A model for prediction of springback and residual stress distribution of a beam/plate
subjected to three-point bending and reverse bending is developed based on a
mechanical-geometrical approach. A converged solution that satisfies both the
Euler–Bernoulli beam theory and the geometrical constraints is obtained by a
recursive scheme. The model can be applied to bending/unbending analyses of plates
when the beam bending approaches a plane strain condition. Springback and residual
stress distribution of a plate is predicted quite accurately by the model as verified by
finite element analyses and experiments. Accuracy of springback and residual
stress prediction of the model is examined with consideration of various
geometry parameters of the beam and the fulcrum/support cylinders. The
goal of this investigation is to develop an accurate and efficient model to
predict the profile and residual stress of plates curved by bending in the
postyield range. The developed model can serve as a unit cell of a more
sophisticated model for leveling analyses of metal plates as multiple rollers are
involved.