Modeling of the thermal stresses in the welded rails of the continuous welded track in the permafrost zone

The article focuses on the numerical methods that are used to solve heat conduction nonlinear problems with the help of the h-matrix to account for the relaxation of thermal stresses in continuously welded rails. A general mathematical model on the basis of the heat conduction nonlinear equation is presented to calculate the thermal field in an infinite unlimited plate. The developed mathematical model can be applied to choose the implementation modes of the continuously welded rails into the optimal thermal mode.