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TECHNICAL PAPERS

A Sequential Optimization Algorithm Using Logarithmic Barriers: Applications to Structural Optimization

[+] Author and Article Information
Ashok V. Kumar

Department of Mechanical Engineering, University of Florida, Gainesville, FL 32611e-mail: akumar@ufl.edu

J. Mech. Des 122(3), 271-277 (Sep 01, 1999) (7 pages) doi:10.1115/1.1288363 History: Received September 01, 1999
Copyright © 2000 by ASME
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References

Schmit,  L. A., and Farshi,  B., 1974, “Some Approximation Concepts for Structural Synthesis,” AIAA J., 12, No. 5, pp. 692–699.
Fleury,  C., 1979, “Structural Weight Optimization by Dual Methods of Convex Programming,” Int. J. Numer. Methods Eng., 14, pp. 1761–1783.
Fleury,  C., and Braibant,  V., 1986, “Structural Optimization: A New Dual Method Using Mixed Variables,” Int. J. Numer. Methods Eng., 23, pp. 409–428.
Bendso̸e,  M. P., and Kikuchi,  N., 1988, “Generating Optimal Topologies in Structural Design Using a Homogenization Method,” Comput. Methods Appl. Mech. Eng., 71, pp. 197–224.
Bendso̸e, M. P., 1995, Optimization of Structural Topology, Shape and Material, Springer Verlag, Berlin.
Kumar, A. V., and Gossard, D. C., 1993, “Geometric Modeling for Shape and Topology Optimization,” Fourth IFIP WG 5.2, Geometric and Product Modeling, Wilson, P. R., Wozny, M. J., Pratt, M. J., eds.
Kumar,  A. V., and Gossard,  D. C., 1996, “Synthesis Of Optimal Shape And Topology of Structures,” ASME J. Mech. Des., 118, No. 1, pp. 68–74.
Zhang,  W. H., and Fleury,  C., 1997, “A Modification of Convex Approximation Methods for Structural Optimization,” Comput. Struct., 64, Nos. 1–4, pp. 89–95.
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Svanberg,  K., 1987, “The Method of Moving Asymptotes—A New Method for Structural Optimization,” Int. J. Numer. Methods Eng., 24, pp. 359–373.
Monteiro,  R. D. C., and Adler,  I., 1989, “Interior Path Following Primal-Dual Algorithms. Part I: Linear Programming,” Math. Program., 44, pp. 27–41.
Bertsekas, D. P., 1999, Nonlinear Programming, 2nd ed., Athena Scientific, MA.
Fleury, C., 1993, “Mathematical Programming Methods for Constrained Optimization: Dual Methods,” Structure Optimization: Status and Promise, Kamat, M. P., ed., series on Progress in Astronautics and Aeronautics, AIAA, Chap. 7, pp. 123–150.
Fleury, C., 1982, “Reconciliation of Mathematical Programming and Optimality Criteria methods,” Foundations of Structural Optimization, Morris, A., ed., Chap. 10, pp. 363–404, Wiley, New York.
Kumar, A. V., 1993, “Shape and Topology Synthesis of Structures Using a Sequential Optimization Algorithm,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
Zhou,  M., and Rozvany,  G. I. N., 1991, “The COC Algorithm, Part II: Topological, Geometrical and Generalized Shape Optimization,” Comput. Methods Appl. Mech. Eng., 89, pp. 309–336.
Michell, A. G. M., 1904, “The limit of Economy of Material in Frame Structures,” Philos. Mag., 8 , No. 4.

Figures

Grahic Jump Location
Contours of the function f(x1,x2)
Grahic Jump Location
Convergence history for example 1
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Weight minimization of cantilever beam
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Convergence history for example 2
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Optimal shape and topology design
Grahic Jump Location
Convergence history for example 3
Grahic Jump Location
Convergence history for example 4

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