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Distortion compensation as a shape optimization problem for a sharp interface model

Please always quote using this URN:urn:nbn:de:0296-matheon-13004
  • A mechanical equilibrium problem for a material consisting of two components with di� erent densities is considered. Due to the heterogeneous material densities, the outer shape of the underlying workpiece can be changed by shifting the interface between the subdomains. In this paper, the problem is modeled as a shape design problem for optimally compensating unwanted workpiece changes. The associated control variable is the interface. Regularity results for transmission problems are employed for a rigorous derivation of suitable � first-order optimality conditions based on the speed method. The paper concludes with several numerical results based on a spline approximation of the interface.

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Metadaten
Author:Kevin Sturm, Michael Hintermüller, Dietmar Hömberg
URN:urn:nbn:de:0296-matheon-13004
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2014/05/20
Release Date:2014/05/20
Tag:distortion, phase transition, shape optimization, speed method, transmission problem
Institute:Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q74 PDEs in connection with mechanics of deformable solids
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Qxx Manifolds [See also 58Exx] / 49Q10 Optimization of shapes other than minimal surfaces [See also 90C90]
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Nxx Phase transformations in solids [See also 74A50, 80Axx, 82B26, 82C26] / 74N15 Analysis of microstructure
Preprint Number:1066
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