Stress field of a radially functionally graded panel with a circular elastic inclusion under static anti-plane shear loading

Abstract

The elastic stress field around a circular elastic inclusion in an infinite functionally graded material (FGM) panel that is subjected to a uniform static anti-plane shear loading at infinity is considered. Assuming the rigidity modulus of the FGM panel to be exponential, the analytical solutions of stress and strain distribution around the circular elastic inclusion are obtained by using the variable separation method. Due the generality of the elastic inclusion, other geometrical discontinuities, such as hole and rigid inclusion, can be seen as special cases of circular elastic inclusion when the inclusion rigidity modulus takes a suitable value. Therefore, the present solutions analytically reduce to some classical solution in some special cases. The present analytical solutions are compared with the existing exact solutions to verify them. Finally, the effects of the relative inclusion rigidity modulus ratio and the inhomogeneous rigidity modulus ratio on the stress distribution and the concentration factor are systematically investigated.

Out-of-Plane Bending of Functionally Graded Thin Plates with a Circular Hole

“…A novel definition is introduced for the SCF in FGM plates with geometrical discontinuities in general. Shi [27] presented an analytical solution of the elastic stress fields around a circular elastic inclusion in a radial FGM plate under a uniform anti-plane shear loading at infinity. Guan and Li [28] analyzed the stress concentration around an arbitrarily shaped hole reinforced with an FGM layer in an infinite plate under anti-plane shear and performed the optimized analysis of the SCF.…”

Stress Concentration and Damage Factor Due to Central Elliptical Hole in Functionally Graded Panels Subjected to Uniform Tensile Traction

“…Dave and Sharma [19] also used the complex variable function method to solve the problem of the FGM plate with rectangular holes. Based on the variable separation method, the analytical solutions of stress and strain distribution around the circular elastic inclusion and elliptical nano-fiber inclusion are obtained by Shi [20,21]. Goyat, et al [22] used the extended finite element method to analyze the stress concentration of the FGM layer in an infinite plate with a pair of circular holes under different loads.…”