8.
Schmit, L. A., “Structural Design by Systematic Synthesis,” Proceedings, 2nd National Conference Electa. Comp., Structural Division, ASCE, N.Y., 1960, pp. 105–122.
9.
Schmit, L. A., and Farshi, B., “Some Approximation Concepts for Structural Synthesis,” AIAA Journal, Vol. 12, No. 5, May, 1974, pp. 692–699.
10.
Venkayya, V. B., “Design of Optimum Structures,” Journal of Computers and Structures, Vol. I, No. 1–2, Aug., 1971, pp. 265–309.

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Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 109Issue 5May 1983
Pages: 1107 - 1117

History

Published online: May 1, 1983
Published in print: May 1983

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Authors

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Moshe B. Fuchs
Sr. Lect., Dept. of Solid Mechanics, Materials and Structures, School of Engrg., Tel‐Aviv Univ., Ramat‐Aviv, Tel‐Aviv 69978, Israel

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