Details
| Original language | English |
|---|---|
| Pages (from-to) | 407-420 |
| Number of pages | 14 |
| Journal | Computational mechanics |
| Volume | 41 |
| Issue number | 3 |
| Publication status | Published - 11 Jul 2007 |
Abstract
In this paper a finite element formulation for frictionless contact problems with non-matching meshes in the contact interface is presented. It is based on a non-standard variational formulation due to Nitsche and leads to a matrix formulation in the primary variables. The method modifies the unconstrained functional by adding extra terms and a stabilization which is related to the classical penalty method. These new terms are characterized by the presence of contact forces that are computed from the stresses in the continuum elements. They can be seen as a sort of Lagrangian-type contributions. Due to the computation of the contact forces from the continuum elements, some additional degrees-of-freedom are involved in the stiffness matrix parts related to contact. These degrees-of-freedom are associated with nodes not belonging to the contact surfaces.
Keywords
- Contact mechanics, Finite element discretization, Lagrangian multipliers, Nitsche method, Penalty method
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational mechanics, Vol. 41, No. 3, 11.07.2007, p. 407-420.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A formulation for frictionless contact problems using a weak form introduced by Nitsche
AU - Wriggers, Peter
AU - Zavarise, G.
PY - 2007/7/11
Y1 - 2007/7/11
N2 - In this paper a finite element formulation for frictionless contact problems with non-matching meshes in the contact interface is presented. It is based on a non-standard variational formulation due to Nitsche and leads to a matrix formulation in the primary variables. The method modifies the unconstrained functional by adding extra terms and a stabilization which is related to the classical penalty method. These new terms are characterized by the presence of contact forces that are computed from the stresses in the continuum elements. They can be seen as a sort of Lagrangian-type contributions. Due to the computation of the contact forces from the continuum elements, some additional degrees-of-freedom are involved in the stiffness matrix parts related to contact. These degrees-of-freedom are associated with nodes not belonging to the contact surfaces.
AB - In this paper a finite element formulation for frictionless contact problems with non-matching meshes in the contact interface is presented. It is based on a non-standard variational formulation due to Nitsche and leads to a matrix formulation in the primary variables. The method modifies the unconstrained functional by adding extra terms and a stabilization which is related to the classical penalty method. These new terms are characterized by the presence of contact forces that are computed from the stresses in the continuum elements. They can be seen as a sort of Lagrangian-type contributions. Due to the computation of the contact forces from the continuum elements, some additional degrees-of-freedom are involved in the stiffness matrix parts related to contact. These degrees-of-freedom are associated with nodes not belonging to the contact surfaces.
KW - Contact mechanics
KW - Finite element discretization
KW - Lagrangian multipliers
KW - Nitsche method
KW - Penalty method
UR - http://www.scopus.com/inward/record.url?scp=36749094499&partnerID=8YFLogxK
U2 - 10.1007/s00466-007-0196-4
DO - 10.1007/s00466-007-0196-4
M3 - Article
AN - SCOPUS:36749094499
VL - 41
SP - 407
EP - 420
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 3
ER -