Structural Optimization

  • Robert J. Vanderbei
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 114)


This final chapter on network-type problems deals with finding the best design of a structure to support a specified load at a fixed set of points. The topology of the problem is described by a graph where each node represents a joint in the structure and each arc represents a potential member.1 We shall formulate this problem as a linear programming problem whose solution determines which of the potential members to include in the structure and how thick each included member must be to handle the load. The optimization criterion is to find a minimal weight structure. As we shall see, the problem bears a striking resemblance to the minimum-cost network flow problem that we studied in Chapter 14.


Structural Optimization Linear Programming Problem Symmetric Matrice Incidence Matrix Incidence Matrice 
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  1. Michell, A. (1904), ‘The limits of economy of material in frame structures’, Phil. Mag. 8, 589–597.Google Scholar
  2. Dorn, W., Gomory, R. & Greenberg, H. (1964), ‘Automatic design of optimal structures’, J. de M’ecanique 3, 25–52.Google Scholar
  3. Hemp, W. (1973), Optimum Structures, Clarendon Press, Oxford.Google Scholar
  4. Bendsøe, M., Ben-Tal, A. & Zowe, J. (1994), ‘Optimization methods for truss geometry and topology design’, Structural Optimization 7, 141–159.CrossRefGoogle Scholar
  5. Recski, A. (1989), Matroid Theory and its Applications in Electric Network Theory and in Statics, Springer-Verlag, Berlin-Heidelberg-New York.Google Scholar

Copyright information

© Robert J.Vanderbei 2008

Authors and Affiliations

  • Robert J. Vanderbei
    • 1
  1. 1.Dept. of Operations Research and Financial EngineeringPrinceton UniversityNew JerseyUSA

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