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Institute of Structural Mechanics 1

Virtual Testing of Aircraft Structures, considering

Postcritical & Thermal Behavior

J. Temer, R. Degenhardt, A. Kling, R. Rolfes, T. Sprwitz, 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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Reality

Experiment

Computer

Model

Model

Validation

ModelQualification

Model

Verification

Computer

Simulation

Analysis

Programming

Conceptual

ModelModel Validation:

Solve the rightequations

Model Verification:

Solve the equations right

Validation / Verification

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Postcritical behavior of stiffened panels

Top plate

Clamping box

Specimen

Clamping Box

Displacement

pickup

Load distributor

Load cells

Drive plate

Panel in Buckling Test Facility Deformation pattern (ARAMIS)

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Non linear FEM using ABAQUS/Standard

rough

estimate

FE-Model

Linear Eigenvalue Analysis

Buckling Load

Nonlinear Analysis

Newton-Raphson-Method + automatic / adaptivedamping to stabilize the analysis (*STATIC, STABILIZE)

scaled imperfektions

Postprocessing

(Load-Shortening-Curve, deformation of the structure, ...)

Buckling Modes

Real Structure

CFRP-Panel

Measured

Imperfections

rough

estimate

FE-Model

Linear Eigenvalue Analysis

Buckling Load

Nonlinear Analysis

Newton-Raphson-Method + automatic / adaptivedamping to stabilize the analysis (*STATIC, STABILIZE)

scaled imperfektions

Postprocessing

(Load-Shortening-Curve, deformation of the structure, ...)

Buckling Modes

Real Structure

CFRP-Panel

Measured

Imperfections

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Experimental Validatition of computational Analysis is expensive & time consuming

Numerical Pre-Test Analysis

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

discretisationexperimental boundary conditions

initial imperfections

...

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Pre-Test Analysis1. 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]

Load[k

N]

STABILIZE = 2e-4

STABILIZE = 2e-5

STABILIZE = 2e-6

STABILIZE = 2e-7

Nominal data

ABAQUS/Standard

Mesh I (3024 elements)

Tsai Hill

Azzi Tsai HillMaximum Stress

Tsai Wu

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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]

Load[kN]

Mesh I: 3024 elements

Mesh II: 2*3024 elements

Mesh III: 16*3024 elements

Nominal data

ABAQUS/Standard

STABILIZE = 2.e-6

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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]

Load

[kN]

Covered width = 25.0 mm

Covered width = 12.5 mm

Only lateral nodes fixed

Nominal data

ABAQUS/Standard

STABILIZE = 2.e-6


Edge support

Filler

Gliding plane

Test panel

Detail

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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]

Load[kN]

No imperfections

Mode 1, 2% skin thickness



Nominal data

STABILIZE = 2.e-6


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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]

Load

[kN]

ABAQUS/Standard, STABILIZE = 2e-6

ABAQUS/Explicit, v=10mm/s, no damping

ABAQUS/Explicit, v=10mm/s, with damping

Nominal data


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Measurement of geometrical Imperfections (1)

Optical 3D - digitalization

ATOS Sensor strip sequenz

Measurment of real radius vs. nominal radius (ca. 6% deviation)

Measurement of initial imperfection

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Measurement of geometrical Imperfections

Fringe plot w.r.t.perfect shell

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

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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

SkalierteL

ast

ABAQUS/Standard ohne Imperfektionen

ABAQUS/Standard mit Imperfektionen

Lokal skin buckling

Global unsymmetric Buckle

Global symmetric

Buckle

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Validation of FEA (Animation)

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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 4


Skalierte

Last

Experiment (1)

Experiment (2)

ABAQUS/Standard mit Imperfektionen

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-10

-5

0

5

10

15

20

25

0 0,5 1 1,5 2 2,5 3


Radialverschiebu

ng[mm]

Wegaufnehmer W88

Knoten 40696; entspricht W88 PositionWegaufnehmer W89

Knoten 46666; entspricht W89 Position

Wegaufnehmer W90


Wegaufnehmer W91


Validation of computational results

Lokale Ebene

W88W89

W90W91

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directSun Radiation

thermalRadiation

Reflected

Sun Radiation

Cross SectionFuselage

InsideOutside

Time

Temperature

Taxiing Stop Take Off

Thermal Problem

FMLs in future aircraft structures

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Modeling (on panel level)

