Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes

Crashworthiness is an essential issue for lightweight automobiles, and thin-walled structures are widely used to improve crashworthiness. Typical thin-walled structures, such as round tubes, have good energy absorption capacity but usually have large peak forces and load fluctuations during the crushing process. This problem can be solved by introducing axial corrugations^1,2,3. The presence of corrugations allows the tube to plastically deform and fold according to a predesigned corrugation pattern, which can reduce the peak force and load fluctuations^4,5. However, this stable and controlled deformation pattern has a drawback: the energy absorption performance decreases. To improve the energy absorption of axial corrugated tubes, researchers have tried many methods, such as using a functional gradient design in the wavelength^6,7 and amplitude⁸, using filling foam^9,10, forming multichamber and multiwall structures¹¹, and forming combined tubes¹².

In addition, researchers have designed lateral corrugated tubes by introducing corrugations into the cross-section of circular tubes^13,14,15,16. The existence of lateral corrugations greatly improves the energy absorption performance of the tube^17,18,19. Eyvazian et al.²⁰ compared the crashworthiness of lateral corrugated tubes and ordinary circular tubes and showed that lateral corrugated tubes had a better energy absorption capacity. One reason for this observation is that the lateral corrugation strengthens the tube wall, which makes it more resistant to plastic folding. In addition, the corrugated wall of the plastic folding part flattens, and this flattening also absorbs energy. However, the high initial peak force is a disadvantage of this type of tube, and this high initial force may seriously affect the safety of the passengers being transported.

Functionally graded structures have a natural advantage in reducing the peak force. Common functionally graded thin-walled tubes are usually formed by changing the geometric parameters (e.g., the diameter and wall thickness)²¹. The most prevalent structures for which the diameter is changed are tapered tubes, including circular tapered tubes²², square tapered tubes^23,24,25, polygonal tapered tubes^26,27, axial corrugated tapered tubes^28,29,30, and tapered tubes with elliptical cross sections³¹. However, there are few studies on lateral corrugated tubes. Typical thickness gradient structures include square tubes^32,33, circular tubes^34,35, tapered tubes³⁶, multicellular tubes^37,38, and lattice structures³⁹. Deng et al.⁴⁰ reduced the initial peak force of lateral corrugated tubes with a thickness gradient design by 44.53%, but there have been no studies on lateral corrugated tapered tubes.

Although experiments are the most accurate and direct method to evaluate the crashworthiness of structures, they also require considerable money and resources. In addition, some important data, such as the stress-strain clouds of the structure and the energy values of different forms, are difficult to obtain in experiments¹⁸. Finite element analysis is a method to simulate the real load conditions by using mathematical approximation. This was first applied in the aerospace field, mainly for solving linear structural problems. Later, it was gradually applied to solve nonlinear problems in many fields, such as civil engineering, mechanical engineering, and material processing³⁴. In addition, with finite element software development, simulation results have become increasingly close to those of the corresponding experiments. Therefore, simulation using finite element analysis is used to investigate the crashworthiness of the structures. In this study, finite element analysis of the quasi-static compression performance of corrugated tapered tubes was conducted. The energy absorption of two types of lateral corrugated tapered tubes (i.e., the single corrugated tapered tube [ST] and the double corrugated tapered tube [DT]) with variable thicknesses was studied numerically. The results were compared with those obtained for a conventional conical tube (CT). The dimensions of the three types of thin-walled tubes are shown in Figure 1A. The geometric parameters of the ST are shown in Figure 1B, and the DT is built by crossing two STs. The thickness gradient is designed as shown in Figure 1C, and the thickness variation is defined by introducing a variation: factor k. In Figure 1C, t_h/2 = 0.44 mm, and k is set to 0, 0.3, 0.6, 0.9, 1.2, and 1.5. The results show that the peak crushing force decreases and the crushing force efficiency increases with increases in k.