Elasticity Solutions for Annular Plates of Functionally Graded Materials Subjected to a Uniform Load
England (2006) proposed a novel theory to study the bending problem of isotropic functionally graded plates subjected to transverse biharmonic loads. His theory is extended here to functionally graded plates of transversely isotropic materials. Using the complex variable method, the governing equations of three plate displacements appearing in the expansions of the displacement field are formulated based on the three-dimensional theory of elasticity for a transverse load satisfying the biharmonic equation. The solutions may be expressed in terms of four analytic functions of the complex variable, in which the unknown constants can be determined from the boundary conditions similar to that in the classical plate theory(CPT). The elasticity solutions of an FGM annular plate under a uniform load are derived. A comparison of the present results for a uniform load with existing solutions is made and good agreement is observed. The influence of boundary conditions, material inhomogeneity and radius-to-radius ratio on the plate deflection and stresses are studied numerically.
B. Yang et al., "Elasticity Solutions for Annular Plates of Functionally Graded Materials Subjected to a Uniform Load", Advanced Materials Research, Vols. 261-263, pp. 853-857, 2011