 | Dillinger J.K.S. Static aeroelastic optimization of composite wings with variable stiffness laminates / Deutsches Zentrum für Luft- und Raumfahrt, Institut für Aeroelastik, Göttingen. - Köln: DLR, 2015. - xiv, 228 p.: ill. - (Forschungsbericht; 2015-05). - Bibliogr.: p.215-223. - ISSN 1434-8454
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Summary ......................................................... i
Samenvatting .................................................. iii
Preface ......................................................... v
Contents ...................................................... vii
List of Symbols ................................................ xi
1 Introduction ................................................. 1
1.1 Composite Technology .................................... 4
1.1.1 Classical Lamination Theory ...................... 6
1.1.2 Lamination Parameters ........................... 10
1.1.3 Membrane Stiffness Visualization ................ 12
1.2 Composite Optimization ................................. 14
1.2.1 Lamination Parameter Optimization ............... 15
1.3 Composites and Aircraft Wings .......................... 15
1.3.1 Wing Structural Layout .......................... 16
1.3.2 Aeroelastic Optimization ........................ 17
1.4 Objectives and Thesis Layout ........................... 19
I Optimization Methodology .................................... 21
2 Basic Concept ............................................... 23
2.1 Optimization Framework ................................ 24
2.1.1 Finite Element Model ............................ 25
2.1.2 Optimization Model .............................. 26
2.1.3 Sensitivity Analysis ............................ 26
2.1.4 Approximation Setup ............................. 26
2.1.5 Optimization .................................... 27
2.2 Static Aeroelastic Responses ........................... 27
2.2.1 Aileron Effectiveness ........................... 27
2.2.2 Divergence ...................................... 29
2.2.3 Wing Twist ...................................... 31
2.3 Stacking Sequence Optimization ......................... 32
2.3.1 Stacking Sequence Table ......................... 33
2.3.2 Genetic Algorithm ............................... 35
2.3.3 Successive Approximations and Shepard's
Interpolation ................................... 38
2.3.4 Response Approximations ......................... 40
2.3.5 Objective Function .............................. 41
2.4 Summary ................................................ 41
3 Parametric Wing Model Generation ............................ 43
3.1 Geometry Model ......................................... 44
3.2 Finite Element Model ................................... 45
3.3 Mass Model ............................................. 46
3.3.1 Interface Model ................................. 47
3.3.2 Fuel Model ...................................... 47
3.4 Double Lattice Model ................................... 48
3.4.1 Control Surfaces ................................ 49
3.4.2 Camber and Twist Correction ..................... 49
3.4.3 Coupling ........................................ 49
3.5 Summary ................................................ 51
4 Optimization Model Setup .................................... 53
4.1 Design Fields .......................................... 53
4.1.1 Subdivision of Structural Entities .............. 54
4.2 Design Variable Definition ............................. 56
4.3 Response Definition .................................... 57
4.4 Finite Element Sensitivity Analysis .................... 59
4.5 Output Definition ...................................... 60
4.5.1 Sensitivities and Responses ..................... 60
4.5.2 Aerodynamics .................................... 61
4.5.3 Displacements ................................... 62
4.5.4 Correcting Alters ............................... 62
4.6 Summary ................................................ 62
5 Response Approximation Formulation .......................... 63
5.1 Approximation Methods in Structural Optimization ....... 63
5.2 General Approximation Form ............................. 64
5.3 Sensitivity Processing ................................. 67
5.4 Sensitivity Convexification ............................ 67
5.5 Sensitivity Convexification Sample ..................... 70
5.6 Structural Responses ................................... 72
5.6.1 Strength ........................................ 73
5.6.2 Buckling ........................................ 74
5.6.3 Mass ............................................ 76
5.7 Aeroelastic Responses .................................. 76
5.7.1 Aileron Effectiveness ........................... 76
5.7.2 Twist ........................................... 77
5.7.3 Divergence ...................................... 78
5.8 Summary ................................................ 78
6 Aero Load Correction ........................................ 79
6.1 Doublet Lattice ........................................ 80
6.2 Correction Methods ..................................... 81
6.2.1 Doublet Lattice Correction ...................... 81
6.2.2 CFD Correction .................................. 85
6.3 Process Methodology .................................... 87
6.4 CFD Correction Module .................................. 90
6.4.1 Mesh Generation ................................. 91
6.4.2 Mesh Deformation and Force Coupling ............. 92
6.4.3 CFD Tools ....................................... 93
6.5 Summary ................................................ 95
II Design Studies ............................................. 97
7 Aeroelastic Optimization of a Swept Back Wing ............... 99
7.1 Model Description ..................................... 100
7.2 Flight Envelope and Load Cases ........................ 101
7.3 Finite Element Model .................................. 103
7.4 Optimization Model .................................... 106
7.4.1 Design Variables and Responses ................. 106
7.4.2 Approximations ................................. 107
7.5 Starting Design ....................................... 107
7.6 Sensitivity Check ..................................... 110
7.7 Numerical Results: Mass Minimization .................. 116
7.7.1 Balanced Laminates ............................. 116
7.7.2 Unbalanced Laminates ........................... 119
7.8 Numerical Results: Aileron Effectiveness
Maximization .......................................... 124
7.8.1 Balanced Laminates ............................. 124
7.8.2 Unbalanced Laminates ........................... 126
7.9 Summary ............................................... 129
8 Aeroelastic Optimization of a Forward Swept Wing ........... 131
8.1 Model Description ..................................... 132
8.2 Flight Envelope and Load Cases ........................ 133
8.3 Finite Element Model .................................. 135
8.4 Optimization Model .................................... 140
8.5 Starting Design ....................................... 141
8.6 Numerical Results: Aileron Effectiveness Constraint ... 143
8.7 Numerical Results: Divergence Pressure Constraint ..... 148
8.8 Numerical Results: Twist Constraint ................... 153
8.9 Some Remarks on Stringers ............................. 156
8.10 Summary ............................................... 158
9 Aeroelastic Optimization With Aero Correction .............. 159
9.1 Finite Element and Optimization Model ................. 160
9.2 CFD Model ............................................. 162
9.3 Aeroelastic Trim Application .......................... 164
9.4 Numerical Results: Mass Minimization .................. 175
9.4.1 Optimization Results ........................... 177
9.4.2 Aeroelastic Results ............................ 179
9.4.3 Aerodynamic Results ............................ 184
9.5 Numerical Results: Mass Minimization Including Shear
Webs .................................................. 190
9.6 Numerical Results: Stacking Sequence Optimization ..... 194
9.7 Summary ............................................... 199
III Summary .................................................. 203
10 Conclusions and Recommendations ............................ 205
10.1 Conclusions ........................................... 205
10.1.1 Stiffness Optimization Process ................. 206
10.1.2 Wing Design with Aeroelastic Constraints ....... 207
10.2 Recommendations ....................................... 210
A Finite Element Analysis Alter ............................... 211
Bibliography .................................................. 215
Curriculum Vitae .............................................. 225
List of Publications .......................................... 227
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