Details
| Original language | English |
|---|---|
| Pages (from-to) | 88-119 |
| Number of pages | 32 |
| Journal | Engineering Computations (Swansea, Wales) |
| Volume | 16 |
| Issue number | 1 |
| Publication status | Published - 1 Feb 1999 |
Abstract
The numerical solution of contact problems via the penalty method yields approximate satisfaction of contact contraints. The solution can be improved using augmentation schemes. However their efficiency is strongly dependent on the value of the penalty parameter and usually results in a poor rate of convergence to the exact solution. In this paper we propose a new method to perform the augmentations. It is based on estimated values of the augmented Lagrangians. At each augmentation the converged state is used to extract some data. Such information updates a database used for the Lagrangian estimation. The prediction is primarily based on the evolution of the constraint violation with respect to the evolution of the contact forces. The proposed method is characterised by a noticeable efficiency in detecting nearly exact contact forces, and by superlinear convergence for the subsequent minimisation of the residual of constraints. Remarkably, the method is relatively insensitive to the penalty parameter. This allows a solution which fulfils the constraints very rapidly, even when using penalty values close to zero.
Keywords
- Acceleration, Contact, Finite element method
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Engineering(all)
- Computer Science(all)
- Computer Science Applications
- Computer Science(all)
- Computational Theory and Mathematics
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In: Engineering Computations (Swansea, Wales), Vol. 16, No. 1, 01.02.1999, p. 88-119.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A superlinear convergent augmented Lagrangian procedure for contact problems
AU - Zavarise, G.
AU - Wriggers, P.
PY - 1999/2/1
Y1 - 1999/2/1
N2 - The numerical solution of contact problems via the penalty method yields approximate satisfaction of contact contraints. The solution can be improved using augmentation schemes. However their efficiency is strongly dependent on the value of the penalty parameter and usually results in a poor rate of convergence to the exact solution. In this paper we propose a new method to perform the augmentations. It is based on estimated values of the augmented Lagrangians. At each augmentation the converged state is used to extract some data. Such information updates a database used for the Lagrangian estimation. The prediction is primarily based on the evolution of the constraint violation with respect to the evolution of the contact forces. The proposed method is characterised by a noticeable efficiency in detecting nearly exact contact forces, and by superlinear convergence for the subsequent minimisation of the residual of constraints. Remarkably, the method is relatively insensitive to the penalty parameter. This allows a solution which fulfils the constraints very rapidly, even when using penalty values close to zero.
AB - The numerical solution of contact problems via the penalty method yields approximate satisfaction of contact contraints. The solution can be improved using augmentation schemes. However their efficiency is strongly dependent on the value of the penalty parameter and usually results in a poor rate of convergence to the exact solution. In this paper we propose a new method to perform the augmentations. It is based on estimated values of the augmented Lagrangians. At each augmentation the converged state is used to extract some data. Such information updates a database used for the Lagrangian estimation. The prediction is primarily based on the evolution of the constraint violation with respect to the evolution of the contact forces. The proposed method is characterised by a noticeable efficiency in detecting nearly exact contact forces, and by superlinear convergence for the subsequent minimisation of the residual of constraints. Remarkably, the method is relatively insensitive to the penalty parameter. This allows a solution which fulfils the constraints very rapidly, even when using penalty values close to zero.
KW - Acceleration
KW - Contact
KW - Finite element method
UR - http://www.scopus.com/inward/record.url?scp=0032666261&partnerID=8YFLogxK
U2 - 10.1108/02644409910251292
DO - 10.1108/02644409910251292
M3 - Article
AN - SCOPUS:0032666261
VL - 16
SP - 88
EP - 119
JO - Engineering Computations (Swansea, Wales)
JF - Engineering Computations (Swansea, Wales)
SN - 0264-4401
IS - 1
ER -