Planar curved beams, one of the basic structural components, are omnipresent in most common engineering design structures. Therefore, the understanding of stress distributions and displacements of such beams is one of the most important issues for designing these structures. In this paper, using 2-D theory of elasticity, a closed-form solution is presented for stress distribution and displacements of functionally graded curved beams under shear force at its free end. The material properties are assumed to vary continuously through the radial direction based on a simple power law model and Poisson's ratio is supposed to be constant. This type of inhomogeneity is due to several causes like phase segregation arising as a result of centrifugal casting. In order to verify the solution, it is shown that all stress and displacement relations are converted to those of a homogenous curved beam when the inhomogeneity constant approaches zero. The effects of inhomogeneity on stress distributions and displacements are investigated. It is shown that specified stress distribution profiles can be obtained by changing the variation of volume fraction of constituents. It is observed that for a specific value of inhomogeneity constant, a proper stress distribution along the radial direction is obtained for designing purposes.
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