Finite Element Modeling of Crushing Behaviour of Thin Tubes with ...

13 th International Conference on 

AEROSPACE SCIENCES & AVIATION TECHNOLOGY, 

ASAT- 13, May 26 – 28, 2009, E-Mail: asat@mtc.edu.eg 

Military Technical College, Kobry Elkobbah, Cairo, Egypt 

Tel : +(202) 24025292 – 24036138, Fax: +(202) 22621908 

Finite Element Modeling of Crushing Behaviour 

of Thin Tubes with Various Cross-Sections 

M. M. Younes * 

1/19 

Paper: ASAT-13-ST-34 

Abstract: Typical steel square plates of 300mm side length and 1mm thickness were used to 

simulate six tubes with different cross-sections. These cross-sections were selected symmetric 

from round-shapes as circle and ellipse and polygon-shapes as triangle, square, pentagon and 

hexagon. The effect of varying configurations of tube cross-section shape on the deformation 

response, collapse mode and energy absorption characteristics of tubes under quasi-static 

axial compression have been studied numerically. The commercial finite element package 

ABAQUS/Explicit was used in the present analysis. The axial load-displacement results 

accompanied by the fold formation of various tubes were investigated and compared with 

published experimental work. Variation of the initial peak load and the mean crushing force 

with the tube side breadth and the fold depth were carefully examined. Based on the finite 

element simulation results, empirical formulas for the absorbed energy and the fold depth 

were developed as a function of the side breadth-to-thickness ratio of the tubes. 

Keywords: Finite element; Initial peak load; Mean crushing force; Fold formation; Axial 

loading; Absorbed energy; Tubes 

Introduction 

Numerical methods are now extensively applied in engineering due to the advances in 

computing. Of all the numerical methods, the finite element method is the most popular 

convenient approach, because it is easy to implement for all kinds of boundary and loading 

conditions and it can be used for the analysis of large complex structures. It is worth 

mentioning that experimental measurements are considered a powerful data required to 

approve most of mathematical models. Paik et al. [1] performed a series of experiments on the 

quasi-static crushing of stiffened square tubes and brought forward an empirical formula for 

the mean crushing load. The experimental results showed that the mean crushing load 

changed with the variation of the stiffener directions. Zhang and Suzuki [2] analyzed the 

effects of longitudinal and transverse stiffeners on the quasi-static crushing of stiffened square 

tubes by using the non-linear finite element program LS-DYNA. The obtained numerical data 

was used in prediction the mean crushing load and the equivalent thickness of the stiffened 

tubes. Recent numerical tools have allowed that a range of quasi-static problems can be 

analyzed effectively. Gupta et al. [3] applied the finite element method to simulate the axial 

compression of the tubes of round cross-sections. An axi-symmetric model was used to obtain 

the deformed shapes and the crushing load at different stages of loading. Gupta and Gupta [4] 

have carried out experimental studies of axial compression of thin walled aluminum and mild 

steel tubes of varying diameter to thickness ratios. The effect of annealing and presence of a 

* Egyptian Armed Forces

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hole at mid height of the tube on the energy absorption characteristics and collapse mode 

transitions was examined. Results revealed that a diamond deformation mode was generated 

in all the tube specimens. A great number of studies have been carried out on the axial 

crushing of thin-walled tubes. Wierzbicki and Abramowicz [5] developed a simplified model 

based on rigid plastic assumptions and obtained the mean crushing force for square tubes. 

Abramowicz and Jones [6,7] conducted a series of experiments, and modified the collapse 

models by taking account of strain-rate sensitivity and effective crushing distance. Grzebieta 

[8] proposed a method for determining the load history between a peak and a minimum during 

an oscillation of the load-compression curve of round tubes. Gupta and Velmurugan [9] 

studied experimentally the internal/external folding of round tubes. The folding parameter 

(ratio of the inside to the total fold length) was determined experimentally and employed in a 

proposed analysis. Wierzbicki et al. [10] studied the axi-symmetric mode of deformation of 

round tubes by considering partly internal and partly external folding. It was shown that the 

load compression curve is dependent on the folding parameter, while the mean collapse load 

and the folding length are independent of it. Closed form solutions were obtained for the 

instantaneous and mean crushing force, the effective crush distance and the length of the local 

folding wave. Singace et al. [11-13] gave an analysis of the axi-symmetric and multi-lobe or 

diamond mode of deformation to determine the eccentricity factor and crushing load. It was 

concluded that measured values of the eccentricity factor and the critical folding angles 

obtained for tubes of different materials and geometric ratios are independent of the tubes 

material and geometric ratios. There is a considerable amount of published data on the 

response of composite tubes to axial crushing [14]. Many of these studies utilize circular 

cross-section tubular specimens to determine the energy absorption capability of the material. 

