A buckling analysis of perfect and imperfect functionally graded columns

Due to the asymmetry of the material properties about the middle plane, perfect columns made of functionally graded materials (FGMs) may not remain straight when a compressive axial point load is concentrically applied. This article analytically derives the displacement functions and the buckling load of both perfect and imperfect Euler-Bernoulli functionally graded columns. The method of derivation is based on the translation of the reference plane to the position at which the coupling between the axial and bending deformations is eliminated, i.e. the physical neutral surface position. Then, all the governing equations and their solutions turn out to have the same form as those of homogeneous columns subjected to an eccentric axial load. The effects of geometric imperfection are studied with the main purpose of finding imperfect shapes that make an imperfect column stronger than a perfect one. Further, the governing equations that are used to find those analytical solutions are expanded so that the equations can deal with large deformation and large strain analysis. These new governing equations are solved by finite element (FE) method based on linear exact shape functions. Then, the FE solutions are used to compare and validate the analytical solutions obtained earlier.