Composite Materials Research Progress

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98 Michaël Bruyneel 8.7. An Industrial Solution for the Pre-design of <strong>Composite</strong> Aircraft Boxes As reported in Krog et al. (2007), the pre-design of an aircraft wing is a large scale optimization problem including (up to now) about 1000 design variables and about 300000 constraints. Those variables are linked to the total thickness of the laminate made of 0, ±45 and 90° plies in the panel and to the dimensions of the cross section for the composite stiffener of each super-stringer defining the box structure (Figure 8.24). The constraints expressed as reserve factors (RF) are amongst others related to buckling and damage tolerance. Figure 8.24. The principle of a composite wing made of super-stringers (from Krog et al., 2007). Taking into account a so large number of design functions in the optimization problem will dramatically increase the CPU time spent in the optimizer. In order to decrease the size of the optimization problem, a technique for scanning the constraints (Figure 8.25) has been implemented in Boss Quattro (www.samcef.com). It consists in feeding the optimizer with the most critical constraints, based on their value at a given iteration. This leads to the definition of 2 sets of active and inactive constraints. The optimizer can only see the active restrictions. Those sets are not updated at each iteration but only when some inactive constraints tend to become violated after a given number of iterations (FREQ in Figure 8.25). When the SAM method (Bruyneel 2006) is used, the information at the previous design point is lost when the sets are updated, and the approximation is therefore only built based on the information at the current design point, that is with GCMMA (Svanberg 1995), for that specific iteration. The SAM approximation was found to be reliable in solving pre-design optimization problems of composite aircraft box structures in wings, center wing box, vertical and horizontal tail planes. Typically 30 iterations were enough to reach a stationary value of the weight and a nearly feasible design where very few constraints (less than 10) were still violated but of an amount of no more than 3 percents (RF larger than 0.97). Details of the results and of the implementation can be found in Krog et al. (2007).
Optimization of Laminated <strong>Composite</strong> Structures… 99 Figure 8.25. Strategy for scanning the constraints in large scale optimization problems (Krog et al. 2007). 8.8. Optimal Design with Respect to Damage Tolerance A simple DCB beam is considered (Figure 8.26). The energy release rates of modes I, II and III are computed at the straight crack front with a specific virtual crack extension method described by Bruyneel et al. (2006). The stacking sequence composed of 32 plies is given by: [θ/−θ/0/−θ/0/θ/θ/04/θ/0/−θ/0/−θ/θ/d/−θ/θ/0/θ/0/−θ/04/−θ/0/θ/0/θ/-θ] where d is the location of the interface where delamination will take place and θ is a variable. The goal is to find the optimal value of the orientation that will decrease the maximum value of GI along the crack front. Figure 8.26. DCB beam and variation of GI along the crack front for the initial design. On the left the displacements of the lips are multiplied by 50.
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COMPOSITE MATERIALS RESEARCH PROGRE
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Copyright © 2008 by Nova Science P
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vi Contents Chapter 9 Recent Advanc
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viii Lucas P. Durand scale transiti
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x Lucas P. Durand machine. In paral
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In: Composite Materials Research Pr
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Multi-scale Analysis of Fiber-Reinf
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T300 fibers (Soden et al., 1998; Ag
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1 I L = L : r v Multi-scale Analysi
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I E ⎡0 ⎢ ⎢0 ⎢ ⎢ ⎢ ⎢0
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Applied macroscopic load Correspond
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Page 67 and 68: Optimization of Laminated Composite
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Page 124 and 125: 110 W.H. Zhong, R.G. Maguire, S.S.
Page 126 and 127: 112 Reinforcement: Advanced materia
Page 144 and 145: 130 Yuanxin Zhou, Hassan Mahfuz, Vi
Page 154 and 155: 140 Heat Flow (W/g) Heat Flow (W/g)
Page 158 and 159: 144 Material Yuanxin Zhou, Hassan M
Page 160 and 161: 146 SEM Analysis Yuanxin Zhou, Hass
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148 Yuanxin Zhou, Hassan Mahfuz, Vi
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150 Governing Equation For the fibe
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152 ⎧ UU = ⎨ ⎩ ⎧ UD = ⎨
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156 Stress (MPa) 120 80 40 0 Yuanxi
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166 Giangiacomo Minak and Andrea Zu
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170 ⎟ ⎞ ⎠ s ⎜ ⎛ ⎝ = a E
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188 A B E (MPa) D 250000 200000 150
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190 D D 1.0 0.9 0.8 0.7 0.6 0.5 0.4
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204 Conclusion Giangiacomo Minak an
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Research Directions in the Fatigue
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Bending force [N] Research Directio
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Damage Variables in Impact Testing
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F peak [kN] 16 14 12 10 8 6 4 2 0 D
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Eletromechanical Field Concentratio
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MV/m. Eletromechanical Field Concen
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276 S.C. Tjong developed in the pas
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278 S.C. Tjong ultrasonic waves gen
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280 S.C. Tjong applications. Goujon
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282 S.C. Tjong nanoparticles were p
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284 S.C. Tjong where DL is lattice
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286 S.C. Tjong stress is temperatur
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288 S.C. Tjong threshold stress res
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290 S.C. Tjong NC Al, and the NC Al
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292 S.C. Tjong (a) (b) Figure 19. T
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294 S.C. Tjong Apart from forming u
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296 S.C. Tjong [29] Saravanan, M.;
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298 braids, 115 broadband, 211 bubb
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300 endothermic, 139 endurance, 32
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302 isostatic pressing, 279, 288 It
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304 piezoelectricity, 261 pitch, 12
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306 67, 69, 70, 71, 72, 73, 84, 94,
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Composite Materials Research Progress

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