# Finite element implementation of an eigenfunction solution for the contact pressure variation due to wear

Yuwei Liu, Yong Hoon Jang, J. R. Barber

Research output: Contribution to journalArticle

3 Citations (Scopus)

### Abstract

The classical eigenfunction method for the solution of contact problems involving wear is formulated in the context of the finite element method. Static reduction is used to reduce the full stiffness matrix to the N contact nodes, after which the assumption of a separated variable solution leads to a linear eigenvalue problem with N eigenvalues and eigenfunctions. A general solution to the transient problem can then be written as an eigenfunction series, with the unknown coefficients being determined from the initial conditions.

Original language English 134-138 5 Wear 309 1-2 https://doi.org/10.1016/j.wear.2013.11.004 Published - 2014 Jan 15

### Fingerprint

Eigenvalues and eigenfunctions
Contacts (fluid mechanics)
eigenvectors
Wear of materials
eigenvalues
stiffness matrix
Stiffness matrix
finite element method
Finite element method
coefficients

### All Science Journal Classification (ASJC) codes

• Condensed Matter Physics
• Mechanics of Materials
• Surfaces and Interfaces
• Surfaces, Coatings and Films
• Materials Chemistry

### Cite this

@article{db176434150b46c4a4ca05c5f988ee63,
title = "Finite element implementation of an eigenfunction solution for the contact pressure variation due to wear",
abstract = "The classical eigenfunction method for the solution of contact problems involving wear is formulated in the context of the finite element method. Static reduction is used to reduce the full stiffness matrix to the N contact nodes, after which the assumption of a separated variable solution leads to a linear eigenvalue problem with N eigenvalues and eigenfunctions. A general solution to the transient problem can then be written as an eigenfunction series, with the unknown coefficients being determined from the initial conditions.",
author = "Yuwei Liu and {Hoon Jang}, Yong and Barber, {J. R.}",
year = "2014",
month = "1",
day = "15",
doi = "10.1016/j.wear.2013.11.004",
language = "English",
volume = "309",
pages = "134--138",
journal = "Wear",
issn = "0043-1648",
publisher = "Elsevier BV",
number = "1-2",

}

In: Wear, Vol. 309, No. 1-2, 15.01.2014, p. 134-138.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Finite element implementation of an eigenfunction solution for the contact pressure variation due to wear

AU - Liu, Yuwei

AU - Hoon Jang, Yong

AU - Barber, J. R.

PY - 2014/1/15

Y1 - 2014/1/15

N2 - The classical eigenfunction method for the solution of contact problems involving wear is formulated in the context of the finite element method. Static reduction is used to reduce the full stiffness matrix to the N contact nodes, after which the assumption of a separated variable solution leads to a linear eigenvalue problem with N eigenvalues and eigenfunctions. A general solution to the transient problem can then be written as an eigenfunction series, with the unknown coefficients being determined from the initial conditions.

AB - The classical eigenfunction method for the solution of contact problems involving wear is formulated in the context of the finite element method. Static reduction is used to reduce the full stiffness matrix to the N contact nodes, after which the assumption of a separated variable solution leads to a linear eigenvalue problem with N eigenvalues and eigenfunctions. A general solution to the transient problem can then be written as an eigenfunction series, with the unknown coefficients being determined from the initial conditions.

UR - http://www.scopus.com/inward/record.url?scp=84939786633&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84939786633&partnerID=8YFLogxK

U2 - 10.1016/j.wear.2013.11.004

DO - 10.1016/j.wear.2013.11.004

M3 - Article

AN - SCOPUS:84939786633

VL - 309

SP - 134

EP - 138

JO - Wear

JF - Wear

SN - 0043-1648

IS - 1-2

ER -