Analytical solution for elastic and elastoplastic bending of a curved beam composed of inhomogeneous materials

We present an analytical solution for elastic and elastoplastic bending problem of a curved beam composed of inhomogeneous materials. Suppose the material is isotropic, ideally elastoplastic and it obeys Tresca's yield criterion and the corresponding associated flow rule. And the elastic modulus and yield limit of the material vary radially according to general power functions. The expressions of stresses and displacements of a curved beam in both purely elastic stress state and partially plastic stress state are derived. The influence of material inhomogeneity on the elastoplastic behavior of a curved beam is demonstrated in numerical examples. Analytical solutions presented here can serve as benchmark results for evaluating numerical solutions.