Energy-decaying and momentum-conserving schemes for transient simulations with mixed finite elements

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

We present the four-field (of displacements, velocities, stresses and strains) and the three-field (of displacements, velocitiesand stresses) mixed variational formulations for structural dynamics, which can be used to derive in an elegant way the energy-decaying and momentum-conserving (EDMC) time-stepping schemes for transient simulations with mixed solid and structuralfinite elements. These mixed variational formulations are in this work applied for the derivation of EDMC schemes for thegeometrically exact, recently proposed, mixed-hybrid, shell finite elements (with excellent performance), which combine mixedinterpolations of the Hu Washizu type or the Hellinger Reissner type with the assumed natural strain concept. To this end, thefirst-order and the second-order accurate EDMC schemes are designed. The superior properties of the considered mixed-hybridshell finite elements, which are reflected in statics by excellent convergence properties, ability to take very large solution steps,and low-sensitivity to mesh distortion, are in this manner extended for (long-term) transient simulations. Numerical examples,which illustrate transient simulations with the EDMC schemes and mixed-hybrid shell finite elements, show (among othereffects) that the underlying structure of the shell motion is numerically preserved even for very large time steps.

• Language: English
• Keywords: civil engineering, mixed functionals for structural dynamics, energy-decaying and momentum-conserving schemes, mixed-hybrid shell elements, transient simulations with mixed finite elements
• Work type: Scientific work
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2021
• Number of pages: Str. 1-34
• Numbering: Vol. 375/113625
• PID: 20.500.12556/RUL-125100
• UDC: 519.651:624.07
• ISSN on article: 0045-7825
• DOI: 10.1016/j.cma.2020.113625
• COBISS.SI-ID: 45180419
• Publication date in RUL: 04.03.2021

Record is a part of a journal

• Title: Computer methods in applied mechanics and engineering
• Shortened title: Comput. methods appl. mech. eng.
• Publisher: Elsevier
• ISSN: 0045-7825
• COBISS.SI-ID: 6695685

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: gradbeništvo, mešani funkcionali za dinamiko konstrukcij, mešani končni elementi

Projects

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