Large deflection stability of axially functionally graded tapered cantilever column

This article studies the large deflection stability of axially functionally graded (AFG) cantilever column for analyzing post-buckling behavior. Consideration is given to a nonlinearly tapered column with a regular polygon cross section, whose volume is constant. The governing differential equations of the problem are derived based on the large deflection beam theory. To calculate the elastica and buckling load of the AFG column, the differential equations are solved with the direct integration method together with the nonlinear solution method. The computed results are compared with those reported in literature and obtained from finite element method. Numerical examples are provided to ascertain the effects of the geometric and material parameters on the elastica and buckling load. The elastica shape is shown to depend on applied load and column properties, and the optimal shape such that the AFG column with fixed volume enables to bear the maximum buckling load is discussed.