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In this paper, bending analysis of curved sandwich beams with transversely and functionally graded (FG) core is studied. Euler-Bernoulli beam theory is used to model the thin face-sheets and high-order shear theory is used to analyze the core. Equilibrium/field equations, compatibility and boundary conditions are used to derive the set of governing equations. The numerical solution of the governing nonlinear differential equations is based on the series Fourier-Galerkin method. Finally, the effect of geometric properties on radial deflection of core and the effect of core radius and Young's modulus on radial deflection, circumferential displacement and stresses are investigated.