Asymptotic analysis of an arbitrary anisotropic plate of variable thickness (sloping shell)

The leading terms of the asymptotics of the solution of the problem of elasticity theory for a thin plane with curved bases are constructed; in addition, the resulting problem (a two-dimensional model) is written out explicitly. Arbitrary anisotropy of elastic properties is allowed; moreover, these properties may depend on the “rapid” transversal and the “slow” longitudinal variables. The substantiation of these asymptotics is carried out on the basis of Korn's weighted inequality. The cases of laminated plates, sloping shells, and plates with sharp edges are discussed separately.