This paper presents a comprehensive numerical investigation into the transient thermo-structural response of axial bellows during start-up and shutdown cycles in long-distance heating pipelines. Using ANSYS-based transient thermal–structural coupling finite element analysis under the pure linear elasticity and constant internal pressure, the spatio-temporal evolution mechanisms of temperature fields, axial deformation, and equivalent stress are systematically analyzed. The results demonstrate the highly synchronized evolution between temperature and deformation fields, with maximum axial deformation and equivalent stress consistently concentrated at the convolution root and transition arcs. Under steady-state high-temperature conditions (130 °C), the maximum equivalent stress reaches 332.78 MPa. However, after complete cooling and unloading, minimal residual deformation (≤0.001 mm) and residual stress (8.86 MPa) are observed, satisfying the pressure vessel shakedown criteria and confirming the inherent self-limiting nature of thermal secondary stresses. A specific decoupling phenomenon is revealed during the high-temperature steady-state holding period, where the deformation stabilizes while the stress undergoes secondary redistribution. The comparative analysis of different temperature change rates indicates that the fast start-up/shutdown (0.55 °C/s) induces severe transient temperature gradients, causing a nearly 50% increase in the maximum equivalent stress compared to the slow start-up/shutdown (0.275 °C/s). This study provides theoretical foundations for the service safety assessment of axial bellows and recommends gradual heating/cooling operation strategies (≤0.3 °C/s) to mitigate structural thermal shock risks.
Wang et al. (Tue,) studied this question.