Finite Element Analysis of Thermoelastic Contact Stability

When heat is conducted across an interface between two dissimilar materials, theimoelastic distortion affects the contact pressure distribution. The existence of a pressure-sensitive thermal contact resistance at the interface can cause such systems to be unstable in the steady-state. Stability analysis for thermoelastic contact has been conducted by linear perturbation methods for one-dimensional and simple two-dimensional geometries, but analytical solutions become very complicated for finite geometries. A method is therefore proposed in which the finite element method is used to reduce the stability problem to an eigenvalue problem. The linearity of the underlying perturbation problem enables us to conclude that solutions can be obtained in separated-variable form with exponential variation in time. This factor can therefore be removed from the governing equations and the finite element method is used to obtain a time-independent set of homogeneous equations in which the exponential growth rate appears as a linear parameter. We therefore obtain a linear eigenvalue problem and stability of the system requires that all the resulting eigenvalues should have negative real part. The method is discussed in application to the simple one-dimensional system of two contacting rods. The results show good agreement with previous analytical investigations and give additional information about the migration of eigenvalues in the complex plane as the steady-state heat flux is varied.