Details
| Original language | English |
|---|---|
| Pages (from-to) | 4299-4322 |
| Number of pages | 24 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 193 |
| Issue number | 39-41 |
| Early online date | 17 Jun 2004 |
| Publication status | Published - 1 Oct 2004 |
Abstract
Numerical methods for the analysis of rolling contact problems are of high importance for the optimization of the components, car tires for example. Today, finite element methods for the computation of stationary rolling contact have been developed for industrial use. However, from a review of the scientific literature it has been concluded that the theoretical foundations of the relative kinematic description, i.e. an arbitrary Lagrangian Eulerian (ALE) formulation, seems to be not well understood in detail. This presentation is aimed to close this gap. Starting from the basic kinematic description of the ALE-formulation of rolling the weak form of the equations of motion are developed. By this careful analysis an additional flux contribution is derived which has not been recognized in the scientific literature so far. The contact problem is described for the treatment of two deformable bodies in rolling contact within the framework of well established methods for the numerical treatment of contact in the Lagrangian picture in general. Essential differences between the Lagrangian description and the ALE-description of rolling are shown up and discussed in detail. For a comprehensive presentation the finite element discretization is restricted to the case of a deformable wheel rolling on a rigid plane surface. However, the sketched algorithmic approach is valid in general. The efficiency of the numerical algorithms developed so far are discussed by the analysis of a simple three-dimensional example. Critical remarks and an outlook to further research in this field concludes this presentation.
Keywords
- Arbitrary Lagrangian Eulerian, Finite element, Large deformation theory, Rolling contact
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- General Physics and Astronomy
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 193, No. 39-41, 01.10.2004, p. 4299-4322.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The ALE-formulation of bodies in rolling contact Theoretical foundations and finite element approach
AU - Nackenhorst, U.
PY - 2004/10/1
Y1 - 2004/10/1
N2 - Numerical methods for the analysis of rolling contact problems are of high importance for the optimization of the components, car tires for example. Today, finite element methods for the computation of stationary rolling contact have been developed for industrial use. However, from a review of the scientific literature it has been concluded that the theoretical foundations of the relative kinematic description, i.e. an arbitrary Lagrangian Eulerian (ALE) formulation, seems to be not well understood in detail. This presentation is aimed to close this gap. Starting from the basic kinematic description of the ALE-formulation of rolling the weak form of the equations of motion are developed. By this careful analysis an additional flux contribution is derived which has not been recognized in the scientific literature so far. The contact problem is described for the treatment of two deformable bodies in rolling contact within the framework of well established methods for the numerical treatment of contact in the Lagrangian picture in general. Essential differences between the Lagrangian description and the ALE-description of rolling are shown up and discussed in detail. For a comprehensive presentation the finite element discretization is restricted to the case of a deformable wheel rolling on a rigid plane surface. However, the sketched algorithmic approach is valid in general. The efficiency of the numerical algorithms developed so far are discussed by the analysis of a simple three-dimensional example. Critical remarks and an outlook to further research in this field concludes this presentation.
AB - Numerical methods for the analysis of rolling contact problems are of high importance for the optimization of the components, car tires for example. Today, finite element methods for the computation of stationary rolling contact have been developed for industrial use. However, from a review of the scientific literature it has been concluded that the theoretical foundations of the relative kinematic description, i.e. an arbitrary Lagrangian Eulerian (ALE) formulation, seems to be not well understood in detail. This presentation is aimed to close this gap. Starting from the basic kinematic description of the ALE-formulation of rolling the weak form of the equations of motion are developed. By this careful analysis an additional flux contribution is derived which has not been recognized in the scientific literature so far. The contact problem is described for the treatment of two deformable bodies in rolling contact within the framework of well established methods for the numerical treatment of contact in the Lagrangian picture in general. Essential differences between the Lagrangian description and the ALE-description of rolling are shown up and discussed in detail. For a comprehensive presentation the finite element discretization is restricted to the case of a deformable wheel rolling on a rigid plane surface. However, the sketched algorithmic approach is valid in general. The efficiency of the numerical algorithms developed so far are discussed by the analysis of a simple three-dimensional example. Critical remarks and an outlook to further research in this field concludes this presentation.
KW - Arbitrary Lagrangian Eulerian
KW - Finite element
KW - Large deformation theory
KW - Rolling contact
UR - http://www.scopus.com/inward/record.url?scp=4444285465&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2004.01.033
DO - 10.1016/j.cma.2004.01.033
M3 - Article
AN - SCOPUS:4444285465
VL - 193
SP - 4299
EP - 4322
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
IS - 39-41
ER -