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

• Published in: Wear Vol. 309; no. 1-2; pp. 134 - 138
• Main Authors: Liu, Yuwei, Hoon Jang, Yong, Barber, J.R.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15.01.2014; Elsevier
• Subjects: Contact; Contact problems; Eigenfunction series; Eigenfunctions; Eigenvalues; Exact sciences and technology; Finite element method; Fundamental areas of phenomenology (including applications); Initial conditions; Mathematical analysis; Mechanical contact (friction...); Physics; Solid mechanics; Stiffness matrix; Structural and continuum mechanics; Wear; Contact problems; Wear; Eigenfunction series; Finite element method; Initial condition; Eigenfunction; Eigenvalue problem; Stiffness
• ISSN: 0043-1648; 1873-2577
• DOI: 10.1016/j.wear.2013.11.004

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. •The redistribution of contact pressure due to wear is determined from a linear eigenvalue problem.•The complete time-evolution of the contact pressure can then be expressed as an eigenfunction series.•The method is much more computationally efficient than a direct finite element solution of the wear problem.•The method can be applied to problems where sliding speed and/or applied loads vary in time.