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.