Abstract
The optimal shape of a Pflüger column is determined by using Pontryagin's maximum principle. It is shown that the boundary value problem relevant for determining the optimal distribution of material (i.e. cross-sectional area function) along the column axis has simple eigenvalue. Necessary conditions for local extremum of column volume are reduced to a boundary-value problem for a single second order nonlinear differential equation. We examined singular points of this equation and formulated extremal complementary variational principles for it. The optimal cross-sectional area function is obtained by numerical integration and by Ritz method. The error of the analytical approximate solution obtained by Ritz method is also estimated.
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