Mathematical justification of an obstacle problem in the case of a plate

Abstract

In this paper the modeling of a thin plate in unilateral contact with a rigid plane is properly justified. Starting from the three-dimensional nonlinear Signorini problem, by an asymptotic approach the convergence of the displacement field as the thickness of the plate goes to zero is studied. It is shown that the transverse mechanical displacement field decouples from the in-plane components and solves an obstacle problem.

Keywords

Signorini problem / Obstacle problem / Asymptotic analysis / Plate

References

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