Virtual Testing of Aircraft STructures, considering Postcritical ... - Core

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

Institute of Structural Mechanics

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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


3

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.:


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)

20

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


1

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


8

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

10

0 0

0.5

1

1.5

2

2.5

3

3.5

4


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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


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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


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


1

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

20

Knoten 46666; entspricht W89 Position Wegaufnehmer W90

Radialverschiebung [mm]

15

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


Stringer

20

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


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


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


0

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


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


-2,7


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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