13941512 25-36

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M. Alisadeghi, J. Fazilati, Optimization of honeycomb impact attenuator using genetic algorithm based on response surface method and design of experiment; Part I:crashworthiness, Modares Mechanical Engineering Vol. 15 No. 12, pp. 25-36, 2015 (in Persian)

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1- 2- * 834-14665 jfazilati@ari.ac.ir

:07 1394 :16 1394

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Optimization of honeycomb impact attenuator using genetic algorithm based on response surface method and design of experiment; Part I: crashworthiness

Maryam Alisadeghi, Jamshid Fazilati*

Aerospace Research Institute, Tehran, Iran. * P.O.B. 14665-834, Tehran, Iran, jfazilati@ari.ac.ir

ARTICLE INFORMATION ABSTRACT Original Research Paper Received 28 June 2015 Accepted 08 October 2015 Available Online 11 November 2015

In this study, the design and optimization of a honeycomb energy absorber is performed using genetic algorithm. The main design goal is to absorb almost all the impact energy. Simultaneously, reduction of the shock force level is also considered as a main objective. In the first part, the crashworthiness behavior of honeycomb structure is parametrically studied. The results are utilized in the second part to optimize shock absorber design. In this part, aluminum honeycomb structure under dynamic loading is investigated using simulation in LS-dyna finite element code. Parametric studies are invoked to identify the influence of different model parameters on crashworthiness characteristics of honeycomb structure. Reducing the computational cost, a repeatable model of 'Y' cross section column is numerically simulated. The effects of changes in material properties including Young's modulus, yield stress, tangent modulus, geometrical properties such as cell size, foil thickness, as well as the effects of impact velocity on the deformation behavior of the structure were investigated. A number of 25 different geometries with same height and various cell sizes and thicknesses are studied and effects of thickness and cell size on the energy absorption properties are investigated. Results showed that crashworthiness parameters such as mean and peak stress depend mainly on cell size and thickness values, while the friction coefficient and young's modulus are of less importance. Any change in absorber’s geometry affects the mean collapse stress more severely than the peak stress. In the meantime, thickness change is more effective in comparison with cell size change.

Keywords: Honeycomb Structure Crashworthiness LS-Dyna Finite Element Code Design Of Experiment Parametric Study

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1 2 0.3

0.2 .-3

2-1 - DARTEC 9600

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.0.002 0.003 .

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Fig. 1 Honeycomb section structure and repeatable “Y” cross section column element

1 Y

1 5052-H39 Table 1 Mechanical properties of aluminum 5052-H39 alloy

)(kg/m3 2680

(GPa) 70 0.33

(MPa) 265 (MPa) 700

1- Automatic single surface contact 2- Automatic nodes to surface contact 3- Belytschko-Tsay

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Fig. 2 Honeycomb deformation in test and simulation (1) and (2) 2 1 :2 :

.(4)

(4) =( )

(5) (6)

(5) =

(6) =

-3

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0.3 0.2 . - - 5 6 . 2 0.3 0.03

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Fig. 3 Stress-shortening curves from test and simulation of test samples 1 and 2

3 - )1) (2(

Fig. 4 Energy-shortening curves from test and simulation of test samples 1 and 2

4 - )1) (2(

Fig. 5 Effect of friction on force-shortening curves

5 -

Fig. 6 Effect of friction on energy-shortening curves

6 -

(2) (1)

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2 Table 2 Effects of contact friction assumptions

%

) J( 0.15 0.15 0 ) mm( 20.28 20.34 0.3

) kN( 0.0074 0.0074 0 ) kN( 0.03098 0.03099 0.03

3-3 -

70 256 . 9 10 .4

74 62 6172 3

.

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3-4 - 60 70 .

11 12

3 Table 3 Tangent modulus effects study

) MPa( 350 700 %

) J( 0.143 0.15 4.7 ) mm( 20.68 20.28 -2 )kN( 0.0069 0.0074 6.8 ) kN( 0.03084 0.03098 0.45

4 Table 4 Yield stress effects study

)MPa( 70 265 %

)J( 0.05706 0.15 62.0 )mm( 19.7 20.28 2.9

)kN( 0.0029 0.0074 60.8 )kN( 0.008581 0.03098 72.3

Fig. 7 Force-shortening curves for different tangent modulus

7 -

Fig. 8 Effects of tangent modulus on energy-shortening curve

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5 Table 5 Young's modulus effects study

) GPa( 60 70 %

) J( 0.15 0.15 0 ) mm( 20.48 20.28 1.0

) kN( 0.0073 0.0074 1.4 ) kN( 0.02647 0.03098 14.6

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Fig. 9 Force-shortening curve for different yield stresses

9 -

Fig. 10 Energy-shortening curves for different yield stresses

10 -

Fig. 11 Force-shortening curves for different Young modulus

11-

Fig. 12 Energy-displacement curves for young's modulus effects study

12 -

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.-] 17.[

(7) = 1 ,

0

0 .D q .

