Lofting and Fabrication of Compound-Curved Plates

Abstract

The fabrication of plates with compound curvature (nonzero Gaussian curvature) from initially flat sheet material necessarily involves some degree of in-plane plastic strain. A basically geometric theory is presented for modeling and controlling this process, leading to a quantitative description of both the strain distribution required to achieve the compounding, and the relationship between points and curves on the curved surface and the flat material. The theory thus provides accurate methods for lofting (expansion or plane development) of curved plates, as well as quantitative control of the compounding process. Several methods of numerical solution are presented, with illustrative examples.