Optimization of structural design

Typical problems of optimal structural design are discussed to indicate mathematical techniques used in this field. An introductory example (Section 2) concerns the design of a beam for prescribed maximal deflection and shows how suitable discretization may lead to a problem of nonlinear programming, in this case, convex programming. The problem of optimal layout of a truss (Section 3) is discussed at some length. A new method of establishing optimality criteria (Section 4) is illustrated by the optimal design of a statically indeterminate beam of segmentwise constant or continuously varying cross section for given deflection under a single concentrated load. Other applications of this method (Section 5) are briefly discussed, and a simple example of multipurpose design (Section 6) concludes the paper.