Most of the current optimization techniques for the design of light-weight structures are unable to generate structural alternatives at the concept stage of design. This research tackles the challenge of developing an optimization method for the early stage of design. The main goal is to propose a procedure to optimize material and shape of stiff shafts in torsion. / Recently introduced for bending stiffness design, shape transformers are presented in this thesis for optimizing the design of shafts in torsion. Shape transformers are geometric parameters defined to classify shapes and to model structural efficiency. The study of shape transformers are centered on concept selection in structural design. These factors are used to formulate indices of material and shape selection for minimum mass design. An advantage of the method of shape transformers is that the contribution of the shape can be decoupled from the contribution of the size of a cross-section. This feature gives the designer insight into the effects that scaling, shape, as well as material have on the overall structural performance. / Similar to the index for bending, the performance index for torsion stiffness design is a function of the relative scaling of two cross-sections. The thesis examines analytically and graphically the impact of scaling on the torsional efficiency of alternative cross-sections. The resulting maps assist the selection of the best material and shape for cross-sections subjected to dimensional constraints. It is shown that shape transformers for torsion, unlike those for bending, are generally function of the scaling direction. / The efficiency maps ease the visual contrast among the efficiency of open-walled cross-sections and that of close-walled cross-sections. As expected, the maps show the relative inefficiency of the former compared to the latter. They can also set the validity range of thin- and thick-walled theory in torsion stiffness design. The analytical results are validated with the numerical data obtained from ANSYS to guarantee the consistency of the models. The thesis concludes with three case studies that demonstrate the method.

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