On the optimal shape of a column with partial elastic foundation |
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| Authors: | Teodor M. Atanackovic Boris B. Jakovljevic Milena R. Petkovic |
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| Affiliation: | 1. Department of Mechanics, Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovica 6, 21000 Novi Sad, Serbia;2. Department of Mathematics, Faculty of Natural Sciences and Mathematics, University of Novi Sad, Trg D. Obradovica 4, 21000 Novi Sad, Serbia;3. Mathematical Institute, Serbian Academy of Arts and Sciences, Kneza Mihaila 36, 11000 Beograd, Serbia;1. Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada H3A 0C3;2. School of Mechanical, Materials and Mechatronic Engineering, University of Wollongong, NSW 2522, Australia |
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| Abstract: | 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. |
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