Stability analysis of composite columns and parameter optimization against buckling

The stability analysis of a vertically standing or hanging composite column under end force and distributed axial load is made. The composite column has varying cross-section and variable material properties. The integral equation method is formulated to deal with this problem. Critical buckling load can be evaluated by seeking the lowest eigenvalue of the resulting integral equation. A characteristic equation is derived and it is a polynomial equation. The effects of self-weight and taper ratio on the buckling load are discussed for clamped-free prismatic and non-prismatic columns. As an application, two optimum design problems of freestanding tapered columns against buckling are considered to enhance the load-carrying capacity of cantilevered non-uniform columns. One is devoted to the parameter optimization of given shape profile for a homogeneous heavy column subjected to gravity load and tip load simultaneously under constant weight or volume constraint, and obtained results are very close to the exact ones of the strongest columns; the other is devoted to material tailoring such that the ratio of buckling load to weight reaches maximum for an axially graded inhomogeneous column made of two constituents with uniform cross-section.