Layout Theory for Grid-Type Structures

The aim of this lecture is to review the theory of optimal layouts for structural systems consisting of intersecting, slender members that occupy only a small proportion of the available space. This layout theory, a generalization of a classical idea by Michell [1] developed by Prager and the author in the seventies and extended by the author in the eighties, is based on two underlying concepts, namely (i) the structural universe (or ground structure), which is a union of all potential members or elements and (ii) continuum-type optimality criteria (COC) which are expressed in terms of a fictitious system termed adjoint structure. After discussing basic features of the above layout theory and demonstrating it on some elementary examples, a brief review of past applications is given and finally recent developments relating to new classes of layouts are discussed. These results involve some new theorems, namely those of “domain incrementation” and “local violations”, which are also outlined briefly. Whilst this lecture discusses analytical solutions for optimal layouts, numerical algorithms based on the same theory will be discussed in the second lecture.

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