## 1 Introduction  
In industrial fields, there are many application examples of crash energy absorbers [1, 2, 3]. Therefore, it is necessary to develop high-performance crash energy absorbers that can maintain stable crushing deformation for as long as possible. In addition, high-quality processing with a simple method is an important research objective. [PERSON] et al. took a thin-walled structure with various cap sections as the object, carried out a detailed study using drop-weight experiments and finite-element method (FEM) analysis, and introduced basic research results for the influence of section shape and material properties [4, 5]. [PERSON] et al. combined multi-cell and multi-corner configurations to enhance the crashworthiness of a thin-walled tube, but previous studies demonstrated that the initial peak load of the crushing reaction force could be further increased [6, 7]. Axial loading has been performed with almost all types of conventional pipe, including round pipes [8, 9], triangle pipes [10, 11], square pipes [12, 13], pentagons [14], hexagonal pipes [15, 16], and octagonal tubes [17, 18]. To improve the phenomenon of transverse bending in the crushing deformation process, [PERSON] et al. proposed a crash absorber with a long compression distance. By introducing grooving in the abdomen and bulging nodes, deformation in the concertina mode was achieved; however, this design could not overcome the defect of an excessive initial peak load during the crashing process [19, 20]. [PERSON] et al., therefore, explored the use of a reversed-spiral origami structure along the direction of the perimeter to obtain characteristics of long-lasting crushing deformation. The initial peak crushing force was eased [21; 22], but the mean crashing force was lower and the energy absorption declined. From these points, it is evident that the de-formation mode can be effectively controlled if an origami structure is applied to a crash absorber. Further studies showed that the performance of a crash absorber can be improved by inserting various patterns along the sidewall [23; 24; 25]. [PERSON] et al. investigated the crash characteristics of a half-cut-type side-member structure, using an optimal design method to improve the energy-absorption ability [26]. These research works adopted cylindrical thin-walled structures, using origami engineering as a front side part, and developed an optimization system for a cylindrical thin-walled structure using origami engineering to improve crashing performance. [27; 28]. Although an origami crash absorber is reasonable, and its energy-absorption characteristics have proved better than those of traditional structures, manufacturing problems persist because of its complex sectional shape. Its shape and characteristics are close to those of a cylinder, so manufacturing inspired by hydroforming has been used. [PERSON] et al. conducted an optimization analysis to improve the formed thickness and avoid fractures [29]. [PERSON] et al. designed and studied a reverse torsion-type crash energy-absorption structure, obtained by an inexpensive partially heated torsion manufacturing method [30; 31]. In summary, origami crash absorbers have great potential to reduce the initial peak force and improve deformation stability and, thus, have been attracting increasing attention. The purpose of this research was to improve the stability of the energy absorption of a thin-walled tube structure and provide some insights for the designer of a thin-walled structure that requires local expansion, and mainly includes the following three aspects: (1) According to the variation law of the ideal energy absorption curve, we designed a cylindrical crash absorber with discontinuous protrusions (CAP). The protrusions can reduce the initial peak force effectively, and the PWS structure formed in the later stage can improve the phenomenon of attenuation. (2) We proposed a new processing method, the successive partial rubber-bulging method, and used this method for cap processing.