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

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  • Peter Nestler

    (Technische Universitat Berlin)

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.

Suggested Citation

  • Peter Nestler, 2013. "Optimal Thickness of a Cylindrical Shell Under a Time-Dependent Force," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 498-520, August.
    • Handle: RePEc:spr:joptap:v:158:y:2013:i:2:d:10.1007_s10957-012-0255-7
    DOI: 10.1007/s10957-012-0255-7
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