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

Kevin Sturm (), Michael Hintermüller () and Dietmar Hömberg ()
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Kevin Sturm: Weierstraß-Institut
Michael Hintermüller: Humboldt-Universität zu Berlin
Dietmar Hömberg: Weierstraß-Institut

Computational Optimization and Applications, 2016, vol. 64, issue 2, No 10, 557-588

Abstract: Abstract A mechanical equilibrium problem for a material consisting of two components with different 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.

Keywords: Distortion; Phase transition; Shape optimisation; Speed method; Transmission problem (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10589-015-9816-7

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