A consistent theory for thin anisotropic layered structures is developed starting from asymptotic analysis of 3D equations in linear elasticity. The consideration is not restricted to the traditional boundary conditions along the faces of the structure expressed in terms of stresses, originating a new type of boundary value problems, which is not governed by the classical Kirchhoff-Love assumptions. More general boundary value problems, in particular related to elastic foundations are also studied.The general asymptotic approach is illustrated by a number of particular problems for elastic and thermoelastic beams and plates. For the latter, the validity of derived approximate theories is investigated by comparison with associated exact solution. The author also develops an asymptotic approach to dynamic analysis of layered media composed of thin layers motivated by modeling of engineering structures under seismic excitation.
Plane Problem for a Rectangular Elastic Strip. Technical Theory for Bernoulli - Coulomb - Euler Beams; Mixed Boundary Value Problems for Single and Two-Layer Rectangular Beam. The Winkler - Fuss Model; Direct Asymptotic Integration of 3D Equations in Elasticity for an Orthotropic Plate; Matching of the Outer Solution and the Boundary Layer for an Orthotropic Plate; Elastic Plates of General Anisotropy; Non-Classical Boundary Value Problems for Anisotropic Plates; Two-Layer Anisotropic Plates. The Modulus of Subgrade Reaction of a Layered Foundation; Asymptotic Analysis of the Outer Problem for an Orthotropic Shell; Boundary Layer in Orthotropic Shells; Non-Classical Boundary Value Problems for Anisotropic Shells.