Shape as a structural design parameter.

The objective of this thesis is to present evidence to demonstrate the importance of layout in economical structural design, to review techniques by which structural shape may be handled as a design parameter and to determine the implications of varying layout in certain design situations. The thesis begins with a study of the theory of Michell structures. The difficulty of applying this theory directly to practical design problems then leads to a review of the linear approximation techniques for satisfying the Michell conditions for maximum material economy. The Michell theory however is restricted in its relevance to engineering practice. Consideration is therefore given to other optimisation techniques of mathematical programming. These methods permit quite general forms of merit criterion to be specified and allow a wide range of constraints to be imposed on the design. The results however can usually be justified only on pragmatic grounds rather than judged against an absolute determinable limit of merit. Dynamic programming is investigated as a means of optimising the layout of simple structures with a specified topology. Limitations in this application of the technique become evident but it is possible to use it to obtain results from which the value of varying layout may be deduced in the particular circumstances of discrete section design and of stability limitations.