Farley [15] studied the effect of specimen geometry on the energy absorption capability of 

composite materials. He found that, changes in section lay-up that lead to an increase in 

modulus lead to higher crush strengths and energy absorption. Mamalis et al. [16-18] 

analyzed the collapse behavior and deformation mechanism of thin-walled non-circular 

composite tube, thin-walled composite conical shell, and braced elliptical tube. They 

contributed with a valuable data of crashworthiness of composite structures. 

The aims of this study are to obtain numerical data on the crushing of different cross-section 

tubes, and to develop simple empirical expressions for predicting the absorbed energy and the 

fold formation of steel tubes. A series of finite element calculations was carried out on six 

tube models crushed axially in a quasi-static condition by using ABAQUS/Explicit. The 

cross-section shapes of the six tubes were circle, ellipse, triangle, square, pentagon and 

hexagon. Effect of the side breadth and the generated fold depth on the initiated peak load and 

the mean crushing force of different tubes were carefully examined. 

Finite Element Model 

The finite element simulation of the case described herein was carried out using the 

commercial code ABAQUS/Explicit version 6.4. Six tubes with different geometrical crosssections 

were modeled in the present study. All the tube models were developed with same 

lengths and equal cross-section perimeters of 300 mm each. A uniform thickness of 1 mm is 

considered for all the wall tubes. The difference between the whole tubes was only the shape 

of the cross-sections. The latter were selected from uniform geometries like a circle, an 

ellipse, a triangle, a square, a pentagon and a hexagon. Detailed description of the tube crosssections 

is illustrated in Fig. (1). For comparing reasons; the material used in the simulation 

was provided from the actual material properties of steel experimentally measured by Paik et 

al. [1]. The mechanical properties of the steel material were assigned into the ABAQUS input

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file. A list of numerical values of the basic material properties required for the tube models is 

given in Fig. (2). All the tube models used in the present finite element simulation were 

generated by using the element S4R. This element is a three-dimensional doubly curved fournode 

shell element. Each node has three-displacement and three-rotation degrees of freedom. 

Moreover, this element is considered a general-purpose shell element where it allows for large 

strains as load increases. In order to predict the overall response accurately, the mesh of finite 

elements was fine and uniform with equal number of elements along the length of the tube 

and through its circumferential direction. On the other side, all the tube models were crushed 

axially between upper and lower rigid parallel plates. These two parallel plates were 

simulated by using three-dimensional four-node rigid elements R3D4. The tubes were crushed 

by pushing down the upper rigid plate. The latter was fixed in all degrees of freedom except 

the vertical downward displacement where the loading was applied. However, the lower rigid 

plate was stationary by constraining its whole degrees of freedom. All tube models rested free 

on the lower rigid plate however the applied force was attained as a reaction created from the 

pushing of the upper plate. The quasi-static loading condition was achieved by moving the 

upper plate slowly downward over a sufficiently long time. It is noted that the tubes were not 

completely free due to the effect of friction between the tube models and the crushing parallel 

plates. The progressive deformation shape was continuously monitored for each tube and the 

corresponding force-axial displacement curve was depicted. 

Experimental Validation 

The validation of the finite element tube model was made by direct comparison with the 

experimental results and the collapse observations of the square tube US-2 subjected to quasistatic 

axial compression and examined by Paik et al. [1]. The structural geometry of the 

specimen and the properties of the used material are shown in Fig. (2). All other testing 

details used in the experimental works were necessarily simulated in finite element model. 

The progressive collapse of the finite element tube model and the examined specimen at 

various stages of the compression are compared in Fig. (3). Visual examination of the pictures 

showed good agreements between the numerical simulations and the experimental outcomes. 

Comparing the predicted load-displacement behaviour with the experimental results in [1] and 

the obtained calculations in [2] revealed good correlation between curves at the same 

displacement values as shown in Fig. (4). 

Table (1) lists the comparison of results between the previously published work and the 

present finite element analysis. 

