ANALYTICAL SOLUTION FOR BENDING OF SIMPLY SUPPORTED FUNCTIONALLY GRADED BEAM SUBJECTED TO UNIFORM PRESSURE

Based on the semi-inverse stress function method, an analytical solution is obtained for bending of simply supported functionally graded beam subjected to uniform pressure with arbitrary property distribution across the thickness, including explicit analytical expressions of the stress, strain and displacement. Firstly, the system of partial differential equations for the stress function is established based on the fundamental equations for plane stress states, and the expressions of streses are obtained according to the boundary conditions for stresses. Then, the distributions of strains and displacements are obtained according to the constitutive relations of functionally graded materials and displacement boundary conditions. Finally, the proposed solution is validated by comparing the degenerated results for a homogeneous isotropic beam to the classic elastic solution. The distributions of stresses and displacements obtained in this paper are for the functionally graded beam whose material properties obey a power law distribution of the constituent volume fraction, and the effects of top-bottom surfaces'Young's modulus ratio λ and volume fraction exponent n on the variation of the stresses and displacements of the functionally graded beam are discussed.