A new calculating method to perform springback predictions for varied curvature sheet bending based on the B-spline function

This paper presents a new method to calculate the bending moments in varied curvature sheet bending. Compared with traditional bending theories which suppose the curvature radii to be constant, the new formulas of stress and strain consider the geometrical characteristics of the profiles, thus they can reflect the internal force in the sheet more accurately. Also, they are consistent with traditional bending theories when the curvature remains unchanged. Springback predictions are performed based on the calculated bending moments. The final shapes of the sheet after springback are obtained by proper discrete and connecting technologies. Two cases are provided to demonstrate the calculating method. In the first case, a cubic non-uniform B-spline curve is used to interpolate the known die profile. This curvature continuity spline gives a relatively accurate expression of the curvature change phenomenon. In the second case, the math expression of a desired bending shape is already known, and the method we proposed is proved to be generally applicable by predicting the final shape of the sheet. The calculating results can reveal how the bending moments change with the curvature radii. They are in great agreement with experiments and also they have been compared with numerical simulations.