An analytical solution for nonlinear static bending of a functionally graded Timoshenko beam

This paper presents an analytical solution for the deformation and stress fields in a functionally graded beamsubjected to transverse loading. Mechanical properties are assumed to vary due to a power law relation across the beamthickness. First-order shear deformation theory along with nonlinear Von-Karman strain-displacement relations areused to derive static equilibrium equations employing the minimum total potential energy principle. Consideringdifferent boundary conditions at the two ends of the beam, analytical expressions are derived for the deformation andstress fields of the beam. Numerical results are presented for different values of the power law index and various loadmagnitudes and are compared to the linear solution.