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...