Boundary layers of hierarchical beam and plate models

The boundary behavior of a family of hierarchical models of linearly elastic, isotropic plates is studied. The hierarchical models are obtained by spectral semidiscretization of the displacement fields in the transverse direction and strain energy projection. The well known Reissner-Mindlin model is contained in the hierarchy as a special case. A decomposition of the boundary layers of any model in the hierarchy into a bending and a torsion layer, both of which are model dependent, is given. It is shown further that the bending and torsion layers arise as Galerkin approximations of certain (nonlinear) eigenvalue problems in the plate cross section with the subspaces used to derive the hierarchical model. It is shown that the bending layers converge, as the order of the plate model tends to infinity, to the so-called Papkovich functions on an elastic strip.The regularity of the solution on polygonal plates is investigated for the whole hierarchy of plate models and shown to equal the regularity of the plane elasticity problem.Partially supported by AFOSR Grant No. F49620-92-J0100.