On stress and deformation accumulation of continuously welded rails under cyclic thermal loading in high-speed railways

•Friction behavior between CWR and substructures is simulated via an improved longitudinal resistance model.•A quasi-dynamic method (QDM) is proposed by extending an explicit integration algorithm from the dynamics field to statics.•Equilibrium equations of CWR in different regions under cyclic thermal loading are formulated and solved using the QDM.•Stress and deformation accumulation of CWR are reproduced theoretically for the first time.