Buckling optimization of axially functionally graded columns having constant volume

In this article, the buckling optimization of axially functionally graded (AFG) columns to maximize the buckling capacity is studied. Consideration is given to an AFG column having a tapered regular polygon cross section and variable material properties. The governing differential equation is derived based on Euler–Bernoulli beam theory with the relevant boundary conditions and is solved using the direct integration method combined with a determinant search algorithm. The computed buckling loads are compared with those presented in the literature and obtained from finite element analysis. Numerical examples for buckling load and buckled mode shape are given to highlight the effect of parameters related to the Young's modulus, cross-sectional shape, tapering and column volume. In particular, the geometry and material parameters that provide buckling optimization at constant volume of the column are analysed.