Performance factors and design charts can be used to quickly model and compare the mass-efficiency of different materials, shapes and structural forms

This thesis presents a new theory of shape transformers for modelling the mass-efficiency of structures at the conceptual stage of design. A shape transformer, S, is a dimensionless parameter which relates a geometric quantity, G, of a cross-section, such as the area, to the geometric quantity, G_D, such as the area, of the envelope which surrounds a cross-section. Shape transformers describe the shape properties of a cross-section and are used to define classes of shapes in a way which is similar to the way in which materials are classified.

The advantage of shape transformers is that the contribution of the shape can be specified separately to the contribution of the sizes of a cross-section. A geometric quantity G of a cross-section can be expressed by the product of the shape properties, S, and the geometric quantity of the envelope, G_D, i.e. G=S×G_D. This allows the fundamental equations of mechanics to be expressed in terms of material properties, M, shape properties, S, and geometric quantity of the envelope, G_D, i.e..M×S×G_D.

Shape transformers are used to produce analytical solutions to the mass-efficiency of cross-sections. A general solution has been produced for performance indices for arbitrarily scaled cross-sections. Shape transformers are also employed to examine structured layered systems with different material and shape properties. Plastic shape transformers are defined also for the case of plastic bending design.

Shape transformers are used to produce selection charts and design maps for materials, shapes and forms. The interaction between the selection of a cross-section and the selection of a structural form is explored when buckling is included. Shape transformers are applied to man-made and natural structures and used to tackle an industrial case study. The theory of the shape transformers provides insight for designers, students and educators.