cross section crash boxes

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5.4. The Crashworthiness Optimization of Tubular Structures The crushing behavior of multi-corner, thin-walled columns was previously optimized using RSM (Liu 2008a). The wall thickness and cross-section edge length were selected independent variables for the maximization of SEA. In another study, a square crush box with multi-cell sections was optimized with optimum cell numbers and cell geometrical parameters using again RMS (Hou, et al. 2008). The objective functions including linear, quadratic, cubic, quadratic and quintic polynomial were implemented, while the minimum error was accomplished by using a quadratic polynomial objective function. In a study of the multi-objective optimization of the frontal crush of an automobile chassis, RSM and radial basis function methodology were implemented together for comparison purpose (Fang, et al. 2005). Both were shown to be effective in the optimization of the intricate structure of automobile frontal section. RMS was also applied to determine the optimum thickness and radius of a cylindrical shell type tubular structure (Yamazaki and Han 2000). An orthogonal polynomial function was chosen as objective function and an orthogonal sampling array was implemented to create the response surface. Additionally, dynamic tests were carried out in order to validate objective function. The crashworthiness optimization of the circular Al tubes was studied by Zarei and Kröger, (Zarei and Kröger 2006). Various shapes of the impact side of circular tubes were investigated for the maximization of crush performance (Chiandussi and Avalle 2002). The taper length and the smallest diameter of tube were selected independent variable and the load uniformity (maximum load divided by mean load) dependent variable. The minimization of the load uniformity was applied to, in an separate study, the optimization of corrugated circular and tapered rectangular tubes (Avalle, et al. 2002). The shape optimization of a non-uniform closed hat front crash absorber section of an automobile was studied using RSM by Y.-B Cho et al.(Cho, et al. 2006). Two different crush initiator shapes, rectangular hole-type and circular dent-type, were investigated to maximize the crush energy absorption. A cross-section shape optimization study was further performed by Giess and Tomas (Giess 1998) by implementing the average mean crushing load as an objective function. The constraint 96
imposed was a constant prismatic cross-section and resulted in a 91% increase in the energy absorption at an impact velocity of 48 km h -1 . The minimum weight optimization of an Al foam filled S-Frame was carried out using an analytical energy absorption equation as an objective function (Kim, et al. 2002). The optimized variables, the thickness and cross-section length of the frame and the foam relative density, were validated with the finite element simulations. The simulation and optimization results showed 5% difference. Zarei and Köreger (Zarei and Kröger 2008b) worked on the optimization of Alporas Al foam-filled Al tubes to maximize SEA for the crush box applications by taking the width of cross-section and foam density as independent variables. The optimum parameters of empty square Al tubes were determined under the maximum mean load constraint of 68.5 kN. Equivalent SEA values of the optimized empty square tubes were compared with those of the optimized foam filled Al tube. Approximately, 20% increase in SEA values was found after the optimization in foam filled tubes. A similar optimization study was conducted on Al honeycomb filled Al square tubular structures (Zarei and Kröger 2008c). With respect to empty counterpart, 14.3% increase in SEA values were found in filled tube. Zhang et al.(Zhang, et al. 2008) performed an optimization study on the honeycomb filled bitubular hexagonal columns using Chebyshev’s orthogonal polynomial as objective function with the independent variables of inner side length and the thickness of inner and outer wall. With the maximized average mean load, 40% increase in SEA values was found in the optimized bitubal honeycomb filled Al tubes. Single and weighted arithmetic and geometrical average methods of multi objective optimization were implemented to foam filled thin-wall structures (Hou, et al. 2009). The applied Pareto analysis showed that geometrical average method was more effective than arithmetic average method in multi objective optimization of foam filled thin-wall structures. The bending properties of Alporas Al foam filled square tubular structures were optimized by Zarei and Kröger (Zarei and Kröger 2008a). Agreements between experimental and numerical results were found under the prescribed constraints and 28.1% increase in SEA values was found in foam filled tubular structures. Square tapered mild steel tubes were optimized in terms of tube thickness and width and taper angle (Liu 2008b). Full factorial design with 27 sampling points and second order objective functions were implemented using RSM. It was shown that taper angle had a 97
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OPTIMIZATION OF THE AXIAL CRUSHING
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ACKNOWLEDGEMENTS My PhD quest has b
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ÖZET KAPALI HÜCRELİ ALUMİNYUM K
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CHAPTER 4 EXPERIMENTAL DETAILS ....