Investigation of Crushing Behaviour 

The present numerical simulation provides an opportunity to predict the fold formation of 

various tubes. Figures (5-10) display the collapse mechanisms accompanied by the 

corresponding axial- and energy-displacement curves of different tube models. Folding modes 

were symmetric about the principal axes of all the tubes cross-sections. Moreover, an axisymmetric 

mode was noticed during the deformation of the circular tube. The entire tube 

models initiated folding from the top end in contact with the movable upper plate. However, 

the circular tube began to fold from the bottom end in contact with the fixed lower plate. It is 

worth mentioning that, the folding process of polygonal tubes was initiated by random interior 

and exterior rotating of the upper edges of sidewalls. Tubes of square and hexagonal crosssections 

created symmetric inward and outward folds on each two opposite sidewalls. Folds 

of the triangular tube initiated by curving its upper edges completely inward. However, the

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initial inward folding of the pentagonal tube was appeared in only two non-successive 

sidewalls. After complete constituting of the initial folds, similar sequential folds were 

regularly created and the crushing was propagated along the sidewalls of all polygonal tubes. 

The folds generated in all tube models were in contact and adjoining each other except for 

that ones of the triangular tube. This may be attributed to the acute inner angles between the 

sidewalls which increase the strength of the triangular tube and allow the rigid body 

behaviour to appear early before occurring a complete adjoining of folds. On the other hand, 

the crushing behaviour of the elliptical tube was quite complex and totally different from the 

deformation characteristics of the other tube models. The upper cross-section of the elliptical 

tube was initially stretched in the direction of maximum diameter as shown in Fig. (6). 

Afterwards, the crushing was propagated suddenly allover a region bounded by the upper 

stretched cross-section and another similar one located nearly at the middle height of the tube. 

Progressive compression generated similar crushing characteristics on the rest of the elliptical 

tube model. When the walls of the tubes stopped folding and behaved as a rigid body, the 

number of folds was observed maximum with fourteen folds in the circular tube and 

minimum with three folds in the triangular tube. 

Load- and Energy-Displacement Characteristics 

Figures (5-10) indicate the initiation and end of the typical axial load- and the energydisplacement 

curves of various tube models. The absorbed energy was obtained by integrating 

the area under the axial load-displacement curve until the folding of the walls ended. 

Afterwards, the mean crushing load was calculated by dividing the absorbed energy by the 

total displacement. Maintaining all parameters of the finite element model, a series of the 

load-displacement curves were obtained from different shape tube models. The general loaddisplacement 

characteristics of all tubes can be described by a rapid rise of the force initiated 

due to the elastic compression of the tubes. After that a rapid drop of the force was observed 

when one end of the tube models started folding. A steep rising of the force was again noticed 

after the first folding of walls ended and the second folding of the adjacent walls started 

generation. A drop of the force occurred again when a new folding started, and the force rose 

if the walls came into contact. This response was repeated until the folding ended and the 

models behaved as a rigid body. A uniform response was noted in all tube curves except for 

the elliptical tube, the response was irregular. It is worth mentioning that all the numerical 

results of the energy-displacement relations were nearly linear all over the crushing intervals. 

Comparing the force-displacement curves seen in Figs. (5-10) can help analyze the behaviours 

of different crushing mechanisms. It was clearly seen in Fig. (5) that the higher number of 

local peaks along the force-displacement curve reflected the great number of folds created in 

the circular tube. The difference between the upper and lower bounds of the load values was 

significantly large in the square and triangular tube curves and quite narrow in the hexagonal 

tube curve. For the pentagonal tube, the difference between upper and lower bounds of the 

load values started large then damped gradually with the compression progress until reaching 

a stable load as shown in Fig.(8). On the other side, the general crushing response of the 

elliptical tube was totally different where the values of the load and consequently the 

absorbed energy were pronouncedly high and the load peaks were scattered in a distinct 

manner all over the curve. This may be attributed to the disturbance occurred during the 

folding process of this tube shape. Figure (11) shows that the absorbed energy of the finite 

element tube model decreases with an increase in the tube side breadth-to-thickness ratio up 

to the tube of four sides. Then, the absorbed energy starts increasing at the triangular tube. 

