The influence of lateral boundary conditions on the asymptotics in thin elastic plates

Here we investigate the limits and the boundary layers of the three-dimensi onal displacement in thin elastic plates as the thickness tends to zero in each of the eight main types of lateral boundary conditions on their edges: hard and soft clamped, hard and soft simple support, friction conditions, sliding edge, and free plates. Relying on construction algorithms [M. Dauge and I. Gruais, Asymptotic Anal., 13 (1996), pp. 167-197], we establish an asymptotics of the displacement combining inner and outer expansions. We de scribe the two first terms in the outer expansion: these are Kirchhoff-Love displacements satisfying prescribed boundary conditions that we exhibit. W e also study the first boundary layer term: when the transverse component i s clamped, it has generically nonzero transverse and normal components, whe reas when the transverse component is free, the first boundary layer term i s of bending type and has only its nonzero in-plane tangential component.