Analytical solution of bending of simply supported functionally graded beam subjected to trapeziform pressure

Based on the stress function method, an analytical solution of bending is presented for simply supported functionally graded beam subjected to trapeziform pressure with arbitrary property distribution across the thickness. A stress function Φ is introduced, and the system of partial differential equations for stress function is established based on the fundamental equations for plane stress states. The expressions of stress function and stresses are given according to the boundary conditions for stresses for the simply supported functionally graded beam subjected to hydrostatic pressure. Then, the explicit analytical expressions of strains and displacements are presented according to the constitutive relations of functionally graded materials and displacement boundary conditions, In the example, the proposed solution is validated by comparing the results with the classical theory on the homogeneous isotropic beam. This paper also studies the distributions of the stresses and displacements of the functionally graded beam whose material properties obey a power law of distribution of the volume fraction of the constituents. 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 also examined. ©, 2015, China Ship Scientific Research Center. All right reserved.