Postbuckling analysis of edge cracked functionally graded Timoshenko beams under end shortening

In this paper, the postbuckling response of beams made of functionally graded materials (FGMs) containing an open edge crack is studied based on Timoshenko beam theory and von Kármán nonlinear kinematics. The cracked section is modeled by a massless elastic rotational spring. It is assumed that material properties follow exponential distributions through thickness direction. Ritz method is employed to derive the nonlinear governing equations, which are then solved by using Newton–Raphson method to obtain the postbuckling load-end shortening curves and postbuckling deflection-end shortening curves. A detailed parametric study is conducted to study the influences of crack depth, crack location, material property gradient, and slenderness ratio on the postbuckling behavior of cracked FGM beams. It is found that both intact and cracked FGM beams exhibit similar postbuckling behavior under end shortening. Unlike isotropic homogeneous beams, bifurcation buckling does not occur for both intact and cracked FGM beams due to the presence of bending–extension coupling effect.