Abstract
Most problems in structural optimization must be formulated as constrained minimization problems. In a typical structural design problem the objective function is a fairly simple function of the design variables (e.g., weight), but the design has to satisfy a host of stress, displacement, buckling, and frequency constraints. These constraints are usually complex functions of the design variables available only from an analysis of a finite element model of the structure. This chapter offers a review of methods that are commonly used to solve such constrained problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kreisselmeier, G., and Steinhauser, R., “Systematic Control Design by Optimizing a Vector Performance Index,” Proceedings of IFAC Symposium on Computer Aided Design of Control Systems, Zurich, Switzerland, pp. 113–117, 1979.
Sobieszczanski-Sobieski, J., “A Technique for Locating Function Roots and for Satisfying Equality Constraints in Optimization,” NASA TM-104037, NASA LaRC, 1991.
Wolfe, P.. “The Simplex Method for Quadratic Programming,” Econometrica, 27(3), pp. 382–398, 1959.
Gill, P.E., Murray, W., and Wright, M.H., Practical Optimization, Academic Press, 1981.
Dahlquist, G., and Bjorck, A., Numerical Methods, Prentice Hall, 1974.
Sobieszczanski-Sobieski, J., Barthelemy, J.F., and Riley, K.M., “Sensitivity of Optimum Solutions of Problem Parameters”, AIAA Journal, 20(9), pp. 1291–1299, 1982.
Rosen, J.B., “The Gradient Projection Method for Nonlinear Programming— Part I: Linear Constraints”, The Society for Industrial and Appl. Mech. Journal, 8(1), pp. 181–217, 1960.
Abadie, J., and Carpentier, J., “Generalization of the Wolfe Reduced Gradient Method for Nonlinear Constraints”, in: Optimization (R. Fletcher, ed.), pp. 37–49, Academic Press, 1969.
Rosen, J.B., “The Gradient Projection Method for Nonlinear Programming—Part II: Nonlinear Constraints”, The Society for Industrial and Appl. Mech. Journal, 9(4), pp. 514–532, 1961.
Haug, E.J., and Arora, J.S., Applied Optimal Design: Mechanical and Structural Systems, John Wiley, New York, 1979.
Zoutendijk, G., Methods of Feasible Directions, Elsevier, Amsterdam, 1960.
Vanderplaats, G.N., “CONMIN—A Fortran Program for Constrained Function Minimization”, NASA TM X-62282, 1973.
Fiacco, V., and McCormick, G.P., Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley, New York, 1968.
Haftka, R.T., and Starnes, J.H., Jr., “Applications of a Quadratic Extended Interior Penalty Function for Structural Optimization”, AIAA Journal, 14(6), pp.718–724, 1976.
Dahlguist, J., “Penalty Function Methods in Optimum Structural Design—Theory and Applications”, in: Optimum Structural Design (Gallagher and Zienkiewicz, eds.), pp. 143–177, John Wiley, 1973.
Shin, D.K, Gürdal, Z., and Griffin, O. H. Jr., “A Penalty Approach for Nonlinear Optimization with Discrete Design Variables,” Engineering Optimization, 16, pp. 29–42, 1990.
Bertsekas, D.P., “Multiplier Methods: A Survey,” Automatica, 12, pp. 133–145, 1976.
Hestenes, M.R., “Multiplier and Gradient Methods,” Journal of Optimization Theory and Applications, 4(5), pp. 303–320, 1969.
Fletcher, R., “An Ideal Penalty Function for Constrained Optimization,” Journal of the Institute of Mathematics and its Applications, 15, pp. 319–342, 1975.
Powell, M.J.D., “A Fast Algorithm for Nonlinearly Constrained Optimization Calculations”, Proceedings of the 1977 Dundee Conference on Numerical Analysis, Lecture Notes in Mathematics, Vol. 630, pp. 144–157, Springer-Verlag, Berlin, 1978.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Haftka, R.T., Gürdal, Z. (1992). Constrained Optimization. In: Elements of Structural Optimization. Solid Mechanics And Its Applications, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2550-5_5
Download citation
DOI: https://doi.org/10.1007/978-94-011-2550-5_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-1505-6
Online ISBN: 978-94-011-2550-5
eBook Packages: Springer Book Archive