The first author would like to acknowledge grants from the National Natural Science Foundation of China (No. 52078152 and No. 12002095), General Program of Guangzhou Science and Technology Plan (No. 202102021113), Guangzhou Government-University Union Fund (No. 202201020532), and&#160;Guangzhou Municipal Science and Technology Project (Grant No. 202102020606).

1. Creating the surface in the CAD software
<ol>
	<li>Open the CAD software (see Table of Materials), left-click on File, left-click on New, and select Part.</li>
	<li>In Part1, right-click on Top, and select Show.</li>
	<li>Create a new plane: Press Ctrl, and left-click to select the Top plane and drag it up. Enter 30 mm as the <stron...

The quasi-static compression performance of tapered tubes was studied by finite element analysis. Two new types of corrugated tapered tubes with variable thicknesses were designed, and their quasi-static compression performance was investigated. In quasi-static compression simulations, some important steps and settings need to be verified.
The material parameters are the basic requirements for the finite element calculation (step 2.2.1 of the protocol). In this study, the material parameters w...

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 corrugations1,2,3. 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 fluctuations4,5. 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 wavelength6,7 and amplitude8, using filling foam9,10, 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 tubes13,14,15,16. The existence of lateral corrugations greatly improves the energy absorption performance of the tube17,18,19. 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.&#160;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 tubes23,24,25, polygonal tapered tubes26,27, axial corrugated tapered tubes28,29,30, and tapered tubes with elliptical cross sections31. However, there are few studies on lateral corrugated tubes. Typical thickness gradient structures include square tubes32,33, circular tubes34,35, tapered tubes36, multicellular tubes37,38, 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.&#160;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).&#160;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&#160;1C, and the thickness variation is defined by introducing a variation: factor k. In Figure&#160;1C, th/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.

<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>ABAQUS</td>
			<td>Dassault SIMULIA</td>
			<td>Finite element software</td>
			<td></td>
		</tr>
		<tr>
			<td>CT</td>
			<td>Botong 3D printing</td>
			<td>Conical tube for experiment</td>
			<td></td>
		</tr>
		<tr>
			<td>SOLIDWORKS</td>
			<td>Dassault Systemes</td>
			<td>CAD software</td>
			<td></td>
		</tr>
		<tr>
			<td>Universal testing machine</td>
			<td>SUNS</td>
			<td>UTM5205, 200kN</td>
			<td></td>
		</tr>
	</tbody>
</table>

finite element modeling for the simulation of the quasi-static compression of corrugated tapered tubes

In this study, the quasi-static compression performance of tapered tubes was investigated using finite element simulations. Previous studies have shown that a thickness gradient can reduce the initial peak force and that lateral corrugation can increase the energy absorption performance. Therefore, two kinds of lateral corrugated tapered tubes with variable thicknesses were designed, and their deformation patterns, load displacement curves, and energy absorption performance were analyzed. The results showed that when the thickness variation factor (k) was 0.9, 1.2, and 1.5, the deformation mode of the single corrugated tapered tube (ST) changed from transverse expansion and contraction to axial progressive folding. In addition, the thickness gradient design improved the energy absorption performance of the ST. The energy absorption (EA) and specific energy absorption (SEA) of the model with k = 1.5 increased by 53.6% and 52.4%, respectively, compared with the ST model with k = 0. The EA and SEA of the double corrugated tapered tube (DT) increased by 373% and 95.7%, respectively, compared with the conical tube. The increase in the k value resulted in a significant decrease in the peak crushing force of the tubes and an increase in the crushing force efficiency.

Several commonly used indicators are used to determine the crashworthiness of structures, including the total energy absorption (EA), specific energy absorption (SEA), peak crushing force (PCF), mean crushing force (MCF), and crushing force efficiency (CFE)42.
The total energy absorption (EA)43 can be expressed as follows:
<img alt="Equation 1" src="/files/ftp_upload/64708/64708eq01.jpg" style="margin: auto;" />&#160; ...

Read this Scientific Article Protocol about Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes at JoVE.com

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

This protocol describes the study of the quasi-static compression performance of corrugated tapered tubes using finite element simulations. The influence of the thickness gradient on the compression performance was investigated. The results show that proper thickness gradient design can change the deformation mode and significantly improve the energy absorption performance of the tubes.

In this study, the quasi-static compression performance of tapered tubes was investigated using finite element simulations. Previous studies have shown ...