Abstract
This paper discusses structural optimization based on the concept of integration of modules of structural analysis, sensitivity analysis, and optimization by mathematical programming.
A system of this kind must possess sufficient flexibility to both cope with problems of minimizing cost subject to several behavioral constraints, and problems of multicriteria optimization for given cost. A convenient and simple way of achieving such flexibility is to cast the latter type of problem in scalar form by stating it as minimization of the maximum of a weighted set of the criteria. Such an interpretation of the multicriterion optimization problem can be formulated as a problem of minimizing an upper bound on the weighted criteria, and this bound formulation is very similar to that of the cost minimization problem. The approach has been implemented in connection with a slightly modified version of Fleury and Braibant’s dual mathematical programming method using mixed design variables, and is illustrated via several examples.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
W. Stadler: “Applications of Multieriterion Optimization in Engineering and the Sciences (A Survey)”, in MCDM -Post Decade and Future Trends (Ed. M. Zeleny), JAI Press, Greenwich, Conn., 1983.
W. Stadler: “A Comprehensive Bibliography on MCDM”, ibid.
H. Eschenauer: “Numerical and Experimental Investigations on Structural Op-timization of Engineering Designs”, Rept. University of Siegen.FRG. 1986.
A. Osyczka and J. Koski: “Selected Works Related to Multicriterion Optimization Methods for Engineering Design”, in Optimization Methods in Structural Design (Eds. H. Eschenauer and N. Olhoff), Proc. Euromech Colloquium 164. Siegen, FRG, 1982, Bibliographisches Institut, Mannheim, FRG, 1983.
M.P. Bendsøe, N. Olhoff and J.E. Taylor: “A Variational Formulation for Multicriteria Structural Optimization”, J. Struct. Mech.. Vol. 11, pp. 523– 544, 1983.
J.E. Taylor, and M.P. Bendsøe: “An Interpretation for Min-Max Structural Design Problems Including a Method for Relaxing Constraints”, Int. J. Solids Structures. Vol. 20, pp. 301–314, 1984.
J.E. Taylor: “Distributed Parameter Optimal Structural Design: Some Basic Problem Formulations and Their Application”, in Computer Aided Optimal Design: Structural and Mechanical Systems (Ed. C.A. Mota Soares) Springer- Verlag, Berlin, FRG, 1987.
C. Fleury: “Computer Aided Optimal Design of Elastic Structures”, ibid.
C. Fleury and V. Braibant: “Structural Optimization: A New Dual Method Using Mixed Variables”, Int. J. Num. Meth. Engrg.. Vol. 23, pp. 409–428, 1986.
N. Olhoff: “Multicriterion Structural Optimization via Bound Formulation and Mathematical Programming”, Structural Optimization (to appear).
S. Kibsgaard: “Multipurpose Optimization of Vibrating Timoshenko Shafts”, in these proceedings.
N. Olhoff and S.H. Rasmussen: “On Single and Bimodal Optimum Buckling Loads of Clamped Columns”, Int. J. Solids Structures. Vol. 13, pp. 605–614, 1977.
N. Olhoff: “Maximizing Higher Order Eigenfrequencies of Beams with Constraints on the Design Geometry”, J. Struct. Mech.. Vol. 5, pp. 107–134, 1977.
N. Olhoff and R. Parbery: “Designing Vibrating Beams and Rotating Shafts for Maximum Difference Between Adjacent Natural Frequencies”, Int. J. Solids Structures. Vol. 20, pp. 63–75, 1984.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin, Heidelberg
About this paper
Cite this paper
Olhoff, N. (1989). Optimal Structural Design via Bound Formulation and Mathematical Programming. In: Eschenauer, H.A., Thierauf, G. (eds) Discretization Methods and Structural Optimization — Procedures and Applications. Lecture Notes in Engineering, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83707-4_32
Download citation
DOI: https://doi.org/10.1007/978-3-642-83707-4_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50784-0
Online ISBN: 978-3-642-83707-4
eBook Packages: Springer Book Archive