Exact solutions for functionally graded micro-cylinders in first gradient elasticity

This work studies a functionally graded (FG) micro-cylinder subjected to internal and external pressures in the framework of the first gradient elasticity. Then a theoretical formulation of the fourth-order governing differential equation and associated boundary conditions with variable coefficients for inhomogeneous isotropic materials have been established. And exact solutions for FG micro-cylinders are obtained, including the inhomogeneity and microstructural effect perfectly. The numerical results reveal that the characteristic length parameter and power index have a considerable effect on the stress distribution of FG micro-cylinders.108