(8) = 1 +/

Fig. 13 Force-shortening curve for impact mass effect study

13 -

Fig. 14 Energy-shortening curves for impact mass effect study

14 -

Fig. 15 Force-shortening curves for different impact velocities

15 -

6 Table 6 Effects of impact mass

) kg ( 0.0032 0.0016 0.0064 0.5

)J( 0.16 0.08 0.32 25 ) J( 0.15 0.08 0.1527 0.1591

) mm( 20.28 10.86 20.42 20.82 ) kN( 0.0074 0.0074 0.0075 0.0076 ) kN( 0.03098 0.03098 0.03101 0.3101

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Fig. 16 Energy-shortening curves for impact velocity effects study

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10 30 70 100 .

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7 Table 7 Effects of impact velocity

) m/s ( 10 30 70 100

)J( 0.16 1.44 7.84 16 ) J( 0.1388 0.1492 0.1793 0.2541

) mm( 20.54 20.92 21 22.4 0.8087 0.8236 0.8268 0.8819 ) kN( 0.0068 0.0071 0.0085 0.0113 ) kN( 0.02775 0.02695 0.02565 0.03099

8 - Table 8 Cowper-Symond coefficients for strain rate sensitivity effects study

q D

0 0 4 6500

3 570

9 Table 9 Simulation results for strain rate sensitivity effects study

)kN(

)kN(

)mm(

)J(

)J(

V=10, D=0, q=0 0.0277 0.0068 0.8087 20.54 0.1388 0.16 V=10, D=6500, q=4 0.0310 0.0074 0.8039 20.42 0.1504 0.16 V=10, D=570, q=3 0.0316 0.0074 0.8008 20.34 0.1509 0.16 V=30, D=0, q=0 0.0269 0.0071 0.8236 20.92 0.1492 1.44 V=30, D=6500, q=4 0.0312 0.0083 0.8272 21.01 0.1744 1.44 V=30, D=570, q=3 0.0321 0.0086 0.8299 21.08 0.1812 1.44 V=70, D=0, q=0 0.0256 0.0085 0.8268 21 0.1793 7.84 V=70, D=6500, q=4 0.0292 0.0099 0.8457 21.48 0.2117 7.84 V=70, D=570, q=3 0.0311 0.0105 0.8535 21.68 0.2271 7.84 V=100, D=0, q=0 0.0310 0.0113 0.8819 22.4 0.2541 16 V=100, D=6500, q=4 0.0360 0.0124 0.8937 22.7 0.2816 16 V=100, D=570, q=3 0.0382 0.0127 0.8937 22.7 0.2875 16

10 ) Table 10 Effects of material’s strain rate sensitivity (in percent)

V=10 D=6500,P=4

V=10 D=570,P=3

V=30 D=6500,P=4

V=30 D=570,P=3

V=70 D=6500,P=4

V=70 D=570, P=3

V=100 D=6500,P=4

V=100 D=570, P=3

)J( 8.4 8.7 16.9 21.4 18.1 26.7 10.8 13.1 0.6 -1 0.4 0.76 2.3 3.2 1.3 1.3

)kN( 8.8 8.8 16.9 21.1 16.5 23.5 9.7 12.4

)kN( 11.9 14.1 16 19.3 14.1 21.5 16.1 23.2

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Fig. 17 Force-shortening curves for cell height effects study

17 -

Fig. 18 Energy-shortening curves for cell height effects study

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0.0255 0.0381 0.0064 0.0762 0.0635 0.0126

4-2 - 20

.

