Corrugated shells: An algorithm for generating double-curvature geometric surfaces for structural analysis

Analysis of corrugated shell structures is an interesting problem in Structural Mechanics, which has many practical applications in Civil Engineering and Architecture. Thanks to corrugation, these structures have a remarkable feature: the wavy (undulated) shape in their edge provides significant enhancements in their structural behaviour, increasing the bending stiffness at the edge and allowing for a non-negligible reduction of its thickness. Moreover, looking at the non-linear behaviour, domes corrugation plays a relevant role in instability phenomena, such as the influence of imperfections and increasing resistance to snap-through. A problem in the study of such kind of shells is the definition of mathematical and geometrical model and the construction of a suitable mesh to perform FE analyses. The aim of this paper is to find an automated way to generate a double-curvature geometric surface that can be used both in static and in non-linear stability analyses of such corrugated shell structures. A method to generate a NURBS surface, suitable for a parametric FE analysis from a geometrical model expressed in a parametric form, is proposed and applied to a shell inspired by the well-known dome designed by Pier Luigi Nervi in 1959 for the roof of the Palasport Flaminio in Rome.