539.3 Asymptotic theory of thin two-layer elastic plates with layer slippage

Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University)


doi: 10.18698/2309-3684-2019-1-326

The problem of deformation of thin two-layer plates, for which a slip condition is speci-fied at the interface between the layers, instead of the classical case of ideal contact, is considered. The method of asymptotic analysis of the general equations of the 3-dimensional theory of elasticity is used to solve this problem under the influence of transverse pressure, longitudinal and shear forces on the end surfaces. Asymptotic analysis is performed using a small geometric parameter representing the ratio of thickness to the characteristic length of the plate. Recurrent formulations of local quasi-one-dimensional problems of elasticity theory with slippage are obtained. For these problems, explicit analytical solutions are obtained. The averaged equations of elastic equilibrium of a two-layer plate with slippage of layers are derived. It is shown that, due to slippage, the order of the averaged equations of the theory of plates increases to 5 orders of magnitude, in contrast to the classical 4th order, which takes place in the theory of Kirchhoff – Love plates. Additional boundary conditions to this 5th order system are formulated and its analytical solution is obtained for the case of a rectangular plate under the influence of uniform pressure. A numerical analysis of the solution of the averaged problem is carried out. It is shown that the presence of layer slippage significantly increases the deflection of the plate in comparison with the conditions of ideal contact of the layers.

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