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A Combination of the Scaled Boundary Finite Element Method with the Mortar Method

  • The simulation of ultrasonic waves in a linearly elastic body can be computationally intensive. The reason is the relatively short wavelength compared to the body size for high frequencies. One possible approach to counteract the high computational costs is to decompose the domain into small parts and strive for parallelization. The Mortar Method is a well-established approach for domain decomposition. A rather new approach to discretize the emerging subdomains is the Scaled Boundary Finite Element Method. This semi-analytical method has many attractive properties. Some of these properties are listed subsequently. The grid consists of polygonal elements, which leaves much freedom in the meshing process. A variety of material distributions, including anisotropic materials, can be considered. High-order shape functions can be used for optimal convergence properties. The approach treats singularities at crack tips and corners analytically. Especially in the frequency domain, the ScaledThe simulation of ultrasonic waves in a linearly elastic body can be computationally intensive. The reason is the relatively short wavelength compared to the body size for high frequencies. One possible approach to counteract the high computational costs is to decompose the domain into small parts and strive for parallelization. The Mortar Method is a well-established approach for domain decomposition. A rather new approach to discretize the emerging subdomains is the Scaled Boundary Finite Element Method. This semi-analytical method has many attractive properties. Some of these properties are listed subsequently. The grid consists of polygonal elements, which leaves much freedom in the meshing process. A variety of material distributions, including anisotropic materials, can be considered. High-order shape functions can be used for optimal convergence properties. The approach treats singularities at crack tips and corners analytically. Especially in the frequency domain, the Scaled Boundary Finite Element Method reduces the dimension of the approximation because only degrees of freedom which are associated with the boundary of a polygonal element are necessary. Those desirable properties make the method particularly suitable for calculating the dynamic responses in bodies with cracks, as it is essential for many non-destructive testing and structural health monitoring applications. In this contribution, we present a combination of the Scaled Boundary Finite Element Method with the Mortar Method in two dimensions. The presentation starts with a theoretical overview of both approaches. Subsequently, numerical examples demonstrate the stability of the combination for the polygonal boundary of the elements. The numerical examples increase in complexity and are compared to results computed on non-divided domains with the Finite Element Method.zeige mehrzeige weniger

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Metadaten
Autor*innen:Jannis BullingORCiD
Koautor*innen:Hauke Gravenkamp
Dokumenttyp:Vortrag
Veröffentlichungsform:Präsentation
Sprache:Englisch
Jahr der Erstveröffentlichung:2021
Organisationseinheit der BAM:8 Zerstörungsfreie Prüfung
8 Zerstörungsfreie Prüfung / 8.4 Akustische und elektromagnetische Verfahren
DDC-Klassifikation:Naturwissenschaften und Mathematik / Chemie / Analytische Chemie
Freie Schlagwörter:Numerical Simulation; Scaled Boundary Finite Element Method, Mortar Method; Ultrasound
Themenfelder/Aktivitätsfelder der BAM:Chemie und Prozesstechnik
Veranstaltung:WCCM-ECCOMAS CONGRESS
Veranstaltungsort:Online meeting
Beginndatum der Veranstaltung:11.01.2021
Enddatum der Veranstaltung:15.01.2021
Verfügbarkeit des Dokuments:Datei im Netzwerk der BAM verfügbar ("Closed Access")
Datum der Freischaltung:17.03.2021
Referierte Publikation:Nein
Eingeladener Vortrag:Nein
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