Exact solutions for bending of Timoshenko curved nanobeams made of functionally graded materials based on stress -driven nonlocal integral model

Size-dependent static bending analysis of functionally graded (FG) curved nanobeams based on the Timoshenko beam theory is performed with the application of a stress-driven nonlocal integral model. The governing equations and corresponding boundary conditions are derived via Hamilton's principle. Through detailed derivation, the integral constitutive equation is equivalent to a differential form equipped with two extra boundary conditions. By using the Laplace transform technique and its inversion, the coupling equations are solved analytically for different boundary and loading conditions. According to the numerical results, it is revealed that for FG Timoshenko curved beam theory, increasing the nonlocal parameter has a consistently stiffening effect on the bending of the curved nanobeams subjected to different boundary and loading conditions. The non-dimensional deflections decrease with the increase of the FG gradient index for all boundary cases, significantly when FG power-law index p < 4. Moreover, through comparing with the results of the Euler-Bernoulli theory, an interesting finding is that for Simply-Clamped, Clamped-Clamped and Clamped-Free nanobeams, the shear-deformable effect becomes more significant with the increase of nonlocal parameter, which cannot be ignored even for larger length-to-height ratio. © 2020 Elsevier Ltd