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FROM SHAPE VARIATION TO TOPOLOGY CHANGES IN CONSTRAINED MINIMIZATION: A VELOCITY METHOD BASED CONCEPT

Please always quote using this URN:urn:nbn:de:0296-matheon-8265
  • The ability of velocity methods to describe changes of topology by creating defects like holes is investigated. For the shape optimization energy-type objective functions are considered, which depend on the geometry by means of state variables. The state system is represented by abstract, quadratic, constrained minimization problems stated over domains with defects. The velocity method provides the shape derivative of the objective function due to fi� nite variations of a defect. Suffcient conditions are derived which allow us to pass the shape derivative to the limit with respect to diminishing defect, thus, to obtain the "topological derivative" of the objective function due to a topology change. An illustrative example is presented for a circular hole bored at the tip of a crack.

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Metadaten
Author:Michael Hintermueller, Victor Kovtunenko
URN:urn:nbn:de:0296-matheon-8265
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2011/05/04
Release Date:2011/05/04
Tag:
Institute:Research Center Matheon
Humboldt-Universität zu Berlin
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J40 Variational methods including variational inequalities [See also 47J20]
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Kxx Optimality conditions / 49K40 Sensitivity, stability, well-posedness [See also 90C31]
Preprint Number:789
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