Abstract
Based on the modified couple-stress theory, the size-dependent behavior of the functionally graded anisotropic elastic composites is analytically investigated when the load is applied on the top surface of the composite plate. The functionally graded material is assumed to be exponential in the thickness direction of the plate. By expanding the solutions of the displacements in terms of the two-dimensional Fourier series, the final governing equations are reduced to an eigenvalue and eigenvector problem. The exact solutions of the elastic fields with the modified couple-stress effect are derived under two kinds of boundary conditions. The classical elastic solutions are reduced from the present solutions as a special case. Numerical examples show the effect of the functional gradient factor and the material length-scale on the elastic fields along the thickness direction of the plate. Some important features observed in this paper could be useful in designing the functionally graded laminated composites with size-dependency.
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