Improved implicit integrators for transient impact problems—geometric admissibility within the conserving framework

By T. Laursen, Gillian Love. International Journal for Numerical Methods in Engineering, 2002

138 citations recorded by the source corpus.

The value of energy and momentum conserving algorithms has been well established for the analysis of highly non‐linear systems, including those characterized by the nonsmooth non‐linearities of an impact event. This work proposes an improved integration scheme for frictionless dynamic contact, seeking to preserve the stability properties of exact energy and momentum conservation without the heretofore unavoidable compromise of violating geometric admissibility as established by the contact constraints. The physically motivated introduction of a discrete contact velocity provides an algorithmic framework that ensures exact conservation locally while remaining independent of the choice of constraint treatment, thus making full conservation equally possible in conjunction with a penalty regularization as with an exact Lagrange multiplier enforcement. The discrete velocity effects are incorporated as a post‐convergence update to the system velocities, and thus have no direct effect on the non‐linear solution of the displacement equilibrium equation. The result is a robust implicit algorithmic treatment of dynamic frictionless impact, appropriate for large deformations and fully conservative for a range of geometric constraints. Copyright © 2001 John Wiley & Sons, Ltd.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/1e1d1da53ec11454174845f448def0ea3a0042af

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Citations in the corpus

Isogeometric analysis and domain decomposition methods (2012, methodology): “They have been applied successfully to contact [26,6,27,15,17,21, 20] as well as to domain decomposition problems [18].”
Unilateral non‐linear dynamic contact of thin‐walled structures using a primal‐dual active set strategy (2007, unknown): “For further details of this approach, we refer to the work by Laursen and Love [18].”
Transient three‐dimensional domain decomposition problems: Frame‐indifferent mortar constraints and conserving integration (2010, methodology): “Energy-conserving time-stepping schemes for largedeformation contact problems have been developed within the framework of the NTS method, see, for example Laursen and Chawla [27], Armero and Petöcz [28], Laursen and Love [29], Hauret and Le Tallec [30], Haikal and Hjelmstad [31] and Betsch and Hesc”
A nonsmooth generalized‐ α scheme for flexible multibody systems with unilateral constraints (2013, background): “It generally results in a scheme of lower order where the contact forces or impulses are treated in a fully implicit manner [26, 27], and where the constraint is expressed at the velocity level [24, 25, 29].”
Energy-momentum conserving integration of multibody dynamics (2007, background): “In this connection, representative works are due to Brank et al. [14], Bauchau and Bottasso [3], Crisfield and Jeleni´ c [15], Ibrahimbegovi´ c et al. [25], Romero and Armero [34], Betsch and Steinmann [9], Puso [33], Laursen and Love [ 28 ], and Armero [2], see also the references cited in these wo”
A mortar method for energy‐momentum conserving schemes in frictionless dynamic contact problems (2009, methodology): “[12] obtain algorithmic energy conservation for their mortar contact description by applying the approach proposed by Laursen and Love [18].”