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 13.
KeywordsStructural Optimization Linear Programming Problem Symmetric Matrice Network Flow Incidence Matrix
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- Structural optimization has its roots in Michell (1904). The first paper in which truss design was formulated as a linear programming problem is Dorn et al. (1964). A few general references on the subject include Hemp (1973), Rozvany (1989), Bendsoe et al. (1994), and Recski (1989).Google Scholar