virtual testing of aircraft structures, considering ...elib.dlr.de/49104/1/tessmer_zaragoza.pdf ·...
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Institute of Structural Mechanics 1
Virtual Testing of Aircraft Structures, considering Postcritical & Thermal Behavior
J. Teßmer, R. Degenhardt, A. Kling, R. Rolfes, T. Spröwitz, S. Waitz (DLR – Institute of Structural Mechanics, Braunschweig, Germany),
COMPOSIT Thematic Network,Workshop on Modeling and Prediction of Composite Transport Structures
in Zaragoza, Spain, 30.06.2003
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Institute of Structural Mechanics 2
Validation / Verification
RealityExperiment
ComputerModel
ModelValidation
ModelQualification
ModelVerification
ComputerSimulation
Analysis
Programming
ConceptualModel
Model Verification:„Solve the equations right“
Model Validation:„Solve the right equations“
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Institute of Structural Mechanics 3
Postcritical behavior of stiffened panels
Deformation pattern (ARAMIS)Panel in Buckling Test Facility
Top plate
Clamping box
Specimen
Clamping Box
Displacementpickup
Load distributor
Load cells
Drive plate
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Institute of Structural Mechanics 4
Non linear FEM using ABAQUS/Standard
roughestimate
FE-Model
Linear Eigenvalue Analysis
Buckling Load
Nonlinear AnalysisNewton-Raphson-Method + automatic / adaptive
damping to stabilize the analysis (*STATIC, STABILIZE)
scaled imperfektions
Postprocessing(Load-Shortening-Curve, deformation of the structure, ...)
Buckling Modes
Real StructureCFRP-Panel
MeasuredImperfections
roughestimate
FE-Model
Linear Eigenvalue Analysis
Buckling Load
Nonlinear AnalysisNewton-Raphson-Method + automatic / adaptive
damping to stabilize the analysis (*STATIC, STABILIZE)
scaled imperfektions
Postprocessing(Load-Shortening-Curve, deformation of the structure, ...)
Buckling Modes
Real StructureCFRP-Panel
MeasuredImperfections
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Institute of Structural Mechanics 5
Numerical Pre-Test Analysis
„Experimental Validatition of computational Analysis is expensive & time consuming“
„Pre-Test Analysis and Pre-Test Planing“
„Validation Experiments“ versus „Phenomenological Experiments“
Goal: Load – Deformation curve showing:- characterristic skin buckling, coupeled with axial stiffness reduction- large load bearing capacity during postbuckling without structural failure
FEA investigation w.r.t.: panel geometriediscretisationexperimental boundary conditionsinitial imperfections...
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Institute of Structural Mechanics 6
Pre-Test Analysis 1. Influence of different STABILIZE parameters 2. Investigation of different failure criteria
0
10
20
30
40
50
60
70
80
0 0.5 1 1.5 2 2.5 3 3.5 4
Shortening [mm]
Loa
d [k
N]
STABILIZE = 2e-4
STABILIZE = 2e-5
STABILIZE = 2e-6
STABILIZE = 2e-7
Nominal dataABAQUS/StandardMesh I (3024 elements)
Tsai HillAzzi Tsai Hill Maximum Stress
Tsai Wu
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Institute of Structural Mechanics 7
Pre-Test AnalysisConvergence study
0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5 3 3.5 4Shortening [mm]
Loa
d [k
N]
Mesh I: 3024 elementsMesh II: 2*3024 elementsMesh III: 16*3024 elements
Nominal dataABAQUS/StandardSTABILIZE = 2.e-6
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Institute of Structural Mechanics 8
Pre-Test AnalysisInfluence of lateral boundary conditions
0
10
20
30
40
50
60
70
80
90
100
0 0.5 1 1.5 2 2.5 3 3.5 4
Shortening [mm]
Loa
d [k
N]
Covered width = 25.0 mm Covered width = 12.5 mm Only lateral nodes fixed
Nominal dataABAQUS/StandardSTABILIZE = 2.e-6Mesh I (3024 elements)
Edge support
Filler
Gliding plane
Test panel
Detail
