Energy-decaying and momentum-conserving schemes for transient simulations with mixed finite elements
ID Lavrenčič, Marko (Author), ID Brank, Boštjan (Author)

URLURL - Source URL, Visit https://doi.org/10.1016/j.cma.2020.113625 This link opens in a new window

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.

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
Number of pages:Str. 1-34
Numbering:Vol. 375/113625
PID:20.500.12556/RUL-125100 This link opens in a new window
ISSN on article:0045-7825
DOI:10.1016/j.cma.2020.113625 This link opens in a new window
COBISS.SI-ID:45180419 This link opens in a new window
Publication date in RUL:04.03.2021
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Record is a part of a journal

Title:Computer methods in applied mechanics and engineering
Shortened title:Comput. methods appl. mech. eng.
COBISS.SI-ID:6695685 This link opens in a new window


License:CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
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

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


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

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