ASYMPTOTIC APPROXIMATIONS TO ONE-DIMENSIONAL PROBLEMS OF QUASI-STATICTHERMOELASTIC CONTACT

We compare solutions to coupled and uncoupled versions of three one-di mensional problems of quasistatic thermoelastic contact which model, r espectively, the mechanical behaviour of one rod, of two rods and of a cylinder. We show that if a is a nondimensional parameter which is pr oportional to the coefficient of thermal expansion, then the differenc e between the temperatures is of order O(a) when the heat exchange is modeled by a coefficient k that depends on the gap size and the contac t stress. The difference is O(a2) when k is constant. The differences in the corresponding displacements are O(a2) and O(a3), respectively. These results lend support to the usual practice in thermoelastic prob lems of neglecting the term corresponding to the work of internal forc es in the heat equation.