Bending and free vibrations of functionally graded annular and circular micro-plates under thermal loading

We introduce solution methods capable of treating static bending and free vibration problems involving thermally loaded functionally graded annular and circular micro-plates. Formulation is based on modified couple stress theory; and related governing partial differential equations and boundary conditions are derived by means of Hamilton's principle. Displacement field is expressed in a unified way so as to produce numerical results in accordance with Kirchhoff, Mindlin, and third-order shear deformation theories. All material properties, including the length scale parameter, are assumed to be functions of the thickness coordinate. The static and dynamic problems are solved by means of differential quadrature method. Proposed procedures are verified through comparisons made to the findings available in the technical literature on thermally stressed axisymmetric plates. Detailed numerical results are presented in order to demonstrate the influences of thermal loading magnitude, and material and geometric parameters upon static deformation profiles, stresses, and natural vibration frequencies.