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A virtual element method for contact modeling and dynamics

Publikation: Qualifikations-/Studienabschlussarbeit › Dissertation

Autorschaft

  • Mertcan Cihan

Organisationseinheiten

Details

OriginalspracheEnglisch
QualifikationDoktor der Ingenieurwissenschaften
Gradverleihende Hochschule
Betreut von
Datum der Verleihung des Grades22 Juni 2023
ErscheinungsortHannover
ISBNs (Print) 978-3-941302-51-8
PublikationsstatusVeröffentlicht - 2023

Abstract

Eine Verringerung von Ressourcen und die damit einhergehende Energieknappheit f ¨uhren zu einem erh¨ohten Bedarf an virtuellen Entwicklungsprozessen und effizienter Produktentwicklung. Dieser Trend verdeutlicht die Bedeutung der Digitalisierung und den daraus resultierenden Bedarf an effizienten und hoch genauen numerischen Vorhersagemethoden f ¨ur die Produktentwicklung. Aufgrund ihrer Flexibilit¨at und mit steigenden Rechnerkapazit¨aten ersetzen numerische Methoden allm¨ahlich und stetig physikalische Tests in der industriellen Produktentwicklung. Die Finite Elemente Methode ist vielleicht die bekannteste und am weitesten verbreitete numerische Methode in Industrie und Wissenschaft. Durch die zunehmenden Rechnerkapazit ¨aten und die Weiterentwicklung dieser Methoden in den letzten Jahren hat sich die Zahl der Anwendungsbereiche vergr¨oßert. Numerische Methoden werden unter anderem im Bauwesen, im Automobilbau, in der Schifffahrt, in der Luft- und Raumfahrt und in der Geotechnik eingesetzt. Bei komplexen Geometrien erweist sich jedoch die r¨aumliche Diskretisierung des Gebiets als ein sehr zeitaufw¨andiger Prozess. Da die klassische Finite Elemente Methode auf einfache, regelm¨aßig geformte Elementgeometrien beschr¨ankt ist, w¨urde eine allgemeinere Auswahl von Elementgeometrien mehr Flexibilit¨at bieten. Innerhalb der netzbasierten Methoden sind polygonale Methoden eine hilfreiche Alternative und haben sich bereits in Industrie und Wissenschaft bew¨ahrt. Allerdings scheinen die meisten dieser Methoden einen h¨oheren Rechenaufwand zu erfordern, und neben dem bereits erw¨ahnten Vorteil der flexiblen Elementgeometrien treten auch gewisse Nachteile auf. Eine relativ neue Methode, die Virtuelle Elemente Methode, verspricht gute numerische Eigenschaften und kann als eine Verallgemeinerung der klassischen Finite Elemente Methode angesehen werden. Wie bei allen neuen Methoden m¨ussen auch hier verschiedene Anwendungen in der Industrie und Wissenschaft untersucht werden, bevor die Methode kommerziell eingesetzt werden kann. Diese Arbeit befasst sich mit der Anwendung der Methode der virtuellen Elemente auf dynamisches und elasto-plastisches Materialverhalten. Um elastische und plastische Inkompressibilit¨at zu behandeln, wird auch eine gemischte virtuelle Elementformulierung vorgestellt. In einem weiteren Schritt wird die Virtuelle Elemente Methode zur Modellierung dreidimensionaler Kontaktprobleme mit verschiedenen Kontaktdiskretisierungen verwendet. Es wird ein neuer Projektionsalgorithmus vorgestellt, welcher das Netz an der Kontaktschnittstelle so manipuliert, dass eine sehr einfache und effiziente Knoten-zu-Knoten Kontaktformulierung verwendet werden kann. Es werden verschiedene numerische Beispiele f ¨ur alle oben genannten Anwendungen behandelt, darunter auch Benchmark-Probleme wie der klassische Patch-Test. Um einen geeigneten Vergleich durchzuf¨uhren, werden die entwickelten Formulierungen mit verschiedene Finite Elemente Formulierungen verglichen. Als letztes Beispiel werden alle Modelle, einschließlich Plastizit¨at, Dynamik und Kontakt, gekoppelt, um einen mechanischen Stoß zu modellieren.

Zitieren

A virtual element method for contact modeling and dynamics. / Cihan, Mertcan.
Hannover, 2023. 136 S.

Publikation: Qualifikations-/Studienabschlussarbeit › Dissertation

Cihan, M 2023, 'A virtual element method for contact modeling and dynamics', Doktor der Ingenieurwissenschaften, Gottfried Wilhelm Leibniz Universität Hannover, Hannover. https://doi.org/10.15488/14600
Cihan, M. (2023). A virtual element method for contact modeling and dynamics. [Dissertation, Gottfried Wilhelm Leibniz Universität Hannover]. https://doi.org/10.15488/14600
Cihan M. A virtual element method for contact modeling and dynamics. Hannover, 2023. 136 S. doi: 10.15488/14600
Cihan, Mertcan. / A virtual element method for contact modeling and dynamics. Hannover, 2023. 136 S.
Download
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