Asymptotic theory of multilayer plates with imperfect contact between layers

An asymptotic theory of the deformation of thin multilayer elastic plates with non-ideal contact between the layers is proposed. The linearized slip conditions of the contacting layers with different slip coefficients for each pair of layers are considered. An asymptotic theory is an expansion over a small geometric parameter of the original 3-dimensional elasticity problem with sliding conditions of the layers. A recurrent sequence of local problems of elasticity theory is obtained. An analytical recurrent solution to these problems is found, which allows one to determine all the components of the stress tensor in the plate. An averaged system of equations of the theory of thin two-layer plates with slipping layers is derived, which has an increased order of partial derivatives compared with the theory of plates with ideal contact. An analytical solution is found to this problem of bending a 2-layer composite plate under the influence of uniform pressure. Specific effects of plate deformation due to the effect of layer slippage are established.