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Optimal Thickness of a Cylindrical Shell -- Shape Optimization with Time-dependent Force

Please always quote using this URN:urn:nbn:de:0296-matheon-11755
  • We discuss shape 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 minimizing the deformation of the tube under the influence of the external force. The main difficulty is that the state equation is a hyperbolic partial differential equation of 4th order. 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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Metadaten
Author:Peter Nestler
URN:urn:nbn:de:0296-matheon-11755
Referee:Dietmar Hömberg
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/10/25
Release Date:2012/10/25
Tag:shape optimization
Institute:Technische Universität Berlin
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Kxx Optimality conditions / 49K20 Problems involving partial differential equations
Preprint Number:988
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