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great effect on the crushing behavior of tube. Lower values of taper angle were shown to improve SEA and mean load/maximum load values. 5.5. Optimization of 1050H14 Al Crush Box – Alulight Al Foam Filler Binary System The optimization process was to maximize SEA of partially filled 1050H14 Al crush box (70.2X67.6X125.2 mm). The fixing parts of the box were also included in the optimization study in order to represent the real <strong>crash</strong> behavior of the box. SEA and mean load values were defined by two independent variables: box wall thickness and foam filler relative density. A quadratic (4 th order) polynomial objective function was used to create the response surface of filled <strong>crash</strong> box. Full factorial design, r s , was used to generate sampling points of the response surface. The created mesh of sampling points had r points spaced intervals in each variable direction. To create an approximation of order of r, at least (r+1) s factorial designs were required. In the optimization study r and s were taken as 4 and 2, respectively. The optimization problem is defined as, Maximize : SEA (t, * ) The constraints were: Mean Load (t, * ) < 55 kN 1 < t < 3.0 mm 0 < * < 0.2 98
The mesh of sampling points are shown in Figure 5.6. Total 25 simulations were run for each design set in the response surface analysis. Figure 5.6. The mesh of sampling points of RSM optimization. The fmincon command of Matlab optimization tool box was implemented to maximum SEA values at the boundaries of independent variables (box thickness and foam relative density). fmincon attempts to find a constraint minimum of a scalar function of several variables starting from an initial estimate. This is generally referred as to constraint nonlinear optimization or nonlinear programming. The details of the Matlab optimization tool box is given in reference (Arora 2004). 99
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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
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(a) (c) Figure 3.10. Deformation mo
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(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 116 and 117: 5.4. The Crashworthiness Optimizati
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
Page 162 and 163: (a) (b) (c) Figure 7.14. Load-displ
Page 164 and 165: 7.4. Simulation of Empty and Partia
Page 166 and 167: 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) (c) Figure 7.22. Load-displ
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(a) (b) (c) Figure 7.24. Load-displ
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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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