Optimal shape of a column with clamped-elastically supported ends positioned on elastic foundation
We determine optimal shape of an elastic column positioned on elastic foundation of Winkler type. The Euler-Bernoulli model of beam is considered. The column is loaded by a compressive force and has one clamped end and the other elastically supported end. In deriving the optimality conditio...
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| Format: | Article |
| Language: | English |
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Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade
2015-01-01
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| Series: | Theoretical and Applied Mechanics |
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| Online Access: | http://www.doiserbia.nb.rs/img/doi/1450-5584/2015/1450-55841503191N.pdf |
| Summary: | We determine optimal shape of an elastic column positioned on elastic
foundation of Winkler type. The Euler-Bernoulli model of beam is considered.
The column is loaded by a compressive force and has one clamped end and the
other elastically supported end. In deriving the optimality conditions, the
Pontryagin’s principle was used. The optimality conditions for the case of
bimodal optimization are derived. Optimal cross-sectional area is obtained
from the solution of a non-linear boundary value problem. A first integral
(Hamiltonian) is used to monitor accuracy of integration. This system is
solved by using standard Math CAD procedure. New numerical results are
obtained. [Projekat Ministarstva nauke Republike Srbije, br. 174005] |
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| ISSN: | 1450-5584 2406-0925 |