The relationship between the absorbed energy and the side breadth-to-thickness ratio of the 

tubes can be empirically expressed as:

11/19 


E 5.19 1.48cos[(0.05 Sb/ t) 

0.6] 

(1) 

where; 

E = Absorbed energy 

Sb = Side breadth, 

T = Tube thickness 

Initial Peak Load and Mean Crushing Force 

Figure (12) depicts the nonlinear relation between the increasing of the number of sides and 

the decreasing of the side breadth of a polygonal tube of 300mm perimeter. Variations of the 

initial peak load and mean crushing force with different number of sides (3-6) and various 

side breadths (50-100 mm) are shown in Figs. (13,14) for the polygonal tubes. Generally, it 

was observed that the initial peak load highly increased with the increasing of the number of 

sides and greatly decreased with the increasing of the side breadth. Moreover, the initial peak 

loads of the triangular and square tubes had closed magnitudes while values of the initial peak 

loads of the pentagonal and hexagonal tubes were sharply far off. On the other side, the mean 

crushing load was changed in a different manner with the number of sides and the side 

breadth of the tubes. The mean crushing load greatly decreased with the increasing of both the 

number of sides and the side breadth until reaching a minimum value at the square tube. 

Subsequently, the mean crushing load began to increase with the increasing of the number of 

sides and the side breadth of the tubes. It is worth mentioning that the initial peak load and 

mean crushing force of the round (circular and elliptical) tubes were greatly higher than that 

obtained from the polygonal tubes as compared in Table (2). 

The Fold Depth and the Side Breadth of Tubes 

The fold depth was investigated through a longitudinal path of the tube. This path was located 

at the middle of one arbitrary face for all the sided tubes. The fold depth of the sided tubes 

was compared with that obtained from the circular tube overall the tube span as shown in Fig. 

(15). The bottom end of all tubes was located at the origin of the horizontal axis, however the 

inward and/or outward fold profiles were recorded on the vertical axis of Fig. (15). It can be 

noticed that the folds of the circular tube have the lowest depth (approximately 8 mm) and 

bulged mainly outward. The profiles of all the folds are not so different except for the 

pentagonal tube where its fold profile was not symmetric about the middle path. On the other 

side and apart from the triangular tube, the fold depth was seen maximum in the square tube 

and it generally decreased with increasing the number of sides of the polygonal tubes. In other 

words, starting from a polygonal tube with four sides, the initiated fold depth is decreased 

with the decreasing of the tube side breadth as depicted in Fig. (16). The relationship between 

the fold depth and the side breadth-to-thickness ratio of the tubes can be empirically 

expressed as: 

where; 

Fd = Fold depth, 

Sb = Side breadth, 

t = Tube thickness 

Fd 8.302exp[0.021( Sb / t)] 

(2)

12/19 


Figure (16) shows that the results of the fold depth formula coincide with the numerical data. 

This relation is valid for the polygonal tubes with number of sides greater than or equal four 

sides. 

Conclusion 

The non-linear finite element model simulations provide much more detailed information than 

other approaches. These are especially efficient in local folding and internal contact of 

structural elements. In this paper, a study on the quasi-static crushing collapse of multi-sided 

and round tubes was performed using a non-linear finite element program ABAQUS/Explicit. 

Based on the numerical data, simple empirical formulas were developed to predict the 

absorbed energy and the fold depth as a function of the side breadth-to-thickness ratio of the 

tubes. From the present study, the following conclusion can be drawn: 

- All the tube models were crushed in symmetric concertina modes. 

- The greatest number of folds was observed fourteen in the circular cylinder and minimum 

with three folds in the triangular tube. 

- The folds of the cylindrical tube were compact with short depth while the triangular tube 

terminated folding without contact between folds. 

- The initial peak load increases with the increasing of the no. of sides of the tube and 

decreases with the increasing of the side breadth. 

- The greatest energy absorption capacity was obtained by the circular cylinder while the 

square tube absorbed minimum energy. 

- The mean crushing load recorded lowest value in case of the square tube however the 

highest magnitude was noticed in the triangular tube. 

References 

[1] J. K. Paik, J. Y. Chung, and M. S. Chun, “On quasi-static crushing of a stiffened square 

tube”, J. Ship Res., Vol. 40, No. 3, pp. 258–267, 1996. 

[2] A. Zhang, and K. Suzuki, “A study on the effect of stiffeners on quasi-static crushing of 

stiffened square tube with non-linear finite element method”, Int. J. of Imp. Eng., Vol. 

34, pp. 544–555, 2007. 

