Application of Discontinuous Galerkin Finite Element Method in Thermoelastic Contact Problems

摘要

A discontinuous Galerkin (DG) finite element method is presented in this paper to solve the thermoelastic coupling contact problems caused by thermal contact resistance (TCR). The existence of the temperature and pressure dependent TCR leads to the coupling of the temperature field and stress field in the sequencial coupling algorithm. The whole analysis procedure is made up of two parts, thermal analysis and mechanical analysis. In thermal analysis, the DG finite element method is employed to simulate the temperature jump phenomenon without using interface element, which satisfies the the imperfect thermal contact condition in a straightforward manner. In mechanical analysis, the impenetrability condition is fulfilled through a DG finite element approach with penalty functions. The Picard iteration procedure with a relaxation technique are also adopted to accelerate the rate of the convergence of the iterative procedure and avoid numerical instability. Several numerical examples are given to demonstrate the accuracy and the reliability of the present DG finite element method. Numerical examples show that the present method is an attractive approach for solving thermoelastic coupling problems caused by TCR. The methodology is also applied to analyze the thermoelastic coupling behaviour of two concentric cylinders with imperfect contact, and the effects of initial radial clearance on structural safety is also investigated therein.