Growing optimal pin-jointed frames

The problem is addressed of growing least-volume trusses, starting from the simplest possible layout rather than from a complex ground structure. This approach to the optimal-layout problem is shown to be well suited to deflection-space methods of solution, which allow geometry and layout to be optimized simultaneously. The method has the advantage that it can produce much simpler, more realistic structures; allows joint-weight to be taken into account; and involves smaller computational problems. The key task at each stage is to generate least-volume linearly-elastic pin-jointed frames with prespecified numbers of joints. This problem is well-posed and is shown by examples to be solvable. The obstacles to be overcome in order to produce a practical computer implementation are analysed.