J. TeÃmer, R. Degenhardt, A. Kling, R. Rolfes, T. Spröwitz, S. Waitz. (DLR â Institute of Structural Mechanics, Braunschweig, Germany),. COMPOSIT Thematic ...
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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Validation / Verification Model Qualification
Reality Experiment Model Validation
Analysis
Conceptual Model
Computer Simulation
Computer Model
Model Verification: „Solve the equations right“
Model Validation: „Solve the right equations“
Programming
Model Verification Institute of Structural Mechanics
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Postcritical behavior of stiffened panels Panel in Buckling Test Facility
Deformation pattern (ARAMIS)
Top plate Clamping box
Specimen
Clamping Box Displacement pickup Load distributor Load cells Drive plate
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Non linear FEM using ABAQUS/Standard Real Structure CFRP-Panel
FE-Model
Linear Eigenvalue Analysis Buckling Modes
Buckling Load
scaled imperfektions
Measured Imperfections
rough estimate
Nonlinear Analysis Newton-Raphson-Method + automatic / adaptive damping to stabilize the analysis (*STATIC, STABILIZE)
Postprocessing (Load-Shortening-Curve, deformation of the structure, ...) Institute of Structural Mechanics
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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.:
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panel geometrie discretisation experimental boundary conditions initial imperfections ... 5
Pre-Test Analysis 1. Influence of different STABILIZE parameters 2. Investigation of different failure criteria 80
Tsai Hill Azzi Tsai Hill
70
Maximum Stress
60
Load [kN]
50
Tsai Wu
40
30 STABILIZE = 2e-4 STABILIZE = 2e-5
Nominal data ABAQUS/Standard Mesh I (3024 elements)
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STABILIZE = 2e-6 STABILIZE = 2e-7
10
0 0
0.5
1
1.5
2
2.5
3
3.5
4
Shortening [mm] Institute of Structural Mechanics
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Pre-Test Analysis Convergence study 60
50
Load [kN]
40
Nominal data ABAQUS/Standard STABILIZE = 2.e-6
30
20
Mesh I: 3024 elements Mesh II: 2*3024 elements Mesh III: 16*3024 elements
10
0 0
0.5
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1.5
2
Shortening [mm]
2.5
3
3.5
4 7
Pre-Test Analysis Influence of lateral boundary conditions 100 Detail
90 80
Edge support Filler
Load [kN]
70
Gliding plane
60
Test panel
50 40 30
Nominal data ABAQUS/Standard STABILIZE = 2.e-6 Mesh I (3024 elements)
20 10
Covered width = 25.0 mm Covered width = 12.5 mm Only lateral nodes fixed
0 0
0.5
1
1.5
2
2.5
3
3.5
4
Shortening [mm] Institute of Structural Mechanics
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Pre-Test Analysis Influence of imperfections 60
50
Load [kN]
40 Nominal data STABILIZE = 2.e-6 Mesh I (3024 elements) 30
20
No imperfections Mode 1, 2% skin thickness Mode 1, 10% skin thickness Mode 1, 100% skin thickness
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0 0
0.5
1
1.5
2
2.5
3
3.5
4
Shortening [mm] Institute of Structural Mechanics
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Pre-Test Analysis ABAQUS/Standard vs. ABAQUS/Explicit 60
50
Load [kN]
40 Nominal data Mesh I (3024 elements)
30
ABAQUS/Standard, STABILIZE = 2e-6
20
ABAQUS/Explicit, v=10mm/s, no damping ABAQUS/Explicit, v=10mm/s, with damping 10
0 0
0.5
1
1.5
2
2.5
3
3.5
4
Shortening [mm] Institute of Structural Mechanics
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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 Institute of Structural Mechanics
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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
…
Fringe – plot w.r.t. perfect shell
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Modification of „perfect“ FE – geometry Application of initial imperfection
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Results of FEA using ABAQUS/Standard 2,5
Lokal skin buckling
Skalierte Last
2
1,5
Global „symmetric“ Buckle
1
0,5
ABAQUS/Standard ohne Imperfektionen
Global „unsymmetric“ Buckle
ABAQUS/Standard mit Imperfektionen
0 0
0,5
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1,5
2
Skalierte Verschiebung
2,5
3
3,5
4
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Validation of FEA (Animation)
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Validation of computational results 2,5
„Globale“ Ebene
Skalierte Last
2
1,5
1
0,5
