On the optimal shape of a column with partial elastic foundation

By using Pontryagin's principle we study the optimal shape of an elastic column with clamped ends and positioned on elastic foundation of Winkler type. Two problems were treated. In the first one, which is a generalization of our previous work, we consider the case of a partially supported colu...

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Bibliographic Details
Published in:European journal of mechanics, A, Solids A, Solids, 2010-03, Vol.29 (2), p.283-289
Main Authors: Atanackovic, Teodor M., Jakovljevic, Boris B., Petkovic, Milena R.
Format: Article
Language:English
Subjects:
Clamping
Constrictions
Cross sections
Elastic foundation
Exact sciences and technology
Foundations
Fundamental areas of phenomenology (including applications)
Optimal shape
Optimization
Physics
Pontryagin principle
Pontryagin's principle
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
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Summary:By using Pontryagin's principle we study the optimal shape of an elastic column with clamped ends and positioned on elastic foundation of Winkler type. Two problems were treated. In the first one, which is a generalization of our previous work, we consider the case of a partially supported column. In the second problem we determine the optimal shape of a column on elastic foundation subjected to restrictions on minimal cross-sectional area. It is shown that in this case the optimization can be both bimodal and unimodal. We determine the transition value between unimodal and bimodal optimization for specified values of parameters.
ISSN:0997-7538
1873-7285
DOI:10.1016/j.euromechsol.2009.08.003