Control of lines of curvature for plate forming in shipbuilding

A ship hull consists of smooth streamlined surfaces satisfying hydrodynamic characteristics such as frictional, pressure, and wave resistances. It contains doubly curved surfaces particularly at the bow and stern. In shipbuilding, surface plates are formed by the mixture of cold and hot bending, which is typically called line heating. An efficient plate forming method based on the lines of curvature has recently garnered the attention of researchers. The initial shape of the plate to be cut, amount of bending angle for cold bending, and amount of contraction for line heating can be determined by flattening the doubly curved surface along the lines of curvature. However, the method suffers if the lines of curvature are wavy, or pass near the umbilical points. We herein propose novel methods for smoothing the lines of curvature and sweeping out the umbilics from each partitioned plate by deforming the surface within a prescribed deviation from the designed surface based on nonlinear optimization. We demonstrated the effectiveness of our proposed method by applying it to the bow of a bulk carrier, which was provided by a shipbuilding yard.