Elasticity Solution of a Cantilever Functionally Graded Beam

This paper considers the plane stress problem of a cantilever functionally graded beam subjected to linearly distributed load. The material properties of the functionally graded beam are assumed to vary continuously through the thickness, according to a power-law distribution of the volume fraction of the constituents. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a functionally graded cantilever beam.