Developable polynomial surface approximation to smooth surfaces for fabrication parameters of a large curved shell plate by Differential Evolution

This paper presents a simple and efficient method to approximate a developable surface to a compound design surface by a polynomial. It is required to predict a final shape of roll bending in the fabrication of a curved shell plate. The roll bending process usually makes the cylindrical or conical curvature from an initial flat plate. It means that the final shape is developable or the surface representation has zero Gaussian curvature. The fabrication shape is important in order to estimate process parameters of roller bending.An optimization problem is formulated to determine the polynomial surface which is in the closest proximity to the design surface or the given shell plate, which is subjected to developability. The results and the efficiency of this algorithm are verified and evaluated by applying it to some shell plates which are obtained from a real ship model. The predicted bending shape becomes fundamental information in determining more process parameters for the fabrication of a compound curved shell plate.