Analyzing and optimizing of a pfluger column

Abstract

The optimal shape of a Pfluger column is determined by using Pontryagin’s  maximum principle (PMP). The governing equation of the problem is reduced to a boundary-value problem for a single second order nonlinear differential equation. The results of the analysis problem are obtained by Spectral method. Necessary  conditions for the maximum value of the first eigenvalue corresponding to given  column volume are established to determine the optimal distribution of cross-sectional area along the column axis.