A simplified algorithm for planar development of 3D surface and its application in the blank design of sheet metal forming

This paper introduces a simplified algorithm for generating planar developments of arbitrarily three-dimensional (3D) surface. The 3D surface is first divided into triangular finite elements, the deformation from the curved surface to its planar development is then modeled by in-plane strains of elemental edges. The developed planar shape corresponding to minimum deformation nonuniformity and volume constancy is obtained by solving a constrained nonlinear programming problem. A multi-step scheme of the algorithm is presented and applied to the blank design of sheet metal parts. Based on the assumption that the thickness strain is one of the principal strains, the deformations from the final part to its initial blank are estimated. Numerical and experimental results as well as application examples demonstrate that the present algorithm can predict the blank shape of 3D sheet metal part within a small range of error with low computing time.