## 1 Introduction  
The layered cylindrical vessel has wide engineering applications [1; 2; 3]. It can be divided into several categories depending on the layered vessel type, such as concentric wrapped shell, coil-wound, shrink fit, and spiral wrapped [4; 5]. It is a common problem to crack propagation in the circumferential weld of a layered cylindrical vessel. It is easy for such cracks to cause structural failure when they are subjected to local stress caused by an external load, thermal stress, and residual stress [6; 7; 8; 9]. Therefore, it is necessary to predict residual welding stress and evaluate it effectively [10]. The welding hoop structure is a kind of constriction structure produced by welding shrinkage in the layered cylindrical vessel during layered binding welding. This tightening structure will generate a large circumferential residual tensile stress on the laminate, especially around the weld. This kind of residual stress greatly increases the risk of cracks in the weld joints and reduces the reliability of the welded structure. However, for large weldments, it is complicated to carry out an overall tempering treatment, and a large number of residual stresses are difficult to be eliminated [11; 12]. Therefore, it is very important to study the residual stress and optimize the welding process of the welding hoop structure. Combining the experimental measurement with numerical simulation is the most effective solution to investigate the residual welding stress [13]. In recent years, the finite element method has been proved to be useful and compelling to evaluate the welding temperature field, residual stress field, and the effect of post-weld heat treatment [14; 15; 16; 17; 18; 19; 20; 21]. There is much software that can perform finite element simulation of the welding process, such as SYSWELD, Simufact Welding, ANSYS, ABAQUS, etc. They can all simulate the welding process very well [22; 23; 24]. At the same time, software such as ANSYS can also simulate the multilayer structure very well [25]. In the case of layered pressure vessels, [PERSON] and [PERSON] et al. improved the welding structure of the layered urea reactor and evaluated the modified structure by ANSYS software [26]. Then, they used ABAQUS to predict the residual stress in layer-to-layer joints [27]. [PERSON] and [PERSON] et al. used ABAQUS to simulate the welding temperature and predict residual stress in welding and the heat-affected zone between nozzle and nozzle [28]. [PERSON] and [PERSON] et al. used ABAQUS to study the distribution of residual stress in the weld and heat-affected zone of the delamination joint with the cladding layer [29]. However, their research ignored the characteristics of the hoop structure. According to the actual manufacturing process and structural characteristics of the wrapped pressure vessel, the inner and outer surfaces of the inner cylinder and the laminate cannot be processed into absolutely smooth surfaces, but instead surfaces with a certain roughness. Therefore, during the bandaging process, whether under the action of the bandaging force or when the longitudinal seam of the laminate cools and contracts, there is interlayer friction in the relative movement of the laminate [30]. In many welding residual stress studies, the simplification of the numerical model generally ignored the characteristics of the interlayer friction and the clamping structure, which would inevitably lead to the gap between the simulation results and the actual data. It could not provide the correct theoretical basis for the analysis and prediction of residual welding stress. Therefore, the analysis of the residual stress distribution rule of the welding hoop structure and the influence of the welding process on the residual welding stress is of great significance for the formulation of the correct welding process, the improvement of the reliability of the welding structure, and the extension of the equipment life.