Computer-Aided Development of Shell Plates

Ship hulls and other curved shells, like gas tanks, aircraft bodies, and even clothes and shoes, offer a common difficulty in their manufacturing: it is necessary to produce them from a set of formerly plane elements. These plane elements, the raw materials like plates and fabric pieces, must be curved and assembled together to form the final product. The reverse of the forming process of these curved elements, is the map of the curved surface onto the plane, which is improperly known as development. To develop a surface, in a proper sense, is to unfold it onto the plane without stretching or bulging. This is not possible with all kinds of shapes, such as spherical and saddle surfaces. Some common developable surfaces are the conical and cylindrical ones. To form a non-developable shell requires much more work than to form an equivalent shell of developable shape. This increases the costs, the processing times and the defect content. Nevertheless, the fluid dynamists and the other designers are not always free to use developable shapes in their concepts; therefore, a pragmatic approach to the construction of curved shells has to cope with non-developable surfaces. These subjects are chiefly of an advanced mathematic nature, and the required background is too widely spread in the bibliography. Therefore the necessary mathematical results are compiled and presented in Chapter 2 - The Mathematics of Developable Surfaces, providing for a unified view of the concepts, the symbols and the nomenclature. Since the advent of the digital computer, the increasing availability of computing power enabled new methods for surface development and for developable surface definition. By examining and comparing the methods reported in the literature, CHAPTER 3 - Plate Development and Developable Surfaces provides a broad view of the surface development issues, along with the developability conditions and the technologies for the definition of developable surfaces. Given the absence of developability conditions in some areas of the shell, a number of methodologies are reported which produce a plate map onto the plane. In Chapter 4 - Concept and Implementation of an Algorithm, the concept and the implementation of a new development algorithm is described, analysed and applied to example cases. By geodesicaly mapping the surface onto the plane, this method avoids the implementation difficulties of both non- developable surfaces, and developable surfaces with ruling lines aligned in any direction. Therefore, the slightly non-developable plates, commonly found in actual ship hulls, are easily accommodated by this process, working as a map onto the plane. In Chapter 5 - Industrial Application of the Improper Geodesic Map, the user interface of the method is presented. The method provides information about the surface developability and fairness, which assists the user in the decision to develop or otherwise to take corrective measures, like re-fairing or editing of seams and butts. Results obtained from analytical plates, and comparisons with results from both a 1/10-scale electrostatic development jig, and a commercial software package, validate the method. Other results, obtained from actual ship plates, are also presented, further confirming the good accuracy of the method's developments and its good behaviour when processing non-developable plates. This method is in current use, as part of a shipyard system