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Titel
From shape variation to topology changes in constrained minimization: a velocity method-based concept
VerfasserHintermüller, Michael In der Gemeinsamen Normdatei der DNB nachschlagen ; Kovtunenko, Victor A.
Erschienen in
Optimization Methods and Software, 2011, Jg. 26, H. 4/5, S. 513-532
ErschienenTaylor & Francis
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (EN)velocity method / structure optimization / shape and topological derivative / constrained minimization / variational methods / domain with hole
Schlagwörter (GND)Variationsrechnung / Variationsungleichung / Optimierung / Online-Publikation
ISSN1029-4937
URNurn:nbn:at:at-ubg:3-840 Persistent Identifier (URN)
DOIdoi:10.1080/10556788.2011.559548 
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From shape variation to topology changes in constrained minimization: a velocity method-based concept [0.23 mb]
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Zusammenfassung (Englisch)

The ability of velocity methods to describe changesof topology by creating defects like holes is investigated. For theshape optimization energy-type objective functions are considered,which depend on the geometry by means of state variables. Thestate system is represented by abstract, quadratic, constrainedminimization problems stated over domains with defects. The velocitymethod provides the shape derivative of the objective functiondue to nite variations of a defect. Sucient conditions arederived which allow us to pass the shape derivative to the limitwith respect to diminishing defect, thus, to obtain the \topologicalderivative" of the objective function due to a topology change.An illustrative example is presented for a circular hole bored atthe tip of a crack.

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