Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-04T03:33:56.985Z Has data issue: false hasContentIssue false
  • English
  • Français

Pontryagin's Maximum Principle Applied to the Profile of a Beam

Published online by Cambridge University Press:  04 July 2016

L. C. W. Dixon
L. C. W. Dixon*
Affiliation:
Department of Mathematics, Lanchester College, Coventry
Get access Rights & Permissions [Opens in a new window]

Extract

Every structural member deforms under the forces acting upon it. In this paper the Maximum Principle, recently developed by Pontryagin is applied to the problem of determining that profile of a beam that deforms least under its own weight. The beam considered is a solid horizontal cantilever having constant density, modulus of elasticity and width. The height is taken as an independent variable subject to the restrictions that it lies between an upper and lower bound and is symmetrically distributed about the centre-line. The method is attractive in that it can readily be extended to take account of variable density, width and/or hollow members by extending the control vector u defined in the analysis.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 71 , Issue 679 , July 1967 , pp. 513 - 515
Copyright
Copyright © Royal Aeronautical Society 1967

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Boltyansku, V. G., Gamkrelidze, R. V. and Pontryagin, L. S. On the Theory of Optimum Processes (in Russian). Doklody Akad Nauk SSSR, 110, No 1, 1956.Google Scholar
2.Pontryagin, L. S., Boltyansku, V. G., Gamkrelidze, R. V. and Mistichento, E. F.The Mathematical Theory of Optimal Processes (English Translation by Trirogoff, K. N.). Interscience, New York, 1962.Google Scholar
3.Kopp, R. E.Pontryagin Maximum Principle in Optimisation Techniques. Academic Press, 1962.Google Scholar