Design for manufacturing using B-spline developable surfaces

A developable surface can be formed by bending or rolling a planar surface without stretching or tearing; in other words, it can be developed or unrolled isometrically onto a plane. Developable surfaces are widely used in the manufacture of items that use materials that are not amenable to stretching such as the formation of ducts, shoes, clothing and automobile parts including upholstery and body panels (Frey & Bindschadler 1993). Designing a ship hull entirely of developable surfaces would allow production of the hull using only rolling or bending. Heat treatment would only be required for removal of distortion, thus greatly reducing the labor required to form the hull. Although developable surfaces play an important role in various manufacturing applications, little attention has been paid to implementing developable surfaces from the onset of a design. This paper investigates novel, user friendly methods to design complex objects using B-spline developable surfaces based on optimization techniques. Illustrative examples show the substantial improvements this method achieves over previously developed methods.