Abstract
Exact relationships between the bending solution of the classical (Kirchhoff) thin plate theory and the sinusoidal shear deformation thick plate theory for homogeneous and functionally graded material plates are derived by using the mathematical similarity of governing equations of the two theories, and the basis of load equivalence. It is assumed in the analysis that the mechanical properties of the functionally graded plates vary continuously through the thickness of the plate and obey a simple power law distribution of the volume fraction of the constituents. Effects of material gradient property and shear deformation on the bending of functionally graded plates are discussed in the framework of the sinusoidal shear deformation plate theory. The boundary conditions at two edges of the functionally graded plate are simply supported while the remaining two edges having the same boundary conditions are, namely, simply supported, clamped, or free. Several examples are presented to illustrate the use and accuracy of these relationships. The effects of many parameters on the deflections and stresses are investigated.
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