NUMERICAL-SOLUTIONS TO THE PROBLEM OF THERMOELASTIC CONTACT OF 2 RODS

We present numerical simulations of a model for quasistatic contact of two rods. The problem consists of determining the temperature and dis placement fields m two collinear rods each held fixed at one end and f ree to come in contact at the other. The assumption of a quasistatic p rocess leads to a decoupling of the displacement from the temperature. The problem can be reduced to considering a coupled system of two non linear parabolic equations for the temperature, with nonlocal terms. T he thermal interaction between the contacting ends is modeled by a coe fficient of heat exchange that depends on the gap between the rods whe n there is no contact and on the contact stress when there is contact. Using the Crank-Nicolson scheme and iterations we show that the model is capable of rather interesting behavior. By appropriate choices of the initial conditions, we obtain solutions with periods of contact an d loss of contact. When the boundary temperature is periodic the solut ion settles very quickly into a periodic pattern of contact and separa tion. The stability of steady-states is investigated in the case when there are three steady-state solutions. Finally, we compare the soluti ons of this model with those of the uncoupled model, that is usually e mployed in applications.