Thermo-electro-mechanical coupling in beam-to-beam contact

This paper is a further step towards the full analysis of the complex behaviour of contacting beams in the coupled thermo-electro-mechanical field. Now we add to our previous work the coupling with the thermal field. The coupling between electric, mechanical and thermal fields is manifested in: dependence of material parameters on the temperature, frictional heating, heat generation by the electric current flow, dependence of the contact area on the temperature, dependence of thermal and electric fields on the change of the contact area and the contact point position. In the present preliminary analysis we take into account only the last aspect. We also consider the indirect influence of thermal contact on the mechanical field using the thermo-mechanical beam element. The contact constraints are enforced with the penalty method within the finite element technique. It is assumed that the heat flow in the contact area is unlimited which leads to the equalling of temperatures between two contacting bodies. This constraint is also introduced by the penalty method. The set of governing equations including the coupling is solved by the monolithic scheme. The problem is nonlinear, hence the linearized version of equations is derived. The consistent linearization leading to the consistent tangent stiffness matrix and the corresponding residual vector is performed to apply efficiently the Newton-Raphson method and to ensure the quadratic convergence. Some numerical examples are presented to show the efficiency of the suggested approach.