11

Table 11 Cell height effects study

12 Table 12 Full factorial method inputs in design of experiments method

) n( ) r (

n=1 C (mm)

n=2 t (mm)

r=1 3.1750 0.0254 r=2 3.9688 0.0381 r=3 4.7625 0.0508 r=4 5.5562 0.0635 r=5 6.3500 0.0762

)mm( 25.4 20 15 10

)J( 0.15 0.1193 0.09131 0.06246 )mm( 20.28 16.05 12.11 8.109

0.7984 0.6319 0.4768 0.3193 )kN( 0.0074 0.0074 0.0075 0.0077

)kN( 0.03098 0.03076 0.03064 0.03019

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13 Table 13 Simulation results

C (mm)

t (mm)

p (MPa)

m

(MPa) SEAm

(kJ/kg)

SEAv

(kJ/m3)

3.175 0.0254 7.0309 1.7128 29.9588 80289 3.175 0.0381 10.9758 3.1743 37.0138 99196 3.175 0.0508 14.4168 5.3575 46.8531 125566 3.175 0.0635 17.9242 7.6174 53.2933 142826 3.175 0.0762 21.4866 10.5127 61.2915 164261

3.9688 0.0254 5.6154 1.1426 24.9824 66952 3.9688 0.0381 8.8204 2.1985 32.0455 85881 3.9688 0.0508 11.5724 3.5830 39.1692 104973 3.9688 0.0635 14.3537 5.4039 47.2599 126656 3.9688 0.0762 17.1540 7.6150 55.4975 148733 4.7625 0.0254 4.6806 0.8498 22.2959 59753 4.7625 0.0381 7.3595 1.6466 28.7994 77182 4.7625 0.0508 9.6952 2.7081 35.5244 95205 4.7625 0.0635 11.9637 3.9746 41.7109 111785 4.7625 0.0762 14.3056 5.6101 49.0621 131486 5.5562 0.0254 4.0074 0.6631 20.2968 54395 5.5562 0.0381 6.3032 1.2725 25.9662 69589 5.5562 0.0508 8.3335 2.1784 33.3389 89348 5.5562 0.0635 10.293 3.2323 39.5747 106060 5.5562 0.0762 12.3133 4.5536 46.4596 124511

6.35 0.0254 3.4971 0.5455 19.0809 51136 6.35 0.0381 5.5131 1.0568 24.6461 66051 6.35 0.0508 7.3023 1.7776 31.0907 83323 6.35 0.0635 9.0148 2.7792 38.8874 104218 6.35 0.0762 10.7845 3.6662 42.7498 114569

.

0.02540.0075 0.0095 0.0020 26.7 0.0762

0.0459 0.0640 0.0181 39.43 .

. 19

4-3 - 21

.

3.175 0.0307 0.0938 0.0631 205.5 6.35 0.0611 0.1883

0.1272 208.18

4-4 - 22

.

.

. 0.02540.0307 0.0611 0.0304

0.0762 0.0938 0.1883 0.0892

4-5 - 23

. .

. 3.1751.71 10.51 8.8

6.35

0.54 3.67 )3.13 ( .

. .

.

4-6 - 24

. .

.

.1.5 .

.

4-7 - 25 .

.

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4-8 - 26 .

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. 0.0254 7.03 3.5 3.53 0.0762 21.49

10.78 10.71 .

.

.

4-9 - 27 .

3.175 6.35 .

3.175 25 50 6.3515 30 .

4-10 - 28

. .

.0.0254 15 24

0.0762 30 50 .

. .

4-11 - 29 30

.

.

-5

.

.

.

25 .

.

15 .

.

.

Fig. 19 Functionality of mean force with cell thickness

19

Fig. 20 Functionality of mean force with cell size

20

Fig. 21 Functionality of peak force with cell thickness

21

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Fig. 22 Functionality of peak force with cell size

22

Fig. 23 Functionality of mean stress with cell thickness 23

Fig. 24 Functionality of mean stress with cell size

24

Fig. 25 Functionality of peak stress with cell thickness

25

Fig. 26 Functionality of peak stress with cell size

26

Fig. 27 Functionality of peak force to mean ratio with cell thickness

27

Fig. 28 Functionality of peak force to mean ratio with cell size

28

Fig. 29 Functionality of SEAm with cell size and thickness

29

Fig. 30 Functionality of SEAv with cell size and thickness

30

6 - ) m2 ( ) m( ) J( ) N( ) m( )J/kg, J/m3( ) m( ) ms-1(

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) Pa ( ) m(

cm cv m P

7 - [1] G. Petrone, S. Rao, S. De Rosa, B. R. Mace, F. Franco, and D. Bhattacharyya,

Behaviour of fibre reinforced honeycomb core under low velocity impact loading, Composite Structures, Vol. 100, No. 0, pp. 356–362, 2013.

