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Comparison of different models for stress singularities in higher order finite element methods for elastic waves

  • The Spectral Element Method (SEM) has been proven to be an efficient numerical method for solving the wave equation in linear elastic bodies. This efficiency is reduced if a stress singularity is present in the body. For example, re-entrant corners, material interfaces, fixed boundaries, and especially crack tips can cause stress singularities. To preserve the efficiency of the SEM, special solution strategies are required. There are many approaches which consider stress singularities, but comparisons are rare for dynamic problems. Finding an efficient model is an important step for many applications. In particular, applications for structural health monitoring and non-destructive evaluation rely on accurate and efficient crack models. In this contribution, we present several models to capture singularities in combination with the SEM. The theory behind the models are shortly summarized and we show results for different benchmark problems in two dimensions. The first model deploys aThe Spectral Element Method (SEM) has been proven to be an efficient numerical method for solving the wave equation in linear elastic bodies. This efficiency is reduced if a stress singularity is present in the body. For example, re-entrant corners, material interfaces, fixed boundaries, and especially crack tips can cause stress singularities. To preserve the efficiency of the SEM, special solution strategies are required. There are many approaches which consider stress singularities, but comparisons are rare for dynamic problems. Finding an efficient model is an important step for many applications. In particular, applications for structural health monitoring and non-destructive evaluation rely on accurate and efficient crack models. In this contribution, we present several models to capture singularities in combination with the SEM. The theory behind the models are shortly summarized and we show results for different benchmark problems in two dimensions. The first model deploys a new class of singular elements. For these singular elements, the crack tip approximation is computed based on the static Scaled Boundary Finite Element Method (SBFEM). The second model uses the continued‐fraction‐based SBFEM, while the third model uses an hp-refinement near the singularity. The models are compared among each other and evaluated in terms of their respective efficiency and accuracy.zeige mehrzeige weniger

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Metadaten
Autoren/innen:Jannis Bulling
Koautoren/innen:Hauke Gravenkamp
Dokumenttyp:Vortrag
Veröffentlichungsform:Präsentation
Sprache:Englisch
Jahr der Erstveröffentlichung:2019
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:Higher order FEM; SBFEM; Stress singularities
Themenfelder/Aktivitätsfelder der BAM:Analytical Sciences
Analytical Sciences / Zerstörungsfreie Prüfung und Spektroskopie
Veranstaltung:GAMM 2019
Veranstaltungsort:Vienna, Austria
Beginndatum der Veranstaltung:18.02.2019
Enddatum der Veranstaltung:22.02.2019
Verfügbarkeit des Volltexts:Volltext-PDF im Netzwerk der BAM verfügbar ("Closed Access")
Datum der Freischaltung:11.04.2019
Referierte Publikation:Nein