Analytical bending solution of functionally graded cantilever beam

Based on the semi inverse method, an analytical solution is obtained for a functionally graded cantilever beam that is clamped at one end and subjected to a concentrated force and a couple at another end. The problem is treated as a plane stress case of an orthotropic elastic body. The mechanical properties of the material have been assumed to have the same dependence on the height coordinate. This solution is valid for arbitrary gradient functions and it can play as a benchmark result for assessing other approximate methodologies or as a basis for establishing simplified functionally graded beam theories. Degenerate results for isotropic homogeneous elastic case are coincided well with existing analytical solutions. Some numerical examples are also given by assuming an exponential gradient function.