On the Optimal Shape of a Rotating Rod

By using Pontryagin’s maximum principle we determine the shape of the lightest rotating rod, stable against buckling. It is shown that the cross-sectional area function is determined from the solution of a nonlinear boundary value problem. Three variational principles for this boundary value problem...

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Veröffentlicht in:	Journal of applied mechanics 2001-11, Vol.68 (6), p.860-864
1. Verfasser:	Atanackovic, T. M
Format:	Artikel
Sprache:	eng
Schlagworte:	Beams, plates and shells Computational techniques Continuum mechanics (soil mechanics...) Exact sciences and technology Fundamental areas of phenomenology (including applications) Mathematical methods in physics Physics Solid mechanics Structural and continuum mechanics Structural mechanics (beam, string...) Theory and numerical methods Variational and optimizational methods Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...) Vibrations and mechanical waves
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Beschreibung
Zusammenfassung:	By using Pontryagin’s maximum principle we determine the shape of the lightest rotating rod, stable against buckling. It is shown that the cross-sectional area function is determined from the solution of a nonlinear boundary value problem. Three variational principles for this boundary value problem are formulated and a first integral is constructed. The optimal shape of a rod is determined by numerical integration.
ISSN:	0021-8936 1528-9036
DOI:	10.1115/1.1409938