Estimating area of inclusions in anisotropic plates from boundarydata

Antonino Morassi; Edi Rosset; Sergio Vessella

doi:10.3934/dcdss.2013.6.501

Article Contents

2013, Volume 6, Issue 2: 501-515. Doi: 10.3934/dcdss.2013.6.501

This issue Previous Article Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions Next Article On a class of sixth order viscous Cahn-Hilliard type equations

Estimating area of inclusions in anisotropic plates from boundary data

1.
Dipartimento di Ingegneria Civile e Architettura, Università degli Studi di Udine, via Cotonificio 114, 33100 Udine
2.
Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, via Valerio 12/1, 34127 Trieste
3.
DIMAD, Università degli Studi di Firenze, via Lombroso 6/17, 50134 Firenze

Received: September 30, 2011

Revised: October 31, 2011

Published: March 2013

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Abstract

We consider the inverse problem of determining the possible presence of an inclusion in a thin plate by boundary measurements. The plate is made by non-homogeneous linearly elastic material belonging to a general class of anisotropy. The inclusion is made by different elastic material. Under some a priori assumptions on the unknown inclusion, we prove constructive upper and lower estimates of the area of the unknown defect in terms of an easily expressed quantity related to work, which is given in terms of measurements of a couple field applied at the boundary and of the induced transversal displacement and its normal derivative taken at the boundary of the plate.

Keywords:

Mathematics Subject Classification: Primary: 35R30, 35R25, 74K20.

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