[3] Gupta N. K., Sekhon G. S. and Gupta P. K., “A Study of Formation in Axi-symmetric 

Axial Collapse of Round Tubes”, Int. J. Impact. Eng., Vol. 27, pp. 87-117, 2002. 

[4] Gupta N. K. and Gupta S. K., “Effect of Annealing, Size and Cutouts on Axial Collapse 

Behaviour of Circular Tubes”, Int. J. of Mech. Sci., Vol. 35, pp. 519-613, 1993. 

[5] Wierzbicki T. and Abramowicz W., “On the Crushing Mechanics of Thin-Walled 

Structures”, J. Appl. Mech., Vol. 50, No. 4a, pp. 727–34, 1983. 

[6] Abramowicz W. and Jones N., “Dynamic Axial Crushing of Square Tubes”, Int. J. 

Impact Eng., Vol. 2, No. 2, pp. 179–208, 1984. 

[7] Abramowicz W. and Jones N., “Dynamic Progressive Buckling of Circular and Square 

Tubes”, Int. J. Impact Eng., Vol. 4, No. 4, pp. 243–70, 1986. 

[8] Grzebeita R. H., “An Alternate Method for Determining the Behaviour of Round Stocky 

Tubes Subjected to an Axial Crush Load”, Thin Wall Struct., Vol., 9, pp. 61-89, 1990. 

[9] Gupta N. K., Velmurugan R., “Consideration of Internal Folding and non Symmetric 

Fold Formation in Axi-symmetric Axial Collapse of Round Tubes”, Int. J. Solids 

Struct., Vol. 34, No. 20, pp. 2611-40, 1997.

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[10] Wierzbicki T., Bhat S. U., Abramowicz W. and Brodikin D., “A Two Folding Elements 

Model of Progressive Crushing of Tubes”, Int. J. Solids Struct., Vol. 29, No. 24, pp. 

3269-88, 1992. 

[11] Singace A. A. and EI-Sobky H., “Further Experimental Investigation on the Eccentricity 

Factor in the Progressive Crushing of Tubes”, Int. J. Solids Struct., Vol. 33, No. 24, pp. 

3517-38, 1996. 

[12] Singace A. A, EI-Sobky H. and Reddy T. Y., “On the Eccentricity Factor in the 

Progressive Crushing of Tubes”, Int. J. Solids Struct., Vol. 32, No. 24, pp. 3589-602, 

1995. 

[13] Singace A. A., “Axial Crushing Analysis of Tubes Deforming in the Multi-Lobe 

Mode”, Int. J. Mech. Sci., Vol. 41, pp. 865-90, 1999. 

[14] Hull D., “A Unified Approach to Progressive Crushing of Fiber-Reinforced Composite 

Tubes”, Comp. Sci. Technol., Vol. 40, pp. 377-421, 1991. 

[15] Farley G. L., “Effects of Specimen Geometry on the Energy Absorption Capability of 

Composite Materials”, J. Comp. Mater., Vol. 20, pp. 390-400, 1986. 

[16] Mamalis A. G., Manolakos D. E., Demosthenous G. A. and Ioannidis M. B., “The 

Deformation Mechanism of Thin-Walled Non-circular Composite Tubes Subjected to 

Bending”, Comp. Struct., Vol. 30, pp. 131-146, 1995. 

[17] Mamalis A. G., Manolakos D. E., Demosthenous G. A. and Ioannidis M. B., “Analysis 

of Failure Mechanisms Observed in Axial Collapse of Thin-Walled Circular Fiberglass 

Composite Tubes”, Thin-Walled Struct., Vol. 24, pp. 335-352, 1996. 

[18] Mamalis A. G., Manolakos D. E., Demosthenous G. A. and Ioannidis M. B., 

“Analytical Modeling of the Static and Dynamic Axial Collapse of Thin-Walled 

Fiberglass Composite Conical Shells”, Int. J. Impact Eng., Vol. 19, No. 5-6, pp. 477- 

492, 1997. 

75 mm 100 mm 95.49 mm 

60 mm 50 100 mm 

Fig. (1) Different shapes of uniform cross-sections used 

in the F.E. analysis of a 300 mm perimeter tube. 

50 mm

Dimensions of 

the test specimen 

L = 450 mm 

b = 100 mm 

t = 2.8 mm 

L 

b 

t 

Fig. (2) Configuration of the test specimen US-2 in Ref. [1]. 

