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Isogeometric finite element methods for shape optimization

  • In this thesis we develop a shape optimization framework for isogeometric analysis in the optimize first–discretize then setting. For the discretization we use isogeometric analysis (iga) to solve the state equation, and search optimal designs in a space of admissible b-spline or nurbs combinations. Thus a quite general class of functions for representing optimal shapes is available. For the gradient-descent method, the shape derivatives indicate both stopping criteria and search directions and are determined isogeometrically. The numerical treatment requires solvers for partial differential equations and optimization methods, which introduces numerical errors. The tight connection between iga and geometry representation offers new ways of refining the geometry and analysis discretization by the same means. Therefore, our main concern is to develop the optimize first framework for isogeometric shape optimization as ground work for both implementation and an error analysis. Numerical examples show that this ansatz is practical and case studies indicate that it allows local refinement.

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Author:Daniela Fußeder
URN (permanent link):urn:nbn:de:hbz:386-kluedo-42643
ISBN:978-3-8440-4123-1
Advisor:Bernd Simeon
Document Type:Doctoral Thesis
Language of publication:English
Publication Date:2016/01/06
Year of Publication:2015
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2015/10/29
Date of the Publication (Server):2016/01/07
Tag:Shape optimization, gradient based optimization, adjoint method
GND-Keyword:B-Spline; Isogeometrische Analyse; NURBS; Optimale Kontrolle; Strukturoptimierung
Number of page:XVI, 133
Source:http://www.shaker.de/shop/978-3-8440-4123-1
Faculties / Organisational entities:Fachbereich Mathematik
CCS-Classification (computer science):J. Computer Applications
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):35-XX PARTIAL DIFFERENTIAL EQUATIONS
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]
65-XX NUMERICAL ANALYSIS
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 30.07.2015