Global buckling of axially functionally graded columns with variable boundary conditions

Abstract

The problem of a stability loss in compressed Euler columns with variable gradation of material properties along their length is addressed. Axial gradation causes that the cross-section has a transverse symmetry, i.e., the coupling matrix of cross-sectional forces is equal to zero. Prismatic columns with I-sections, differing in length, minimal moment of inertia and boundary conditions, were analysed in detail. A continuous change in material mechanical properties was discretized by assuming different numbers of column segments of the given length, with a linear alternation in them. The eigenproblem was solved with an analytical method, and the obtained results were compared to the solutions attained with the FEM Abaqus package. In the analytical solution, the Euler-Bernoulli beam theory for conservative systems was adopted. A particularly good correspondence of the results from those methods was obtained, the error in eigenvalues did not exceed 3%. The adoption of 20 segments on the FG column length can be treated as a continuous distribution of the material gradation along the column length. A further increase in their number is pointless. Finally, a procedure for determining minimal global eigenloads (i.e., fundamental buckling eigenloads) in the form of a modified Euler formula was put forward.