Fig. (3) Gradual crushing of the square tube US-2 [1] using the 

present ABAQUS solution. 

Fig. (4) Comparison between the crushing curves of the 

square tube US-2 [1]. 

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Material properties required for 

finite element model 

Density = 7860 kg/m 3 

Young’s modulus = 205.8 GPa 

Poisson’s ratio = 0.3 

Yield strength = 310 MPa 

Ultimate stress = 363.3 MPa 

Fracture strain = 0.354 

1 

2

Load(kN) 

15/19 


Fig. (5) Gradual collapse and crushing results of the cylindrical tube. 

Load (kN) 

Fig. (6) Gradual collapse and crushing results of the elliptical tube. 

Load (kN) 

Fig. (7) Gradual collapse and crushing results of the hexagonal tube. 

100 

80 

60 

40 

20 

0 

450 

360 

270 

180 

90 

0 

60 

48 

36 

24 

12 

0 

Load 

Energy 

0 50 100 150 200 250 

Displacement (mm) 

Load 

0 50 100 150 200 250 


Load 

Energy 

Energy 

0 50 100 150 200 250 


7 

5.6 

4.2 

2.8 

1.4 

0 

45 

36 

27 

18 

9 

0 

5 

4 

3 

2 

1 

0 

Energy (kJ) 

Energy (kJ) 

Energy (kJ)

Load (kN) 

45 

36 

27 

18 

9 

0 


0 50 100 150 200 250 


Fig. (8) Gradual collapse and crushing results of the pentagonal tube. 

Load (kN) 

Fig. (9) Gradual collapse and crushing results of the square tube. 

Load (kN) 

40 

32 

24 

16 

40 

32 

24 

16 

8 

0 

8 

0 

Energy 

Load 

0 50 100 150 200 250 


Load 

Energy 

Energy 

Load 

0 50 100 150 200 250 


Fig. (10) Gradual collapse and crushing results of the triangular tube. 

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4 

0 

4.5 

3.6 

2.7 

1.8 

0.9 

0 

3.2 

2.4 

1.6 

0.8 

5 

4 

3 

2 

1 

0 

Energy (kJ) 

Energy (kJ) 

Energy (kJ)

Fig. (11) Variation of the absorbed energy 

of polygonal tubes with the side 

breadth-to-thickness ratio. 

Initial peak load 

Mean crushing load 

55 

50 

45 

40 

35 

30 

2 3 4 5 6 7 

No. of sides 

27 

24 

21 

18 

15 

Side breadth 

17/19 


0 

0 20 40 60 


Fig. (13) Variation of the initial peak load with the number of sides 

(left) and with the side breadth (right) of the polygonal tubes. 

12 

2 3 4 5 6 7 


120 

100 

80 

60 

40 

20 

Fig. (12) Variation of the side breadth of 

a polygonal tube of 300mm perimeter with 

the number of sides. 

Initial peak load 

Mean crushing Load 

55 

50 

45 

40 

35 

30 

40 60 80 100 

side breadth (mm) 

27 

24 

21 

18 

15 

12 

40 60 80 100 120 

Side breadth (mm) 

Fig. (14) Variation of the mean crushing load with the number of 

sides (left) and with the side breadth (right) of the polygonal tubes

Fig. (15) Variation of the fold formation along axial path at 

the mid side breadth of tubes. 

Fig. (16) Variation of the fold depth with the side 

breadth-to-thickness ratio of the tube models. 

18/19 

Paper: ASAT-13-ST-34

Table (1) Comparison between the presented results of F.E.M., 

experimental results in Ref.[1] and numerical solution in Ref.[2] 

Parameter Ref.[1] Ref.[2] F.E.M. 

Peak load (kN) 337.12 357.23 348.25 

Mean load (kN) 100.98 101.32 102.78 

Table (2) Effect of variation of the tube cross-section on 

the obtained finite element results 

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Cross-section 

Max. load 

(kN) 

Mean load 

(kN) 

Max. deformation 

(mm) 

Absorbed energy 

(kJ) 

Triangular 34.07 23.53 191 4.41 

Squarer 34.43 16.84 234.73 3.75 

Pentagonal 38.64 19.47 217 4.22 

Hexagonal 52.59 22.76 218.92 4.90 

Circular 92.92 37.82 235.39 6.42 

Elliptical 268.98 162.71 233.29 40.59

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