Integrated shape and material selection for single and multi-performance criteria

A shape and material selection method, based on the concept of shape transformers, has been recently introduced to characterize the mass efficiency of lightweight beams under bending and shear. This paper extends this method to deal with the case of torsional stiffness design, and generalize it to single and multi-crieria selection of lightweight shafts subjected to a combination of bending, shear, and torsional load. The novel feature of the paper is the useful integration of shape and material to model and visualize multi-objective selection problems. The scheme is centered on concept selection in structural design, and hinges on measures that govern the shape properties of a cross-section regardless of its size. These measures, referred as shape transformers, can classify shapes in a way similar to material classification. The procedure is exemplified by considering torsional stiffness as a constraint. The performance charts are developed for single and multi-criteria to visualize in a glance the whole range of cross-sectional shapes for each material. Each design chart is explained with a brief example.