Isogeometric algorithm for one-step inverse forming of sheet metal

The isogeometric one-step inverse forming method aims to predict the shape of blanks and the formability of stamping parts using accurate geometry without meshing. In this paper, the discrete surface Ricci flow algorithm in computational conformal geometry is introduced as an unfolding algorithm for one-step inverse forming of isogeometric membrane elements. A combination of discrete surface Ricci flow algorithm and elastic iteration is proposed to predict the initial solution. It is proved applicable, even for the extremely curled parts which have negative angles and vertical walls. In addition, we propose a method that the external force of the punch is equivalent to the control point by means of Greville abscissae. A nonlinear equation system is established based on the principle of minimum potential energy. The Newton–Raphson iteration is used to calculate the blank shape and the thickness distribution of the stamping parts. The examples of square box, flower box, and L shape prove that the algorithm can predict the contour of the initial configuration and the formability of sheet metal stamping.