[2] M. Li, Z. Deng, R. Liu, and H. Guo, Crashworthiness design optimisation of metal honeycomb energy absorber used in lunar lander, International Journal of Crashworthiness, Vol. 16, No. 4, pp. 411–419, 2011.

[3] R. K. McFarland, Hexagonal cell structures under post-buckling axial load, AIAA, Vol. 1, No. 6, pp. 1380–1385, 1963.

[4] T. Wierzbicki, Crushing Analysis of metal honeycomb, Impact Engineering, Vol. 1, No. 2, pp. 157–174, 1983.

[5] G. H. Liaghat, H. A. Serailoo, Optimum design of honeycomb core structures under compressive load, Modares Mechanical Engineering, Vol. 9, No. 37, pp. 73-82, 1388 (In persian )

[6] N. Pirmohammadi, G. H. Liaghat, M. H. Pol, and H. Sabouri, Analytical , experimental and numerical investigation of sandwich panels made of honeycomb core subjected projectile impact, Modares Mechanical Engineering , Vol. 14, No. 6, pp. 153–164, 2014. (In persian )

[7] H. Zhao and G. Gary, Crushing behaviour of aluminium honeycombs under impact loading, Impact Engineering, Vol. 21, No. 10, pp. 827–836, 1998.

[8] M. Yamashita and M. Gotoh, Impact behavior of honeycomb structures with various cell specifications—numerical simulation and experiment, International Journal Impact Engineering, Vol. 32, No. 1, pp. 618–630, 2005.

[9] S. Deqiang, Z. Weihong, and W. Yanbin, Mean out-of-plane dynamic plateau stresses of hexagonal honeycomb cores under impact loadings, Composite Structures, Vol. 92, No. 11, pp. 2609–2621, 2010.

[10] M. K. Khan, T. Baig, and S. Mirza, Experimental investigation of in-plane and out-of-plane crushing of aluminum honeycomb, Materials Science & Engineering, Vol. 539, pp. 135–142, 2012.

[11] S. Xu, J. H. Beynon, D. Ruan, and G. Lu, Experimental study of the out-of-plane dynamic compression of hexagonal honeycombs, Composite Structures, Vol. 94, No. 8, pp. 2326–2336, 2012.

[12] A. P. Meran, T. Toprak, and A. Mu an, Numerical and experimental study of crashworthiness parameters of honeycomb structures, Thin Walled Structures, Vol. 78, pp. 87–94, 2014.

[13] Z. Wang, H. Tian, Z. Lu, and W. Zhou, High-speed axial impact of aluminum honeycomb – Experiments and simulations, Composits Part B, Vol. 56, pp. 1–8, 2014.

[14] L. Aktay, A. Johnson, and B. Kröplin, Numerical modelling of honeycomb core crush behavior, Engineering Fracture Mechanics, Vol. 75, No. 9, pp. 2616–30, 2008.

[15] B. Hou, H. Zhao, S. Pattofatto, J. G. Liu, and Y. L. Li, Inertia effects on the progressive crushing of aluminium honeycombs under impact loading, International Journal of Solids and Structures, Vol. 49, No. 19, pp. 2754–62, 2012.

[16] F. Zhu, L. Zhao, G. Lu, and E. Gad, A numerical simulation of the blast impact of square metallic sandwich panels, International Journal Impact Engineering, Vol. 36, No. 5, pp. 687–699, 2009.

[17] N. Jones, Structural impact, pp. 327-350, New York: Cambridge university, 1989.

[18] H. Yin, G. Wen, and N. Gan, crashworthiness design for honeycomb structures under axial dynamic loading, International Journal of Computational Methods, Vol. 8, No. 4, pp. 863–877, 2011.

[19] S. Hou, Q. Li, S. Long, X. Yang, and W. Li, Design optimization of regular hexagonal thin-walled columns with crashworthiness criteria, Finite Elements in Analysis and Design, Vol. 43, No. 6, pp. 555–565, 2007.

[20] Technology Brochures: Honeycomb Attributes and Properties, Accessed 20 June 2015; www.hexcel.com/Resources

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