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

Peter Nestler ()
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Peter Nestler: Technische Universitat Berlin

Journal of Optimization Theory and Applications, 2013, vol. 158, issue 2, No 11, 498-520

Abstract: 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.

Keywords: Calculus of variations and optimal control; Problems involving partial differential equations; Optimization of shapes other than minimal surfaces (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10957-012-0255-7

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