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http://dx.doi.org/10.18419/opus-13653
Autor(en): | Bieber, Simon Auricchio, Ferdinando Reali, Alessandro Bischoff, Manfred |
Titel: | Artificial instabilities of finite elements for nonlinear elasticity : analysis and remedies |
Erscheinungsdatum: | 2023 |
Dokumentart: | Zeitschriftenartikel |
Seiten: | 2638-2675 |
Erschienen in: | International journal for numerical methods in engineering 124 (2023), S. 2638-2675 |
URI: | http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-136728 http://elib.uni-stuttgart.de/handle/11682/13672 http://dx.doi.org/10.18419/opus-13653 |
ISSN: | 0029-5981 1097-0207 |
Zusammenfassung: | Within the framework of plane strain nonlinear elasticity, we present a discussion on the stability properties of various Enhanced Assumed Strain (EAS) finite element formulations with respect to physical and artificial (hourglassing) instabilities. By means of a linearized buckling analysis we analyze the influence of element formulations on the geometric stiffness and provide new mechanical insights into the hourglassing phenomenon. Based on these findings, a simple strategy to avoid hourglassing for compression problems is proposed. It is based on a modification of the discrete Green-Lagrange strain, simple to implement and generally applicable. The stabilization concept is tested for various popular element formulations (namely EAS elements and the assumed stress element by Pian and Sumihara). A further aspect of the present contribution is a discussion on proper benchmarking of finite elements in the context of hourglassing. We propose a simple bifurcation problem for which analytical solutions are readily available in the literature. It is tailored for an in-depth stability analysis of finite elements and allows a reliable assessment of its stability properties. |
Enthalten in den Sammlungen: | 02 Fakultät Bau- und Umweltingenieurwissenschaften |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
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NME_NME7224.pdf | 3,19 MB | Adobe PDF | Öffnen/Anzeigen |
Diese Ressource wurde unter folgender Copyright-Bestimmung veröffentlicht: Lizenz von Creative Commons