Boundary layers of hierarchical beam and plate models (Q1805175)

The boundary layer behaviour of the complete hierarchy of beams and plates is investigated. A unified analysis of the boundary layers for the whole hierarchy is made for the first time. The boundary layers of each model in the hierarchy are decomposed into a bending and a torsion layer. When the model order tends to infinity for a fixed plate thickness, it is shown that the bending layers converge to certain exponential solutions of the elastic strip, the so-called Papkovich functions, and the torsion layers converge to exponential solutions of the Laplace equation on the infinite strip. The rate of convergence is estimated. The quality of the approximate bending layers has also been studied in the case when the material becomes incompressible.