An improved existence theorem for rigid nonlinearly elastic plates

Abstract

A plate is rigid if its admissible displacement fields inducing vanishing two-dimensional strain tensors must vanish. We prove that the nonlinear model of Kirchhoff-Love for such a plate has a solution for any applied forces and boundary conditions. Then we give sufficient conditions on the data ensuring the rigidity of the plate. Together, these results substantially generalize an existence theorem by Rabier whereby the plate is assumed to be clamped on its entire boundary.