Nonlinear bending of a two-dimensionally functionally graded beam

A novel beam model is derived to investigate the nonlinearized bending behaviors of a two-dimensionally functionally graded (FG) beam based on the Euler-Bernoulli beam kinematic theory. The geometric nonlinearity due to the mid-plane stretching is only taken into account. For the considered two-dimensionally FG material, we assume the Young's modulus varying along the length or axial direction obeys an exponential distribute function, and the Young's modulus varying along the thickness direction obeys a power-law function. A generalized differential quadrature method (GDQM) is developed to calculate the linearized and nonlinearized displacements of two-dimensionally FG beams. Some illustrative examples are given to study the effects of the value of force and various material compositions on the linearized and nonlinearized deflections as well as the nonlinear deflection ratio.