Chapter 2 of this work brings together a full set of analytical tools to generate structural layouts which satisfy dual-material optimality conditions. Chapter 3 of the dissertation is concerned with methods to suppress local and global instability of least-weight structures. Perforated webs placed between structural members, structural member shape optimization and light-weight foam inserts are methods investigated in the research to address the instability problems. Simply supported least-weight arch beams were designed and mechanically tested. The experimental results were compared with FEA. In Chapter 4 matrix operator methods used to generate optimal layouts with straight boundaries were extended to include curved boundaries. A program previously written to solve straight boundary problems was generalized to generate layouts for cantilevers with curved boundaries by using this method. In Chapter 5 the design of an arch structure with a continuous profiled-thickness web was analyzed. In Chapter 6 optimal layouts with 2 and 3-bar trusses were investigated for two alternate loading cases. A program was written to determine the minimum-weight from alternative structures.

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