Static bending of a functionally graded microscale Timoshenko beam based on the modified couple stress theory

A microscale functionally graded Timoshenko beam model is developed for the static bending analysis based on the modified couple stress theory (MCST). The material properties of the FG microbeams are assumed to vary in the thickness direction and are estimated through the Mori–Tanaka homogenization technique and the classical rule of mixture. The equilibrium equations and the related boundary conditions are derived by using the principal of the minimum total potential energy. The governing equations are solved analytically for a simply-supported beam subjected to a point and uniformly distributed load. The inclusion of an additional material parameter enables the new beam model to capture the size effect. The new non-classical beam model reduces to the classical beam model when the length scale parameter is set to zero. The influences of the volume fraction index, the different estimation method of the material properties, length scale parameter, the aspect ratio and the Poisson effect on the static bending behavior are examined. Some of the present results are compared with the previously published results to establish the validity of the present formulation. It is found that the deflections of the microbeam by the classical beam theory are always larger than those by the modified couple stress theory.