Optimal shape of an elastic column on elastic foundation |
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| Institution: | 1. School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China;2. Institute of Port, Coastal and Offshore Engineering, Ocean College, Zhejiang University, Zhoushan 316021, Zhejiang, China;3. Centre for Optical and Electromagnetic Research, State Key Laboratory for Modern Optical Instrumentation, Zhejiang Provincial Key Laboratory for Sensing Technologies, Zhejiang University, Hangzhou 310058, China;4. School of Civil Engineering, The University of Queensland, St Lucia 4072, Queensland, Australia;5. Engineering Research Center of Oceanic Sensing Technology and Equipment, Zhejiang University, Ministry of Education, China;1. IRSTEA, UR ETGR, 2 rue de la Papeterie, 38402 Saint Martin d''Hères Cedex, France;2. Université Grenoble Alpes, 38041 Grenoble, France;3. School of Civil Engineering, University of Sydney, NSW 2006, Australia;4. Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan;5. Aalto University School of Engineering, Aalto University, FIN-00076 Aalto, Finland;6. Institute of Mountain Risk Engineering, 82 Peter Jordan-Straße, 1190 Vienna, Austria;7. IGEMA-UMSA, Calle 27, Campus Universitario Cota Cota, Casilla 35140, La Paz, Bolivia;8. LGGE, CNRS-UJF, 54 rue Molière, 38402 Saint Martin d''Hères cedex, France;9. INSA-Lyon, UR LGCIE, 20 Av. Albert Einstein, 69621 Villeurbanne, France;10. ENSG, IGN, 6 et 8 Avenue B. Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne la Vallée Cedex 2, France |
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| Abstract: | By using Pontryagin's maximum principle we determine the shape of an elastic compressed column on elastic, Winkler type foundation. We assume that the column has clamped ends. The optimality conditions for the case of bimodal optimization are derived. It is shown that the optimal cross-sectional area function is determined from the solution of a nonlinear boundary value problem. In the special case of a compressed column with no foundation, the optimality condition and the solution obtained earlier are recovered. |
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