' Introduction T concept of optimization is intrinsically tied to natural phenomena as well as to the human desire to excel. Sir George Cayley (1773-1857) measured the shape of a trout and noted, without mathematical proof, that the trout was ideally proportioned to minimize flow resistance. Theodore von Kdrmdn observed that this is precisely the shape of a lowdrag airfoil. Oliver Wendell Holmes (1809-1894), in his classic verse, Deacon's Masterpiece; or, The Wonderful OneHoss Shay, recorded man's desire to produce a uniformly strong, durable product. In this case it was the structural design of a shay to last a hundred years. Perhaps the first analytical work in structural optimization was by Maxwell in 1869, followed by the better-known work of Michell in 1904. These works provided theoretical lower bounds on the weight of trusses, and, although highly idealized, offer considerable insight into the structural optimization problem and the design process. The 1940s and early 1950s saw development of component optimization in such works as Shanley's Weight-Strength Analysis of Aircraft Structures. Also during this period, availability of the digital computer led to application of linear programming techniques to plastic design of frames, for example, the work of Heyman. This early numerical work is particularly significant in that it used mathematical programming techniques developed in the operations research community to solve structural design problems. Schmit in 1960 was the first to offer a comprehensive statement of the use of mathematical programming techniques to solve the nonlinear-inequality-constrained problem of designing elastic structures under a multiplicity of loading conditions. This work is significant, not only in that it ushered in an era of structural optimization, but also because it offered a new philosophy of engineering design which is only now beginning to be broadly applied. In Ref. 9 Schmit provides an excellent historical review of the development of this concept. Although this discussion will emphasize numerical design techniques, it is important to note that there has been an extensive amount of research in analytical methods of design. That work, although sometimes lacking the practicality of being applied to realistic structures, is nonetheless of fundamental importance because it provides insight into the design problem and because it often provides theoretical lower bounds against which more practical designs may be judged. References 10 and 11 provide an extensive review of the state-of-the-art in analytical design techniques. It is the use of numerical techniques in structural optimization that is emphasized here. The purpose is not to offer a tutorial on optimization or a comprehensive literature survey, although such works are referenced. Rather, it is to look briefly at the short history of modern structural optimization and assess the state-of-the-art from a somewhat more philosophical viewpoint. In this way we may begin to understand the ramifications of this fascinating approach to design. By learning what is now possible and what is not now possible, we may encourage the use of these techniques by practicing designers as well as identify research and development needs of the future.
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Feb 1, 1985
Robert M. O'Keefe 
Open Access