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A size-dependent model for functionally graded micro-plates for mechanical analyses

In this paper, a size-dependent formulation is presented for mechanical analyses of inhomogeneous micro-plates based on the modified couple stress theory. The plate properties can arbitrarily vary through the thickness. The governing differential equations of motion are derived for functionally graded (FG) plates with arbitrary shapes utilizing a variational approach. Moreover, the boundary conditions are provided at smooth parts of the plate periphery and also at the sharp corners of the periphery. Utilizing the derived formulation, the free-vibration behavior as well as the static response of a rectangular FG micro-plate is investigated.