Thermo-mechanical behavior of functionally graded circular sector plates

Abstract

By reformulating the governing equations of the first-order theory into those describing the interior and edge-zone problems of the plate, closed-form solutions are presented for analysis of functionally graded circular sector plates with vertex angle \({\theta_0 \leq \pi /2}\) whose radial edges are simply supported and subjected to transverse loading and heat conduction through the plate thickness. Various types of clamped, simply supported, and free-edge boundary supports are considered on the circular edge of the plate. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The effects of material property, boundary conditions, sector angle \({\theta_0}\), and boundary-layer phenomena on various response quantities in a circular sector plate are studied and discussed. Under a mechanical load, radial stress resultants in an FG circular sector plate with various clamped supports are zero, and consequently, their responses are seen to be identical. Simply supported FG circular sector plates which are immovable in radial direction do not show a neutral plane in bending, while in FG circular sector plates with other types of boundary supports this plane exists and its z-coordinate depends on the material constant. It is observed that the boundary-layer width is approximately equal to the plate thickness both in thermal and mechanical loadings with the boundary-layer effects being the strongest near a free edge.