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345

350

355

360

365

370

375

380

-2,70

Thickness-Coordinate of skin (mm)

Temperatur(K)

layered skin

smeared homogenous skin

Model Verification

Convergence study with 6 different

discretisations

(1 to 36 elements in thickness direction)

Homogenisation of smeared layers with:

_ ,

_ ,

/ ( / ) ,

( ) / .

out plane i i i normal i i

in plane i plane i ii i

k t t k

k k t t

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Infrared Radiator

Isolation (optional)

Skin

Water

Frame

Stringer

Experimental Test in THERMEX B test site

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20

30

40

50

60

70

0 2000 4000 6000 8000 10000

Zeit (sec)

Temperatur(C) MP43/TE43

MP43_RF1

MP34/TE04

MP34_RF1

MP24/TE09

MP24_RF1

Validation

Experiment vs. Computation

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Modeling of large fuselage structure

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2D Finite Elements for Thermal Analysis of FMLs

Motivation

Reduction of modeling effort by using 2D geometrical models

Reduction of CPU-time

Compatible temperature field for thermo-mechanical calculations

Scientific Challenge

3D temperature field description based on 2D geometry

Shape functions in z-direction

2D-3D-Coupling (Connection to local 3D meshes)

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3D temperature distribution by 2D finite elements

Layerwise Thermal Lamination Theories

Idealisation as layered structure

Homogenisation of layers

including heat conduction,

radiation, convection

z

t

t

z +d-z

z

N

z=0

1

1

k

k kk

b

1

k

2

Linear Layered

Theory (LLT)

Quadratic

Layered Theory

(QLT)

T

T

T

0

0 , z

( k )

( k )

( z )

Face sheet

Honeycombcore

Hybrid composite structures

Composite structures

Sandwich structures

Aluminum sheet

Fiber/resin

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Assumptions and Prerequisites

perfect thermal contact at interfaces

monolithic conduction within layers

no internal heat sources

temperature independent material

properties

convection

conduction

radiation

radiation

equivalent thermal conductivity

conductionconvection

homogenisation

N

1

2

k

b

t1

tk

z

z = 0

z1

zk + d

k

-zk

approximation by layered construction

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FE-Formulation

(Weak form for heat conduction)

( ) 0ddd W+G+W WGW

vTvnqTKv &rcgradgrad TT

Boundary conditions

- Convection(Robin)

- Heat flux density(Neumann)

q

q T Tc c - a Wandb g

q nT

cq q +

FE-Formulation

Weak form for heat conduction

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FE-Formulation

(Weak form for heat conduction)

h r a h r h r

a h

T T

zA

c

T T T T

zA

cT T

z A c z A

T q

SKS RR RR

R

d d d d d

d

zz z zzz

+ +

-

G

G

G

G

b g

$K SKS

S K S

z

z+

T

z

kT

k k

z

z

k

N

z

z

k

k

d

dbg bgbge j

1

1

Composite-heat-conduction-matrix Composite-heat-capacity-matrix

$

( )

C RR

R R

z

z+

c z

c z

T

z

k k

k T k

z

z

k

N

k

k

d

dr c h bg1

1

FE-Formulation

Weak form for heat conduction

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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)

Temperatur(

K)

layered skin

smeared homogenous skin

Thermal Lamination Theory (QLT)

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Summary

Experimental data basis for validation of non linear FEA w.r.t. postbuckling of

stiffened shells under axial loading

Investigation of sensitivity w.r.t. to different modeling parameters

Excellent agreement between experimental and computational results deep into

elastic postcritical regime (global & local)

Reliable thermal analysis of FML structures by verification of discretisation throughfine 3D model on panel level

Validation of thermal panel model by experiments in THERMEX B test site

Application of thermal model to large fuselage structures

Description of fast 2D Finite-Element-Formulation

Question: How many experiments are needed for validation

of a specified parameter space?

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