Defining developable ship surfaces considering material properties

Abstract

This paper presents a practical method to define a quasi-developable surface that leans on two boundary curves or directrices. As a main difference with the rest of literature that works with quasi-developable surfaces assuming the fact that most of practical materials allow for a little bit of stretching, this paper presents how to quantify this developability in terms of a geometrical factor, the limit warp angle. The limit warp angle has been calculated numerically for steel and aluminum, applying a bending moment to plates of different geometries until a given percentage of the material's yield stress is surpassed. It has been demonstrated that developability depends on the material properties, thickness and aspect ratio of the plates that will be used to construct the real surface. The presented approach considers both physics and geometry and links them together. By considering the limit warp angle, a quasi-developable surface can be obtained without altering the directrices shape, unless the directrix curves present a very different shape between each other. This is very useful in engineering applications that produce designs based on curves and ease the use of parametric design techniques into the object definition. The constrained or parametric definition of ship hulls is beneficial during the initial phases of the ship design because it speeds up the creation process, provides more clarity about the influence of various parameters, and allows for the development of a range of concept hull surfaces. All the designs and calculations in this paper have been developed with a single, affordable and non specialized CAD software, indicating the capabilities of CAD products currently available for any designer.