An approximate model for optimizing Bernoulli columns against buckling

Proposed herein is a simple but powerful method for optimization of inhomogeneous, elastically restrained columns against buckling when subjected to both compressive concentrated and distributed axial loads that include self-weight. Unlike previously published studies on the subject, we do not have to specify any prescribed geometrical variation and analysis may be readily performed on columns with any complex geometrical shape. In the proposed method, the differential equation governing the buckling of Euler columns is discretized by adopting the Hencky bar-chain model, and critical buckling loads are evaluated by seeking the lowest eigenvalue of the resulting system of algebraic equations. The discrete nature of the formulation, as well as the reduced number of parameters to be optimized, is well suited for the adopted optimization process that is based on evolutionary algorithms. We propose an optimization scheme based on a parallel genetic algorithm. A comparison study between the obtained optimal column shape and buckling loads on homogeneous and isotropic columns with circular cross section, and the numerical and analytical solutions found in the open literature shows fast convergence, high accuracy and flexibility of the proposed method.