Three-dimensional elasticity solution of layered plates with viscoelastic interlayers

An analytical solution for simply supported layered plates with viscoelastic interlayers under a transverse load is proposed. The deformation of each plate layer is described by the exact three-dimensional elasticity equations. The viscoelastic property of interlayer is simulated by the generalized Maxwell model. The constitutive relation of the interlayer is simplified by the quasi-elastic approximation, which significantly simplifies the analytical process. The solution of stress and displacement fields with undetermined coefficients is derived by solving a group of ordinary differential equations. The undetermined coefficients can be efficiently deduced by using the recursive matrix technique for the plate with any number of layers. The practical convergence is observed during numerical tests. The comparison analysis indicates that the present solution has a close agreement with the finite element solution. However, the solution based on the Mindlin–Reissner hypothesis is significantly different from the present solution for thick plates. Finally, the effect of interlayer thickness on stress and displacement distributions of a five-layer plate is discussed in detail.