Experiment (1) Experiment (2)
ABAQUS/Standard mit Imperfektionen 0 0
0,5
1
1,5
2
2,5
3
3,5
4
Skalierte Verschiebung Institute of Structural Mechanics
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Validation of computational results 25
Wegaufnehmer W88 Knoten 40696; entspricht W88 Position Wegaufnehmer W89
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Knoten 46666; entspricht W89 Position Wegaufnehmer W90
Radialverschiebung [mm]
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W91 W90 W89 W88
Knoten 52636; entspricht W90 Position Wegaufnehmer W91 Knoten 58606; entspricht W91 Position
10
5
0 0
0,5
1
1,5
2
2,5
3
-5
„Lokale“ Ebene -10 Institute of Structural Mechanics
Skalierte Verschiebung
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Thermal Problem
Cross Section Fuselage
direct Sun Radiation
Temperature
FML’s in future aircraft structures
Taxiing
Reflected Sun Radiation thermal Radiation
Stop
Take Off
Outside Inside
Time
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Modeling (on panel level)
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Model Verification 4 Convergence study with 6 different discretisations (1 to 36 elements in thickness direction) 4 Homogenisation of smeared layers with:
kout _ plane = ∑ i ti / ∑ i (ti / ki , normal ) , kin _ plane = ∑ i (ki , plane ⋅ ti ) / ∑ i ti . 380 375
Temperatur (K)
370 365 360 355
layered skin
350 345
smeared homogenous skin 0
-2,7 Thickness-Coordinate of skin (mm)
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Experimental Test in THERMEX – B test site
Infrared Radiator Isolation (optional)
Fra me Skin Water
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Stringer
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Validation 70
Experiment vs. Computation
Temperatur (°C)
60
MP43/TE43
MP43_RF1
50
MP34/TE04
MP34_RF1
MP24/TE09
MP24_RF1 40
30
20 0
2000
4000
6000
8000
10000
Ze it (se c)
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Modeling of large fuselage structure
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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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Layerwise Thermal Lamination Theories Composite structures
•Linear Layered • Idealisation as layered structure Theory (LLT) • Homogenisation of layers including heat conduction, radiation, convection
Hybrid composite structures
• Quadratic Layered Theory (QLT) T
(z)
N Fiber/resin Aluminum sheet
z z=0
b
Sandwich structures Face sheet
z k +d k tk t1
Honeycomb core
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k 2 1
-z k
(k)
T0 (k)
z1
T 0,z
3D temperature distribution by 2D finite elements 24
Assumptions and Prerequisites convection
radiation
convection
conduction
homogenisation radiation
equivalent thermal conductivity
conduction
4 perfect thermal contact at interfaces
approximation by layered construction
4 monolithic conduction within layers
N
4 no internal heat sources 4 temperature independent material properties
z
zk tk t1
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z=0
b
k 2 1
+dk
-zk
z1
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FE-Formulation FE-Formulation form for Weak form for(Weak heat conduction T ( ) grad v K ∫
grad T d Ω +
Ω
Boundary conditions
heat conduction )
T q ∫ n v dΓ + cρ ∫ T v d Ω =
Γ
Ω
qT n = qc + q
b
- Convection (Robin)
qc = a c TWand - T•
- Heat flux density (Neumann)
q
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g 26
FE-FormulationFE-Formulation (Weak form for heat conduction)
Weak form for heat conduction
z z h
A
T
z
T
T
T
S KS dz r dA + a c h R Rr dG + G
z
z z h
T
T c R R dz r dA
A
z
=
ba T - q gz h R T
c •
T
dG
G
Composite-heat-conduction-matrix
z
z
C = c RT R d z
= S T KS dz K z
N
=Â
ze
zk +1
k =1 z k
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Composite-heat-capacity-matrix
z
j
Sb kg Kb k gSb k g dz T
z
N z k +1
=Â
k =1 zk
c h Rb g dz
ck r k R
(k ) T
k
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Example: 3D vs. 2D FEA
GLARE skin with 3D finite elements (Nastran) 380 375 Temperatur (K)
370 365 360 355
layered skin
350
Number of 3D-elements: 2
smeared homogenous skin
345
Thermal Lamination Theory (QLT)
0
Number of 3D-elements: 36
-2,7
Number of 2D-elements: 1
Thickness-Coordinate of skin (mm)
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Summary 4 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? Institute of Structural Mechanics
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