Estimating the area of extreme inclusions in Reissner–Mindlin plates

Abstract

We derive upper and lower estimates of the area of unknown defects in the form of either cavities or rigid inclusions in Mindlin–Reissner elastic plates in terms of the difference $\delta W$ of the works exerted by boundary loads on the defected and on the reference plate. It turns out that the upper estimates depend linearly on $\delta W$, whereas the lower ones depend quadratically on $\delta W$. These results continue a line of research concerning size estimates of extreme inclusions in electric conductors, elastic bodies and plates.

COMMUNICATED BY:

• G. Alessandrini

Keywords:

• Inverse problems
• Reissner–Mindlin elastic plates
• size estimates
• cavities
• rigid inclusions

Mathematics Subject Classification (2010):

• Primary 35B60
• Secondary 35B30
• 35Q74
• 35R30

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Antonino Morassi is supported by PRIN 2015TTJN95 ‘Identificazione e diagnostica di sistemi strutturali complessi’. Edi Rosset is supported by PRIN 201758MTR2 ‘Direct and inverse problems for partial differential equations: theoretical aspects and applications’, by Progetto GNAMPA 2019 ‘Proprietà delle soluzioni di equazioni alle derivate parziali e applicazioni ai problemi inversi’ Istituto Nazionale di Alta Matematica (INdAM) and by FRA2016 ‘Problemi inversi, dalla stabilità alla ricostruzione’, Università degli Studi di Trieste.