A new type of boundary layers, a representative model, and surface wrinkling in inhomogeneous plates
We find a new type of boundary layers that occur at the top and bottom surfaces of an inhomogeneous plate. The boundary layers of this type never occur in homogeneous plates or plates made of layers of homogeneous materials. The thickness of such a boundary layer is usually less than that of a one single fiber of the plate. Moreover, we introduce a new notion of representative plate as a plate whose stress-strain state in some parts is similar to the stress-strain state in the original plate. In addition, every part of the original plate has a corresponding part in the representative plate. We demonstrate that a three-layered plate can be representative of a plate formed of an arbitrary number of layers. We also demonstrate a wrinkling phenomenon that happens on the top and bottom surfaces of inhomogeneous plates. This effect does not occur in homogeneous plates or plates made of layers of homogeneous materials. Such wrinkling can become a significant adverse effect, and thus should be given utmost attention.