Isogeometric boundary element analysis and structural shape optimization for Helmholtz acoustic problems

Dissertation, Bauhaus-Universität Weimar, 2022

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Bibliographische Detailangaben
1. Verfasser:	Shaaban Mohamed, Ahmed Mostafa (VerfasserIn)
Körperschaft:	Bauhaus-Universität Weimar (Grad-verleihende Institution)
Weitere Verfasser:	Rabczuk, Timon (AkademischeR BetreuerIn)
Format:	UnknownFormat
Sprache:	ger
Veröffentlicht:	Weimar 2022
Schriftenreihe:	ISM-Bericht 2022,6
Schlagworte:	Hochschulschrift > Akustik > Helmholtz-Schwingungsgleichung > Randelemente-Methode > Isogeometrische Analyse > Gestaltoptimierung
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Beschreibung
Zusammenfassung:	Dissertation, Bauhaus-Universität Weimar, 2022 In this thesis, a new approach is developed for applications of shape optimization on the time harmonic wave propagation (Helmholtz equation) for acoustic problems. This approach is introduced for different dimensional problems: 2D, 3D axi-symmetric and fully 3D problems. The boundary element method (BEM) is coupled with the isogeometric analysis (IGA) forming the so-called (IGABEM) which speeds up meshing and gives higher accuracy in comparison with standard BEM. BEM is superior for handling unbounded domains by modeling only the inner boundaries and avoiding the truncation error, present in the finite element method (FEM) since BEM solutions satisfy the Sommerfeld radiation condition automatically. Moreover, BEM reduces the space dimension by one from a volumetric three-dimensional problem to a surface two-dimensional problem, or from a surface two-dimensional problem to a perimeter one-dimensional problem. Non-uniform rational B-splines basis functions (NURBS) are used in an isogeometric setting to describe both the CAD geometries and the physical fields. ...
Beschreibung:	xxi, 173 Seiten Illustrationen, Diagramme