An improved existence theorem for rigid nonlinearly elastic plates

TL;DR

This paper proves the existence of solutions for a nonlinear elastic plate model under broad conditions, extending previous results to more general boundary conditions and providing criteria for plate rigidity.

Contribution

It generalizes Rabier's existence theorem for elastic plates by allowing partial boundary conditions and establishing new rigidity criteria.

Findings

Existence of solutions for the nonlinear Kirchhoff-Love plate model under general conditions.

Sufficient conditions for the rigidity of elastic plates.

Extension of previous theorems to more general boundary scenarios.

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.