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Can I arbitrarily pick the nodes to constrain for a springback analysis?

It depends on the problem. Many people simply pick the constrain nodes, and after spring back analysis, they use rigid body motion and rotation to get the final spring back analysis.

If the part is very stiff and the gravity effect is small, the above method works just fine. However, if the part is very flexible and the gravity effect play a significant role, then the constrained nodes should be picked exactly as that used in experimental measurement.