Hybrid-mixed low-order finite elements for geometrically exact shell models: overview and comparison

Lavrenčič, Marko (author), Brank, Boštjan (author)

We critically review and compare ffteen mixed and mixed-hybrid nonlinear shell fnite element formulations with 4 nodes in order to identify those that are closest to the "optimal" one. We consider formulations that are based either on Assumed Natural Strain concept, Enhanced Assumed Strain concept, Hellinger-Reissner functional or Hu-Washizu functional, and those that efectively combine several of the mentioned approaches. Most of the formulations are state-of-the-art, but some are also presented for the frst time. We show that the fexibility of mixed-hybrid formulations requires careful consideration of theoretical and numerical aspects in the process of design of a high-performance element. We make extensive numerical experiments in order to assess convergence properties, mesh distortion sensitivity, and computational speed (that is associated with the ability to achieve large steps during the solution search) of the considered formulations. We show that the application of the idea to combine mixed-hybrid formulations of the Hellinger-Reissner and Hu-Washizu type with the Assumed Natural Strain and/or the Enhanced Assumed Strain concepts generates the formulations that perform excellent. We also identify the formulations that are currently closest to the "optimal" one.

• Language: English
• Keywords: shells, finite elements, hybrid formulations, mixed formulations
• Work type: Scientific work
• Typology: 1.02 - Review Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2021
• Number of pages: Str. 1-35
• Numbering: Letn. XX, št. X
• PID: 20.500.12556/RUL-125105
• UDC: 624.074.4
• ISSN on article: 1134-3060
• DOI: 10.1007/s11831-021-09537-2
• COBISS.SI-ID: 51354627
• Publication date in RUL: 04.03.2021

Record is a part of a journal

• Title: Archives of computational methods in engineering
• Shortened title: Arch. comput. methods eng.
• Publisher: Springer, International Center for Numerical Methods in Engineering
• ISSN: 1134-3060
• COBISS.SI-ID: 1758230

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.
• Licensing start date: 04.03.2021

Secondary language

• Language: Slovenian
• Keywords: lupine, končni elementi, hibridne formulacije, mešane formulacije

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: J2-1722
• Name: Numerično modeliranje porušitve v krhkih, kvazi-krhkih in duktilnih konstrukcijah
• Acronym: ComFrac