Virtual Testing of Aircraft STructures, considering ...elib.dlr.de/49104/1/Tessmer_Zaragoza.pdf · Virtual Testing of Aircraft Structures, considering Postcritical & Thermal ... Modeling

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


Validation / Verification

RealityExperiment

ComputerModel

ModelValidation

ModelQualification

ModelVerification

ComputerSimulation

Analysis

Programming

ConceptualModel

Model Verification:„Solve the equations right“

Model Validation:„Solve the right equations“


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


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


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...


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


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


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


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)


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)


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


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


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


Validation of FEA (Animation)


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


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


Wegaufnehmer W90


Wegaufnehmer W91


„Lokale“ Ebene

W88W89W90

W91


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


Modeling (on panel level)


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


Experimental Test in THERMEX – B test site

Infrared Radiator

Isolation (optional)

Skin

Water

Frame

Stringer


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


Modeling of large fuselage structure


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)


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


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


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


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

=

=

zzÂ +

=

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

=

=

zzÂ +

=

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


Example: 3D vs. 2D FEA

Number of 3D-elements: 2



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)


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?

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Virtual Testing of Aircraft STructures, considering ...elib.dlr.de/49104/1/Tessmer_Zaragoza.pdf · Virtual Testing of Aircraft Structures, considering Postcritical & Thermal ... Modeling