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Shape Optimization for a Sharp Interface Model of Distortion Compensation

Please always quote using this URN:urn:nbn:de:0296-matheon-12301
  • We study a mechanical equilibrium problem for a material consisting of two components with different densities, which allows to change the outer shape by changing the interface between the subdomains. We formulate the shape design problem of compensating unwanted workpiece changes by controlling the interface, employ regularity results for transmission problems for a rigorous derivation of optimality conditions based on the speed method, and conclude with some 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-12301
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2015/12/23
Release Date:2015/12/23
Tag:distortion, phase transition, shape optimisation, 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:1087
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