2011
DOI: 10.1137/100791440
|View full text |Cite
|
Sign up to set email alerts
|

Time-Integration Schemes for the Finite Element Dynamic Signorini Problem

Abstract: A large variety of discretizations have been proposed in the literature for the numerical solution of the dynamic Signorini problem. We classify the different discretizations into four groups. The first three groups correspond to different ways of enforcing the contact condition: exact enforcement, enforcement with penalty, and enforcement with contact condition in velocity. The fourth approach is based on a modification of the mass matrix. Numerical simulations on two one-dimensional benchmark problems with a… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1

Citation Types

0
118
0

Year Published

2012
2012
2021
2021

Publication Types

Select...
6
1

Relationship

0
7

Authors

Journals

citations
Cited by 67 publications
(118 citation statements)
references
References 27 publications
0
118
0
Order By: Relevance
“…In the Finite Element Method (FEM), the displacement commonly takes the form u.x; t/ D P i i .x/u i .t /, where u i .t / is the i -th displacement participation and i .x/, the corresponding shape function. This leads to spurious oscillations, dispersion, and energy dissipation, for most numerical schemes dealing with unilateral contact conditions [11]. Additionally, an impact law is required to uniquely describe the time-evolution of a space semi-discretized formulation [5].…”
Section: Introductionmentioning
confidence: 99%
“…In the Finite Element Method (FEM), the displacement commonly takes the form u.x; t/ D P i i .x/u i .t /, where u i .t / is the i -th displacement participation and i .x/, the corresponding shape function. This leads to spurious oscillations, dispersion, and energy dissipation, for most numerical schemes dealing with unilateral contact conditions [11]. Additionally, an impact law is required to uniquely describe the time-evolution of a space semi-discretized formulation [5].…”
Section: Introductionmentioning
confidence: 99%
“…Direct-substitution methods. Energy-momentum and symplecticmomentum methods have been extended to the inequality case by the direct substitution of a nonsmooth constraint force (Laursen and Chawla (1997); Kane et al (1999);Stewart (2000); Laursen and Love (2002); Pandolfi et al (2002); Deuflhard, Krause, and Ertel (2008); Boumediène Khenous, Laborde, and Renard (2008); Krause and Walloth (2012) ;Doyen, Ern, and Piperno (2011)). Following the time-continuous case discussed above, the extended value Hamiltonian for inequality-constrained systems is naturally composed by concatenating the unconstrained system's potential with the extended value indicator function.…”
mentioning
confidence: 99%
“…Similarly, energy-momentum-based direct methods and a variety of extensions and stabilizations are an active and promising area of research (Doyen, Ern, and Piperno (2011)). Although behaviors comparable to direct symplectic schemes are currently observed in practice (Doyen, Ern, and Piperno (2011)), drift and stability properties of these methods remain under investigation.…”
mentioning
confidence: 99%
See 2 more Smart Citations