A simplified theory of FG curved beams

Abstract The FG (functionally graded) curved beams are investigated in this paper. Starting from the general mode, the higher-order circumferential displacement is re-expressed in an orthogonal form by virtue of the assumptions and the shear stress free condition. On this basis, generalized stresses and strains are defined, and the uncoupled constitutive relationships are built for an FG curved beam as if the beam were homogeneous. According to the principle of virtual work, the higher-order beam theory is established, including equilibrium equations and corresponding boundary conditions. The lower-order beam theory is then established by ignoring the contributions of higher-order moment and higher-order shear force to the virtual wok, and hence it is correlated with the higher-order beam theory. A procedure is suggested to analytically solve FG curved beam problems with the lower-order theory. The results for the clamped-free and clamped-clamped curved beams validate the present theory and the results for the simply-supported beam shed light on the nature of the Navier's solution.