Design of Hyperboloid Structures

The industrial manufacturing is making more widespread use of three-dimensional object recognition techniques. The shapes of many 3D objects can be described using some basic surface elements. Many of these basic surface elements are quadric surfaces, such as spheres and cylinders. For some industrial parts, the surface located at the junction of two other surface elements can often be regarded as either a hyperbolic surface (concave) or a parabolic surface (convex). Therefore, the recognition of hyperboloids and paraboloids is necessary for the recognition or inspection of such kinds of 3D objects. The objective of surface fitting is to fit some kind of mathematical model, such as an equation under a certain kind of coordinate system, to the sample data. For centered quadric surfaces, such an equation can be expressed in a form where fit parameters have a clear geometric meaning, such as a distance or a rotation angle Min & Newman [1] As hyperboloid structures are double curved, that is simultaneously curved in opposite directions, they are very resistant to buckling. This means that you can get away with far less material than you would otherwise need, making them very economical. Single curved surfaces, for example cylinders, have strengths but also weaknesses. Double curved surfaces, like the hyperboloids in question, are curved in two directions and thus avoid these weak directions. This means that you can get away with far less material to carry a load, which makes them very economical. The second reason, and this is the magical part, is that despite the surface being curved in two directions, it is made entirely of straight lines. Apart from the cost savings of avoiding curved beams or shuttering, they are far more resistant to buckling because the individual elements are straight URL-1, URL-2. This is an interesting paradox: you get the best local buckling resistance because the beams are straight and the best overall buckling resistance because the surface is double curved. Hyperboloid structures cunningly combine the contradictory requirements into one form. The hyperboloid is the design standard for all nuclear cooling towers and some coal-fired power plants. It is structurally sound and can be built with straight steel beams.