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Institute of Structural Mechanics 9
Pre-Test AnalysisInfluence of imperfections
0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5 3 3.5 4
Shortening [mm]
Loa
d [k
N]
No imperfectionsMode 1, 2% skin thicknessMode 1, 10% skin thicknessMode 1, 100% skin thickness
Nominal dataSTABILIZE = 2.e-6Mesh I (3024 elements)
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Institute of Structural Mechanics 10
Pre-Test AnalysisABAQUS/Standard vs. ABAQUS/Explicit
0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5 3 3.5 4
Shortening [mm]
Loa
d [k
N]
ABAQUS/Standard, STABILIZE = 2e-6
ABAQUS/Explicit, v=10mm/s, no damping
ABAQUS/Explicit, v=10mm/s, with damping
Nominal dataMesh I (3024 elements)
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Institute of Structural Mechanics 11
Measurement of geometrical Imperfections (1)Optical 3D - digitalization
ATOS – Sensor strip sequenz
4 Measurment of real radius vs. nominal radius (ca. 6% deviation)
4 Measurement of initial imperfection
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Institute of Structural Mechanics 12
Measurement of geometrical Imperfections
Data points (ASCII-Format):
1093.6441 211.5491 1.6805
1093.1718 211.1541 1.6764
1093.8102 210.6003 1.6764
1093.0879 210.3660 1.6910
…
Modification of „perfect“ FE – geometry
Application of initial imperfection
Fringe – plot w.r.t.perfect shell
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Institute of Structural Mechanics 13
Results of FEA using ABAQUS/Standard
0
0,5
1
1,5
2
2,5
0 0,5 1 1,5 2 2,5 3 3,5 4
Skalierte Verschiebung
Ska
lierte
Las
t
ABAQUS/Standard ohne Imperfektionen
ABAQUS/Standard mit Imperfektionen
Lokal skin buckling
Global „unsymmetric“ Buckle
Global „symmetric“Buckle
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Institute of Structural Mechanics 14
Validation of FEA (Animation)
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Institute of Structural Mechanics 15
Validation of computational results
„Globale“ Ebene
0
0,5
1
1,5
2
2,5
0 0,5 1 1,5 2 2,5 3 3,5 4Skalierte Verschiebung
Skal
ierte
Las
t
Experiment (1)Experiment (2)ABAQUS/Standard mit Imperfektionen
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Institute of Structural Mechanics 16
Validation of computational results
-10
-5
0
5
10
15
20
25
0 0,5 1 1,5 2 2,5 3
Skalierte Verschiebung
Rad
ialv
ersc
hieb
ung
[mm
]
Wegaufnehmer W88
Knoten 40696; entspricht W88 Position
Wegaufnehmer W89
Knoten 46666; entspricht W89 Position
Wegaufnehmer W90
Knoten 52636; entspricht W90 Position
Wegaufnehmer W91
Knoten 58606; entspricht W91 Position
„Lokale“ Ebene
W88W89W90
W91
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Institute of Structural Mechanics 17
direct Sun Radiation
thermal Radiation
Reflected Sun Radiation
Cross SectionFuselage
InsideOutside
Time
Tem
pera
ture
Taxiing Stop Take Off
Thermal ProblemFML’s in future aircraft structures
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Institute of Structural Mechanics 18
Modeling (on panel level)
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Institute of Structural Mechanics 19
Model Verification4 Convergence study with 6 different
discretisations (1 to 36 elements in thickness direction)
4 Homogenisation of smeared layers with:
_ ,
_ ,
/ ( / ) ,
( ) / .out plane i i i normali i
in plane i plane i ii i
k t t k
k k t t
=
= ⋅
∑ ∑∑ ∑
345
350
355
360
365
370
375
380
-2,70
Thickness-Coordinate of skin (mm)
Tem
pera
tur
(K)
layered skin
smeared homogenous skin
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Institute of Structural Mechanics 20
Experimental Test in THERMEX – B test site
Infrared Radiator
Isolation (optional)
Skin
Water
Frame
Stringer
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Institute of Structural Mechanics 21
