E Sh Khoram-Nejad, - M.Sc. student, Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
S Moradi - Professor, Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
M Shishesaz - Professor, Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Post-buckling behavior of cracked axially functionally graded (AFG) beam under mechanical compressive uniaxial load is investigated in this paper. It is assumed that the crack is open and modeled with a rotational linear spring. Two sub-beams are connected with this spring and the beam has an initial geometric imperfection. Nonlinear differential equations of the beam are derived from the equilibrium relations. Then, these equations have been converted to a set of nonlinear algebraic equations using the differential quadrature method and have been solved by an arc-length strategy. The accuracy of the results is confirmed by comparing them with those of the finite elements method and other literature. The results show that the presence of the crack, its location and depth, and the distribution of the material in the AFG beam significantly affect the post-buckling behavior of the beam. The effect of using an AFG beam instead of a homogeneous one has also been investigated.

Post-Buckling, Differential quadrature method, Arc-length strategy, Axially Functionally Graded (AFG),beam, edge crack