Stable determination of the Winkler subgrade coefficient in a nanoplate

TL;DR

This paper establishes a stable method to determine the Winkler subgrade coefficient in a nanoplate using a single interior deflection measurement, within a strain gradient elasticity framework.

Contribution

It provides the first global stability estimate for the inverse problem of identifying the Winkler coefficient in a nanoplate model.

Findings

Proves a global Hölder stability estimate for the inverse problem.

Demonstrates the feasibility of determining the subgrade coefficient from a single interior measurement.

Utilizes a strain gradient elasticity model for isotropic materials.

Abstract

We study the inverse problem of determining the Winkler coefficient in a nanoplate resting on an elastic foundation and clamped at the boundary. The nanoplate is described within a simplified strain gradient elasticity theory for isotropic materials, under the Kirchhoff-Love kinematic assumptions in infinitesimal deformation. We prove a global H\"older stability estimate of the subgrade coefficient by performing a single interior measurement of the transverse deflection of the nanoplate induced by a load concentrated at one point.