Validation
20
30
40
50
60
70
0 2000 4000 6000 8000 10000
Zeit (sec)
Tem
pera
tur (
°C) MP43/TE43
MP43_RF1MP34/TE04MP34_RF1MP24/TE09MP24_RF1
Experiment vs. Computation
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Institute of Structural Mechanics 22
Modeling of large fuselage structure
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Institute of Structural Mechanics 23
2D Finite Elements for Thermal Analysis of FML‘s
Motivation
4 Reduction of modeling effort by using 2D geometrical models
4 Reduction of CPU-time
4 Compatible temperature field for thermo-mechanical calculations
Scientific Challenge
4 3D temperature field description based on 2D geometry
4 Shape functions in z-direction
4 2D-3D-Coupling (Connection to local 3D meshes)
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Institute of Structural Mechanics 24
Layerwise Thermal Lamination Theories
Composite structures
3D temperature distribution by 2D finite elements
• Idealisation as layered structure
• Homogenisation of layers including heat conduction, radiation, convection
zt
t
z +d-z
z
N
z=0
11
k
k kk
b
1
k2
•Linear Layered Theory (LLT)
• Quadratic Layered Theory (QLT)
T
T
T
0
0,z
(k)
(k)
(z)Hybrid composite structures
Aluminum sheet
Fiber/resin
Sandwich structuresFace sheet
Honeycombcore
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Institute of Structural Mechanics 25
Assumptions and Prerequisites
convection
conduction
radiation
radiation
equivalent thermal conductivity
conductionconvection
homogenisation
N
12k
b
t1
tk
z
z = 0
z1
zk +dk -zk
approximation by layered construction4 perfect thermal contact at interfaces
4 monolithic conduction within layers
4 no internal heat sources
4 temperature independent material properties
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Institute of Structural Mechanics 26
FE-Formulation(Weak form for heat conduction)
( ) 0ddd =Ω+Γ+Ω ∫∫∫ΩΓΩ
vTvnqTKv ρcgradgrad TT
Boundary conditions
- Convection (Robin)
- Heat flux density (Neumann)
q
q T Tc c= - •a Wandb g
q nT cq q= +
FE-FormulationWeak form for heat conduction
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Institute of Structural Mechanics 27
FE-Formulation(Weak form for heat conduction)
h r a h r h r
a h
T T
zAc
T T T T
zA
cT T
z A c z A
T q
S KS R R R R
R
d d d d d
d
zz z zz
z
+ +
= -•
G
G
G
G
b g
K S KS
S K S
=
=
zz +
=
T
z
k T k k
z
z
k
N
z
zk
k
d
db g b g b ge j1
1
Composite-heat-conduction-matrix Composite-heat-capacity-matrix
( )
C R R
R R
=
=
zz +
=
c z
c z
T
z
k kk T k
z
z
k
N
k
k
d
dr c h b g1
1
FE-FormulationWeak form for heat conduction
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Institute of Structural Mechanics 28
Example: 3D vs. 2D FEA
Number of 3D-elements: 2
Number of 3D-elements: 36
Number of 2D-elements: 1
GLARE skin with 3D finite elements (Nastran)
345
350
355
360
365
370
375
380
-2,70
Thickness-Coordinate of skin (mm)
Tem
pera
tur
(K)
layered skin
smeared homogenous skin
Thermal Lamination Theory (QLT)
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Institute of Structural Mechanics 29
Summary4 Experimental data basis for validation of non linear FEA w.r.t. postbuckling of
stiffened shells under axial loading
4 Investigation of sensitivity w.r.t. to different modeling parameters
4 Excellent agreement between experimental and computational results deep into elastic postcritical regime (global & local)
4 Reliable thermal analysis of FML structures by verification of discretisation through fine 3D model on panel level
4 Validation of thermal panel model by experiments in THERMEX – B test site
4 Application of thermal model to large fuselage structures
4 Description of fast 2D Finite-Element-Formulation
4 Question: How many experiments are needed for validation of a specified parameter space?