peteroznewman
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What is the Winkler foundation? What is a LPB analysis?
What is the skin material and thickness of the sandwich?
What is the core material and thickness of the sandwich?
Wrinkling is a local buckling phenomenon. The geometry should have a small perturbation in the shape that you expect the model to buckle.
One simple way to model this is with shell elements on the skin sharing nodes with solid elements for the core.