On the optimal shape of a Pfluger column

The optimal shape of a Pfluger column is determined by using Pontryagin's m aximum 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 condition s for local extremum of column volume are reduced to a boundary-value probl em for a single second order nonlinear differential equation. We examined s ingular points of this equation and formulated extremal complementary varia tional principles for it. The optimal cross-sectional area function is obta ined by numerical integration and by Ritz method. The error of the analytic al approximate solution obtained by Ritz method is also estimated. (C) 1999 Editions scientifiques et medicales Elsevier SAS.