THE BOUNDARY-LAYER FOR P-MODEL PLATE PROBLEMS .1. ASYMPTOTIC ANALYSIS

P-model plate problems are described in this paper, and the structures of their solutions are investigated in their dependence on the plate thickness in the cases of clamped-in, soft clamped, hard simply suppor ted, soft simply supported and free boundary conditions. By adopting s ingular perturbation method, asymptotic expansions of the solutions wi th respect to the plate thickness are obtained to arbitrarily high ord er, assuming that the domain and the transverse load force are suffici ently smooth. Rigorous bounds for the errors in the expansions are als o given. In Part II, these results will be adopted to study the bounda ry layer behaviour for the p-model plate problems.