Comparison of numerically dissipative schemes for structural dynamics: Generalized-alpha versus energy-decaying methods. (December 2020)

• Record Type: Journal Article
• Authors: Lavrenčič, Marko; Brank, Boštjan
• Is Part Of: Thin-walled structures. Volume 157(2020)
• Publication Date: 2020-12
• Subjects: Structural dynamics -- Implicit schemes -- Numerical dissipation -- Generalized-methods -- Energy-decaying and momentum-conserving methods -- Stiff equations -- Shell-like examples; Thin-walled structures -- Periodicals; 690.1
• DOI: 10.1016/j.tws.2020.107075
• Languages: English
• ISSNs: 0263-8231

Abstract

Abstract: We revisit some existing time-stepping schemes for structural dynamics with the algorithmic dissipation that fall either into the class of generalized- α 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. Highlights: Comparison of generalized- α and energy-decaying schemes was summarized. Jansen, Whiting and Hulbert scheme was analyzed for nonlinear regime. Performance of generalized- α and energy-decaying schemes was illustrated for stiff case.