An Elasticity Solution for Static Analysis of Functionally Graded Curved Beam Subjected to a Shear Force

In this paper, using 2-D theory of elasticity, a closed-form solution is presented for stressdistributions and displacements of a FG curved beam under shear force at its free end. The materialproperties are assumed to vary continuously through the radial direction based on a simple power lawmodel and Poisson’s ratio is supposed to be constant. In order to verify the solution, it is shown that allstress and displacement relations are converted to those of a homogenous curved beam when theinhomogeneity constant approaches zero. The effects of inhomogeneity on stress distributions areinvestigated. It is shown that specified stress distribution profiles can be obtained by changing thevariation of volume fraction of constituents. It is observed that for a specific value of inhomogeneityconstant, a proper stress distribution along the radial direction is obtained for designing purposes.