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

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.