ABSTRACT
The work is concerned with asymptotic analysis of linearly elastic plates of periodically rapidly varying heterogeneities. For the sake of simplicity we assume that the structure of heterogeneity is homogeneous in direction perpendicular to the mid-surface of the plate. We want to derive a homogenized two-dimensional model which is independent of the magnitude of the applied load. Consequently, we have to proceed in the following manner. Firstly, we consider a two-dimensional model of the plate expanding the displacement field by Fourier-Series expansion in a plate thickness direction, with respect to a basis of scaled Legendre polynomials. We consider a second order approximation of the displacement field which gives a good com-promise between the accuracy of the approximate solution and the complexity of the approximate problem. Considering standard argument for this kind of a problem, we formulate two-dimensional homogenized boundary value problem for the plate.
