Hybrid-mixed shell quadrilateral that allows for large solution steps and is low-sensitive to mesh distortion

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

We compare three nearly optimal quadrilateral finite elements for geometrically exact inextensible-director shell model. Two of them are revisited and one is novel. The assumed natural strain (ANS) element of Ko et al. (Comput Struct 185:1-14, 2017) shows low sensitivity to mesh distortion and excellent convergence behavior for most types of shell problems. The Hu Washizu element with ANS shear strains of Wagner and Gruttmann (Int J Numer Methods Eng, 64:635-666, 2005) allows for large solution steps and is computationally fast. However, both formulations have undesirable weak spots, which we clearly identify by a comprehensive set of numerical examples. We show that a straightforward combination of both formulations results in a novel element that synergizes the positive features and eliminates the weak spots of its predecessors.

• Language: English
• Keywords: nonlinear shells, quadrilateral element, assumed natural strain, hybrid-mixed formulation, mesh distortion, large solution steps, mesh-distortion sensitivity
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2020
• Number of pages: Str. 177-192
• Numbering: Letn. 65, št. 1
• PID: 20.500.12556/RUL-114876
• UDC: 624.07
• ISSN on article: 0178-7675
• DOI: 10.1007/s00466-019-01759-3
• COBISS.SI-ID: 8875617
• Publication date in RUL: 23.03.2020

LAVRENČIČ, Marko and BRANK, Boštjan, 2020, Hybrid-mixed shell quadrilateral that allows for large solution steps and is low-sensitive to mesh distortion. Computational mechanics [online]. 2020. Vol. 65, no. 1, p. 177–192. [Accessed 17 May 2025]. DOI 10.1007/s00466-019-01759-3. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=114876

Record is a part of a journal

• Title: Computational mechanics
• Shortened title: Comput. mech.
• Publisher: Springer
• ISSN: 0178-7675
• COBISS.SI-ID: 6668037

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: 23.03.2020

Projects

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