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Optimal shape of a heavy compressed column

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Abstract

By using Pontryagin’s maximum principle we determine the shape of a heavy compressed rod, stable against buckling. It is assumed that the eigenvalue pair corresponding to the optimal rod is simple. With this assumption (unimodal optimization) it is shown that the cross-sectional area function is determined from the solution of a nonlinear boundary value problem. A variational principle for this boundary value problem is formulated and two first integrals are constructed. The optimal shape of a rod is determined by numerical integration.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Technical Sciences, University of Novi Sad, POB 55, 21121, Novi Sad, ??

    T.M. Atanackovic & V.B. Glavardanov

Authors
  1. T.M. Atanackovic
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  2. V.B. Glavardanov
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Correspondence to V.B. Glavardanov.

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Atanackovic, T., Glavardanov, V. Optimal shape of a heavy compressed column. Struct Multidisc Optim 28, 388–396 (2004). https://doi.org/10.1007/s00158-004-0457-1

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  • DOI: https://doi.org/10.1007/s00158-004-0457-1

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