Analytical three-dimensional solutions of anisotropic multilayered composite plates with modified couple-stress effect

Modified couple-stress theory has found many applications in fields related to nanocomposites. However, most investigations so far are based on the corresponding thin-plate or beam theories where the modified couple-stress theory was introduced. In this paper, we present analytical three-dimensional solutions of anisotropic multilayered composite plates with consideration of the modified couple-stress theory. We first expand the solutions in terms of the two-dimensional Fourier series in the horizontal plane to reduce the governing equations to a system of ordinary differential equations, from which we drive analytically the general solution in each layer. We then introduce the propagator matrix method to propagate the solutions from one layer to the next. Numerical examples are carried for homogeneous thick-plates and sandwich plates to show the effect of the non-local parameters on the displacements and stresses induced by the surface load. These results can serve as benchmarks to various thick plate theories in the modeling of layered composite structures with couple-stress effect.