Computational Methods for Debonding in Composites

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242 J.A. Oliveira et al. 20. Suquet PM (1987) Elements of homogenization theory for inelastic solid mechanics. In: Sanchez-Palenzia E, Zaoui A (eds) Homogenization techniques for composite media. Lecture Notes in Physics. Springer, Berlin 21. Terada K (1996) Global-local modeling for composites by the homogenization method. Ph.D. thesis, Michigan University, Michigan 22. van der Vorst HA (2003) Iterative Krylov methods for large linear systems. Cambridge University Press, Cambridge 23. Whitney JM, Riley MB (1966) Elastic properties of fiber reinforced composite materials. AIAA J 4:1537–1542 24. Xia Z, Zhang Y, Ellyin F (2003) A unified periodical boundary conditions for representative volume elements of composites and applications. Int J Solids Struct 40:1907–1921 25. Zienkiewicz OC, Taylor RL (1989) The finite element method, Vol. I. McGraw-Hill, London
Chapter 12 On Buckling Optimization of a Wind Turbine Blade Erik Lund and Leon S. Johansen Abstract The design of composite structures such as wind turbine blades is a challenging problem due to the need for pushing the material utilization to the limit in order to obtain light and cost effective structures. As a consequence of the minimum material design strategy the structures are becoming thin-walled, such that buckling problems must be addressed, and in this work the aim is to obtain buckling optimized multi-material designs of wind turbine blades. The design problem consists of distributing multiple materials within a given design domain, and the candidate materials may be fiber-reinforced materials, oriented at given discrete fiber angles, together with isotropic materials like foam materials used for sandwich structures. The discrete design optimization problem is converted to a continuous problem using the so-called Discrete Material Optimization (DMO) approach based on ideas from multi-phase topology optimization where interpolation functions with penalization are introduced. In this way traditional gradient based optimization techniques including efficient methods for design sensitivity analysis and mathematical programming can be used for solving the multi-material distribution problem. The multi-material topology optimization approach is demonstrated for buckling optimization of a 9 m generic wind turbine blade test section. 12.1 Introduction Fiber-reinforced composite laminates are popular because of high stiffness-toweight and strength-to-weight ratios compared with isotropic materials, and they are, for example, used in naval, aerospace, automobile and other mechanical applications. Such composite laminates consist of layers of one or more materials stacked at different orientation angles, and they permit the designer to tailor the structure or component to achieve the specified objectives. E. Lund and L.S. Johansen Department of Mechanical Engineering, Aalborg University, Pontoppidanstraede 101, DK-9220 Aalborg East, Denmark, e-mail: el@ime.aau.dk 243
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Mechanical Response of Composites
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Pedro P. Camanho • C.G. Dávila S
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Preface The methodology for designi
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Acknowledgements The Editors of thi
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x Contents 3 Practical Challenges i
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xii Contents 8.2.4 Modelling Effect
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xiv Contents 13.1.2 EffectiveProper
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xvi List of Contributors Clara Schu
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Chapter 1 Computational Methods for
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1 Computational Methods for Debondi
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28 R. Rolfes et al. functions by me
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30 R. Rolfes et al. Microscale fibe
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32 R. Rolfes et al. symmetric, whic
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34 R. Rolfes et al. Fig. 2.5 Discre
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36 R. Rolfes et al. Unit cell (a) S
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38 R. Rolfes et al. stress state. T
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40 R. Rolfes et al. biaxial compres
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42 R. Rolfes et al. Damage Evolutio
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44 R. Rolfes et al. Fig. 2.14 Radia
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46 R. Rolfes et al. Table 2.2 Elast
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48 R. Rolfes et al. A dev is the de
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50 R. Rolfes et al. uniaxial compre
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52 R. Rolfes et al. Stress in MPa -
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54 R. Rolfes et al. 2.4.2 Results o
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56 R. Rolfes et al. 12. Hughes TJR
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58 B.N. Cox et al. inform models; a
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60 B.N. Cox et al. 3.2 The Structur
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62 B.N. Cox et al. be successfully
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64 B.N. Cox et al. high fluxes of c
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66 B.N. Cox et al. provides poor in
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68 B.N. Cox et al. For example, a c
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70 B.N. Cox et al. failures in comp
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72 B.N. Cox et al. mixed-mode crack
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74 B.N. Cox et al. 24. Elices M, Gu
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Chapter 4 Analytical and Numerical
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4 Analytical and Numerical Investig
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Chapter 6 Study of Delamination in
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6 Study of Delamination with in Com
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7 Interaction Between Intraply and
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Chapter 8 A Numerical Material Mode
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8 A Numerical Material Model for Pr
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180 N. Zobeiry et al. There are sev
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182 N. Zobeiry et al. for construct
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184 N. Zobeiry et al. In compressio
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186 N. Zobeiry et al. c = 38.7 mm h
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188 N. Zobeiry et al. displacement
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296 H. Miled et al. Fig. 15.2 Diffe
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298 H. Miled et al. Each member of
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300 H. Miled et al. temperature is
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302 H. Miled et al. Fig. 15.7 Compa
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306 H. Miled et al. Eqs. 15.28 and
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308 H. Miled et al. 15.4.2 Effectiv
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310 H. Miled et al. Fig. 15.13 Comp
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312 H. Miled et al. 9. Carreau P, D
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