Boundary layer realization in thin elastic three-dimensional domains and two-dimensional Hierarchic plate models

Herein we address the behavior of the linear elastic solution in three-dimensional thin domains, especially near the boundaries, and compare it to the approximated solution obtained by dimension reduced two-dimensional hierarchic plate models. The mathematical analysis is backed-up by numerical simulations using the p-version of the finite element method. We identify mathematically, and more importantly, quantify the engineering quantities which are rapidly changing in a boundary layer. We also investigate how well (if at all) the two-dimensional plate-models solutions approximate the three-dimensional solution inside and outside of the boundary layers.