Reformulation of Mindlin–Reissner governing equations of functionally graded circular plates

Abstract

The governing equations of the first-order shear deformation plate theory for FG circular plates are reformulated into those describing the interior and edge-zone problems. Analytical solutions are obtained for axisymmetric and asymmetric behavior of functionally graded circular plates with various clamped and simply-supported boundary conditions under mechanical and thermal loadings. The material properties are graded through the plate thickness according to a power–law distribution of the volume fraction of the constituents. The results, which are in closed form and suitable for design purposes, are verified with known results in the literature. It is shown that there are two boundary-layer equations. The effects of material property, plate thickness, boundary conditions, and boundary-layer phenomena on various response quantities in a solid circular plate are studied and discussed. Under a mechanical load, the responses of FG solid circular plates with various clamped supports are seen to be identical. It is observed that the boundary-layer width is approximately equal to the plate thickness with the boundary-layer effects in clamped FG plates being stronger than those in simply-supported plates. Also an exact solution is developed for the one-dimensional heat conduction equation with variable heat conductivity coefficient.