 | Führer T. Composite structures' stiffness degradation due to strength and stability: Diss. … Dr.-Ing. / Deutsches Zentrum für Luft- und Raumfahrt, Institut für Faserverbundleichtbau und Adaptronik, Braunschweig. - Köln: DLR, 2013. - xi, 123 p.: ill. - (Forschungsbericht; 2013-24). - Res. also Germ. - Bibliogr.: p.91-99. - ISSN 1434-8454
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1 Introduction ................................................. 1
1.1 Structure of the thesis ................................. 3
1.2 Optimisation software LAGRANGE .......................... 3
1.3 Overview on other optimisation methods .................. 5
2 Failure of composite structures .............................. 9
2.1 Introduction to composite materials ..................... 9
2.2 Calculation of failure initiation ....................... 9
2.3 Degradation methods for composite structures ........... 15
2.4 Progressive failure analysis ........................... 17
2.5 Buckling behaviour of composite structures ............. 19
2.5.1 Calculation of buckling onset and post
buckling in LAGRANGE ............................ 22
2.5.2 Eigenvalue and nonlinear buckling analysis in
ABAQUS .......................................... 25
2.5.3 Summary ......................................... 29
3 Implementation of the progressive stiffness degradation
analysis .................................................... 31
3.1 Main structure of progressive stiffness degradation
analysis ............................................... 31
3.2 Implementation of progressive stiffness degradation
including strength ..................................... 33
3.3 Integration of buckling behaviour ...................... 39
3.3.1 ABAQUS analyses ................................. 40
3.3.2 Implementation in the progressive stiffness
degradation analysis ............................ 46
3.4 Progressive stiffness degradation analysis
considering strength and stability ..................... 49
4 Testing of the progressive stiffness degradation analysis ... 53
4.1 One skin field example .................................. 53
4.1.1 Comparison of load displacement curves for
uniaxial loading ................................ 55
4.1.2 Additional calculation of stress distribution
for uniaxial compression ........................ 59
4.1.3 Comparison of load displacement curves for
shear loading ................................... 63
4.2 Example with 16 skin fields ............................. 66
4.2.1 Load cases 1 .................................... 66
4.2.2 Load cases 2 .................................... 69
4.2.3 Comparison of simply supported to stiffened
model ........................................... 71
4.2.4 Summary ......................................... 72
5 Structural adjustment after the progressive stiffness
degradation analysis ........................................ 75
5.1 Parameters for the initial progressive stiffness
degradation analysis ................................... 75
5.2 Modification of element thicknesses .................... 77
5.3 Modification of material properties .................... 80
5.4 Comparison of two different stacking sequences ......... 81
5.5 Modification of failure initiation and degradation
criteria ............................................... 83
5.6 Summary ................................................ 85
6 Summary and Outlook ......................................... 87
Bibliography ................................................ 91
Appendix ...................................................... 101
A Material properties and stacking sequences ................. 101
В Equations and boundary conditions for ABAQUS analyses ...... 103
B.1 Uniaxial Loading ...................................... 103
B.2 Biaxial Loading ....................................... 103
B.3 Simple shear loading .................................. 104
B.4 Combined load cases ................................... 105
С Weaver and ESDU method in LAGRANGE buckling analysis ....... 107
C.1 Equations for Weaver method ........................... 107
C.2 Comparison of Weaver and ESDU method .................. 108
D Buckling load for uniaxial compression from Wiedemann
[67] ....................................................... 109
E Adaption of the A matrix depending on the load case ........ 110
F Derivation of degradation factor for the progressive
stiffness degradation analysis from each loading
condition within the element ............................... 111
F.2 Uniaxial compression .................................. 111
F.3 Biaxial compression ................................... 112
F.4 Shear loading ......................................... 113
F.5 Combination of shear and uniaxial compression ......... 114
F.6 Combination of shear and uniaxial tension ............. 116
F.7 Combination of shear and biaxial compression .......... 116
G Description of script generating fdeebuck and p-u-curve
from ABAQUS analyses ....................................... 117
H Equations for 16 skin field ABAQUS model ................... 118
I Implementation of dummy node by means of one beam example .. 121
J Recommended settings for the input file of the PSDA ........ 123
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