Theoretical analysis of composite beams under uniformly distributed load

The bending problem of a functionally graded cantilever beam subjected to uniformly distributed load is investigated. 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 practical example is presented to show the application of the method.