Instructor: Antonino Morassi
Number of hours: 8
SSD: ICAR/08

In these lectures we review some recent results concerning inverse problems for thin elastic nanostructures. A simplified strain gradient linear elasticity theory for isotropic materials is used to derive the mechanical models of nanobeams and nanoplates, under Euler-Bernoulli and Kirchhoff- Love kinematic assumptions, respectively. A first group of results concerns the use of nanobeams as mass-resonant sensors to identify an unknown added mass density by the measurement of a finite number of lower resonant frequencies. In a second group of results, we deal with the diagnostic problem of detecting an unknown elastic inclusion possibly present in a nanoplate. We determine constructive upper and lower estimates of the area of the inclusion given in terms of the work exerted by force and couple fields applied at the boundary of the nanoplate. Finally, we consider the inverse problem of determining the Winkler coefficient in a nanoplate resting on an elastic foundation and clamped at the boundary. We prove a global Holder 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. Key ingredients for the last two topics are quantitative versions of the unique continuation principle for solutions to the static equilibrium equation of a nanoplate in bending.

Teaching methods: lectures

Assessment methods: final written report

Additional information: the course can be delivered in English if required