In this series of two papers, we investigate the limit behaviors and the boundary layers of the three-dimensional 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. This part is devoted to the first four types of conditions. Relying on construction algorithms, we establish an asymptotics of the displacement combining inner and outer expansions. We describe the two first terms in the outer expansion: these are Kirchhoff-Love displacements satisfying prescribed boundary conditions that we exhibit. We also study the first boundary layer term: it has generically non-zero transverse and normal components in each of these four types of lateral conditions. See also Part II. A new condensed version published in SIMA is available.

Preprint IRMAR 97-28 (Dec. 97)

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