Two-scale analytical solutions of multilayered composite rectangular plates with in-plane small periodic structure

We present a two-dimensional analytical solution of an orthotropic multilayered rectangular plate, which, in addition, has a small periodic structure along one in-plane direction. The two-scale asymptotic expansion method is first employed to develop a homogenized model of each individual layer in the plate. The laminated plate with homogenized layers is then analyzed exactly using the state-space approach. Two sets of approximate stresses (i.e. the homogenized model stresses and the zeroth-order two-scale model stresses) are presented analytically. Numerical examples are considered and comparison with the finite element simulation is made. It is shown that the two-scale model can give accurate predictions of the transverse normal stress even it varies sharply in a unit cell. It is also confirmed that the developed analytical solution can be used to investigate the effect of microstructure on the macroscopic behavior of the multilayered composite plate. This work presents an effort to take both advantages of the two-scale asymptotic expansion method and the state space method in the analyses of laminated composite structures with in-plane small periodicity.