On the optimal shape of a Pflüger column

✍ Scribed by Teodor M. Atanackovic; Srboljub S. Simic

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 108 KB
• Volume: 18
• Category: Article
• ISSN: 0997-7538
• DOI: 10.1016/s0997-7538(99)00128-x

✦ Synopsis

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.