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Optimal Thickness of a Cylindrical Shell Under a Time-Dependent Force

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Abstract

We discuss thickness optimization problems for cylindrical tubes that are loaded by time-dependent applied force. This is a problem of shape optimization that leads to optimal control in linear elasticity theory. We determine the optimal thickness of a cylindrical tube by minimizing the deformation of the tube under the influence of an external force. The main difficulty is that the state equation is a hyperbolic partial differential equation of the fourth order. The first order necessary conditions for the optimal solution are derived. Based on them, a numerical method is set up and numerical examples are presented.

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Acknowledgements

The author thanks L. Bittner and W. Schmidt (Greifswald) for introducing me to this topic. Moreover, he is very grateful to F. Tröltzsch (Berlin) for this support and extensive discussion during a revision of this paper.

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  1. Technische Universitat Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Peter Nestler

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  1. Peter Nestler
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Correspondence to Peter Nestler.

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Communicated by Z. Mróz.

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Nestler, P. Optimal Thickness of a Cylindrical Shell Under a Time-Dependent Force. J Optim Theory Appl 158, 498–520 (2013). https://doi.org/10.1007/s10957-012-0255-7

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