Numerical modeling of heat conduction in bodies with cracks

All structural materials contain certain microdefects. Various elements of aircraft and spacecraft made from these materials are subjected to high mechanical loads and thermal effects during operation, which, in turn, can lead to the evolution of defects and total fracture of individual parts of the mechanism. Therefore, a quantitative and qualitative estimation of the stress and temperature fields in different bodies with complex configuration of external loading and temperature disturbances is needed. This paper presents a technique for numerical modeling of the temperature field in a medium weakened by a large system of partially heat penetrable cracks, including the possibility of considering it as an infinite periodic system. The method is based on a numerical algorithm, which uses the expansion of the solution into a finite series. Every term of this series is a certain analytical solution of the heat conduction theory obtained by the authors. To verify the method, the numerical results were compared with the well-known analytical solutions both for a configuration with finite number of cracks and for the periodic system. Also the heat flux intensity factors for a doubly periodic system were determined.