FINITE ELEMENT ANALYSIS OF THE STABILITY OF STATIC THERMOELASTIC CONTACT

Abstract

The steady-state conduction of heat across an interface between two contacting bodies can become unstable as a result of the interaction between thermoelastic distortion and a pressure-dependent thermal contact resistance. Analytical solutions for the stability boundary have been obtained for simple systems using perturbation methods but become prohibitively complex for finite geometries. This paper presents a finite element formulation of the perturbation method in which the linearity of the governing equations is exploited to obtain separated-variable solutions for the perturbation with exponential variation in time. The problem is thus reduced to a linear eigenvalue problem with the exponential growth rate appearing as the eigenvalue. Stability of the system requires that all eigenvalues have negative real part. The method is tested against an analytical solution of the two-dimensional problem of a strip in contact with a rigid wall. Excellent results are obtained for the stability boundary even with a relatively coarse discretization.

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Notes on contributors

J. R. Barber

Address correspondence to James R. Barber, Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109-2125.