Abstract
This paper describes some methods for producing developable surfaces with practical applications for creating useful lightweight, rigid, jig-less and elegant structural forms from sheet materials. Multiple related techniques based on the same fundamental principle can be used to generate a variety of interesting singly curved and doubly curved shapes. The system requires a minimum of specialist software, and is described in simple steps that can be followed by the reader with access to basic 3D CAD tools.
Highlights
Curved surface shell structures can be used to create very useful, lightweight, rigid structural forms.This paper looks at just one technique of producing shell structures, utilising bent strips of sheet material such as steel plate or plywood, joined together into rigid tubes or shells.Sheet materials can only be bent/curved in particular ways, essentially limited to the surfaces of cylinders and cones, or combinations of various sized cylinders and cones.What is not generally practical is deforming sheet materials into doubly-curved spherical or saddle-shaped/twisted shapes, as these require plastic deformation possible only by applying large forces and/or heat.So what we need is what are called developable surfaces, or rather, shapes that can be assembled from more than one developable surface
A developable surface is a shape that can be formed by simple bending of a sheet material without any twisting or other plastic deformation of the material
This paper introduces a productive technique that works by limiting the range of doubly-curved shapes to a subset that can be broken down into developable surfaces
Summary
Curved surface shell structures can be used to create very useful, lightweight, rigid structural forms. This paper introduces five related techniques for generating such surfaces that allow a vast variety of previously impractical shapes to be produced Most approaches to this problem to date have been to generate doubly-curved shapes with tools such as NURBS patches and attempt to find developable surfaces that approximate these shapes. This paper introduces a productive technique that works by limiting the range of doubly-curved shapes to a subset that can be broken down into developable surfaces. This limitation is that the surfaces are rulings between pairs of carefully constructed splines rather than free-form NURBS patches
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