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CHAPTER 8 ALUMINUM CRASH BOX OPTIMI
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Figure 3.7. Simulations of the defo
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Figure 4.9. Dimensions of tensile t
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Figure 6.21. Sequential deformation
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Figure 7.20. Sequential deformation
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LIST OF TABLES Table Page Table 4.1
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Figure 1. 1. The body in white stru
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Figure 1. 4. Commercial crash boxes
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CHAPTER 2 AL CLOSED CELL FOAMS: PRO
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The processing methods and mechanic
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Figure 2. 5 The preferred particle
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Figure 2. 8. Typical cellular struc
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Figure 2. 10. Manufacturing cost of
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Figure 2. 12. Laser assisted foamed
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Figure 2.16. Shear strength, normal
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Figure 2. 19. Yield strength vs. re
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Figure 2. 21. Unit cell geometry an
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Figure 2. 24. Load-displacement cur
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Figure 2. 26. The photographs of a
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CHAPTER 3 CRUSHING BEHAVIOR OF TUBU
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Figure 3.2. Diamond deformation mod
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deformation mode transition from ax
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Figure 3.8. Energy absorption of qu
Page 61: (a) (c) Figure 3.10. Deformation mo
Page 65 and 66: (a) (b) Figure 3.13. a) Schematic o
Page 67 and 68: (a) (b) (c) Figure 3.15. a) Load-di
Page 72 and 73: Figure 3.18. The crush terminology.
Page 75 and 76: The quasi-static compression behavi
Page 77 and 78: Figure 3.22. The variation of speci
Page 79 and 80: Figure 3.24. Deformation modes of e
Page 81 and 82: Figure 3.27. SEA values of empty an
Page 83 and 84: Figure 3.29. (cont.) 3.5. Motivatio
Page 85 and 86: CHAPTER 4 EXPERIMENTAL DETAILS 4.1.
Page 87 and 88: (a) (b) Figure 4.3.Pictures of a) f
Page 89 and 90: oxes are shown in Figure 4.6. The l
Page 91 and 92: Figure 4.7. The method of trigger m
Page 93 and 94: 4.4. Compression Tests of Crash Box
Page 95 and 96: 4.5.2. Uniaxial Compression Testing
Page 97 and 98: Table 4.1 (Cont.) G1 T3 F2 G1T3F2 3
Page 99 and 100: Table 4.2 (Cont.) G1 T2.5 WP F2 G1T
Page 101: CHAPTER 5 SIMULATION AND OPTIMIZATI
Page 105: considered in axial and transverse
Page 109 and 110: were constrained. Since the width o
Page 118 and 119: great effect on the crushing behavi
Page 120: CHAPTER 6 EXPERIMENTAL RESULTS 6.1.
Page 124 and 125: Figure 6.3.Tensile stress-strain cu
Page 126 and 127: (a) (b) Figure 6.5. Sequential defo
Page 128 and 129: plate (Figure 6(b)). The trigger is
Page 130 and 131: (a) (b) Figure 6.9. Deformation seq
Page 132 and 133: Figure 6.12. Sequential deformation
Page 138 and 139: Figure 6.18. (cont.) (c) (a) (b) Fi
Page 140 and 141: Figure 6.20.(cont.). (b) (c) 6.5.4.
Page 142 and 143: Figure 6.21.(cont.) (b) (c) 122
Page 144 and 145: Figure 6.22.(cont.) (c) Figure 6.23
Page 146 and 147: Figure 6.24.(Cont.) (b) (c) (a) Fig
Page 148 and 149: Figure 6.26.(cont.) (b) (c) 6.6. Dy
Page 150 and 151: Figure 6.27. (cont.) (b) (c) 130
Page 152 and 153: CHAPTER 7 MODELING RESULTS OF FOAM,
Page 154 and 155: experimental tensile stress-strain
Page 156 and 157: significant effect of weld seem ope
Page 158 and 159: Figure 7.7. Deformation photo of fi
Page 160 and 161: Figure 7.11. Deformation photos of
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(a) (b) (c) Figure 7.14. Load-displ
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7.4. Simulation of Empty and Partia
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Figure 7.16. (cont.) (c) (a) Figure
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(a) (b) Figure 7.18. Sequential def
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Figure 7.19. (cont.) (b) (c) 150
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Figure 7.20. (cont.) (c) (a) Figure
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(a) (b) Figure 7.26. Experimental a
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The constructed response surface of
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Table 8.1. R 2 , Radj 2 and RMSE va
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(a) (b) Figure 8.7. Response surfac
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an empty tube wall thickness higher
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where, K is a dimensionless constan
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The dynamic simulation and analytic
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Figure 9.4. (cont.) (c) (d) Figure
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Figure 9.6. (cont.) (c) (d) (a) Fig
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Equation 9.7 can also be rewritten
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(a) (b) Figure 9.10. Energy-absorbi
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Figure 9.11. (cont.) (d) The variat
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foam filling were evaluated. The re
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13. The interaction between foam fi
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Arora, J. S.,2004,Introduction to O
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Dannemann, K. A. and Lankford, J.,
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Hall, I. W., Guden, M. and Yu, C. J
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Kim, D-K. and Lee, S., 1999, Impact
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Mamalis, A. G., Manolakos, D. E., I
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Pugsley, A. G. and Macaulay, M., 19
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T. Miyoshi, M. Itoh S. Akiyama A. K
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Zhao, H., Elnasri, I. and Girard, Y
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