Static and eigenvalue problems of Sigmoid Functionally Graded Materials (S-FGM) micro-scale plates using the modified couple stress theory

Bending, vibration and buckling analysis of Sigmoid Functionally Graded Materials (S-FGM) micro-scale plates using the modified couple stress theory is presented in this paper. The micro-scale effects of S-FGM micro-scale plates are captured using the single material length scale parameter of a modified couple stress theory. The material properties are assumed to vary only through the thickness of the S-FGM micro-scale plate, by mixing two different materials. The shear deformation effects are included, using the third-order shear deformation theory. The present theory does not require a shear correction factor, because of the parabolic distribution of the transverse shear strains through the thickness. The third-order theory that accounts for the functionally graded material, and the micro-scale effects have been derived using the principle of virtual displacements. In the present theory, the variation of two materials through thickness is embedded into the plate constitutive relation. The static and eigenvalue problems are solved by the Navier method. Numerical examples of bending, vibration and buckling problems are presented, to illustrate the effects of the sigmoid power-law distribution of the two materials, and the dimensionless material length scale parameter. In particular, in the case of biaxial compression and tension, the magnitude and direction of the buckling load should be considered simultaneously.