Comparison of numerically dissipative schemes for structural dynamics - generalized-alpha versus energy-decaying methods

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

We revisit some existing time-stepping schemes for structural dynamics with the algorithmic dissipation that fall either into the class of generalized- methods or into the class of energy-decaying (and momentum-conserving) methods. Some of the considered schemes are designed for the second-order and some for the first-order form of the differential equations of motion. We perform a comparison (for linear dynamics) of their accuracy, dissipation, dispersion, as well as of the overshoot. In order to study how these features extend to nonlinear dynamics, we choose numerical tests on shell-like examples. Shell models are a difficult check for dynamic schemes because numerically stiff equations need to be solved as an effect of a large difference between the bending (and shear) and the membrane deformation modes. For the considered schemes we illustrate their ability to decay/dissipate energy, their ability to fully/approximately conserve the angular momentum, and nonlinear order of accuracy by error indicators.

• Language: English
• Keywords: civil engineering, thin-walled structures, structural dynamics methods, momentum-conserving methods, stiff equations, hell-like examples
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Submitted to the publisher
• Publication version: Author Accepted Manuscript
• Year: 2020
• Number of pages: Str. 1-22
• Numbering: Letn. 157, št. 107075
• PID: 20.500.12556/RUL-120701
• UDC: 624.07
• ISSN on article: 0263-8231
• DOI: 10.1016/j.tws.2020.107075
• COBISS.SI-ID: 29701379
• Publication date in RUL: 24.09.2020

LAVRENČIČ, Marko and BRANK, Boštjan, 2020, Comparison of numerically dissipative schemes for structural dynamics - generalized-alpha versus energy-decaying methods. Thin-walled structures [online]. 2020. Vol. 157, no. 107075, p. 1–22. [Accessed 15 April 2025]. DOI 10.1016/j.tws.2020.107075. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=120701

Record is a part of a journal

• Title: Thin-walled structures
• Shortened title: Thin-walled struct.
• Publisher: Elsevier
• ISSN: 0263-8231
• COBISS.SI-ID: 26529536

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: 24.09.2020

Secondary language

• Language: Slovenian
• Keywords: gradbeništvo, gradbene konstrukcije, dinamika konstrukcij, implicitne sheme, numerična disipacija, posplošene metode, metode, ki disipirajo energijo in ohranjajo vrtilno količino, toge enačbe primeri z lupinami, primeri z lupinami

Projects

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