thermal analysis of hybrid composite structures

25th INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES

THERMAL ANALYSIS OF HYBRID COMPOSITESTRUCTURES

Jan Tessmer*, Tom Sproewitz*, Tobias Wille**DLR, Institute of Composite Structures and Adaptive Systems, Structural Mechanics,

Lilienthalplatz 7, 38108 Braunscheig, GermanyPhone: +49-(0)531-295-2288, FAX: +49-(0)531-295-2232

Keywords: thermal analysis, thermal testing, finite element analysis, hybrid structures, validation

Abstract

A strategy for accurate, efficient and economicthermal investigation of hybrid composite struc-tures by means of the Finite Element Method(FEM) will be presented. It includes test predic-tion, validation tests, validation analysis, and anindustrial application. Drawbacks of commercialsoftware codes are identified and current researchwork for the solving of these disadvantages arepresented.

Nomenclature

a diffusity coefficient [m2/s]c heat capacity [J/kgK]h convection [W/m2K]q heat flux [W/m2]t layer thickness [m]v fluid velocity [m/s]A cross section [m2]H height [ f t]L characteristic length [m]P Power [W/s]T temperature [K] or [◦C]α convection heat transfer [W/m2K]ε infrared emissivity [−]λ thermal conductivity [W/mK]η efficieny [−]ρ density [kg/m3]σ Boltzman constant 5.67 ·10−8W/m2K4

Λ solid heat transfer coefficient [W/mK]

1 Introduction

In design and development of aircraft structuresrequirements like enhancement of safety, clean-liness and stiffness as well as reduction of mass,fuel consumption, production and manufacturingcosts, to name a view, are major issues for basicconceptual decisions. Though the ways to copewith these problems can be manyfold there aretwo specific topics that are pursued in industrywhich are also subject to resent research workat the German Aerospace Center (DLR) Instituteof Composite Structures and Adaptive Systems.These are:

1. increased usage of composite materialsin a wide range of structural parts of air-frame structures for weight reduction

2. reduction of development costs by min-imizing the amount of experimental test-ing –especially for large scale structures–based on reliable simulation abilities.

In this context the meaning of composite ma-terial must not only be understood as common fi-bre reinforced epoxy but also as hybrid materialslike sandwich constructions with different facesheet and core materials or fibre-metal-laminates(FML) as glas fibre-aluminum reinforced epoxy(GLARE). In general these materials are char-acterized by superior stiffness properties in con-junction with a lower specific density comparedto conventional isotropic materials. They further-more allow for a design of stiffness properties

1

JAN TESSMER*, TOM SPROEWITZ*, TOBIAS WILLE*

depending on their specific field of application.Together with these favourable mechanical mate-rial properties under normal environmental con-ditions comes their strong dependence on the ex-isting temperature niveaus, which can range from−50◦C ≤ T ≤ 100◦C or worse. At low tempera-tures the matrix systems may become brittle andas temperatures rise near transition temperaturethe mechanical properties are deteriorating no-tably. Critical thermal loadcases which may havemajor influence on the mechanical performanceof an aircraft structure are e.g.:

• aircraft parking and taxiing in hot ambientenvironment and under sun illuminationprior to take-off,

• warming near air conditioning system heatexchangers in the center wing box,

• failure of pneumatic or hydraulic systems,• fire events.

The temperature field is also very important forthe evaluation of stresses induced by thermal ex-pansion. This concerns not only hybrid structuresas such but also the complete airframe structureas common aircrafts are made of a mixture ofboth conventional isotropic and composite mate-rials. To ensure a safe operation of airframe struc-tures in service thermal issues must be addressed.Hence, it is mandatory to know the temperaturefields that are likely to occure throughout the dif-ferent missions as accurate as possible. In theearly design process the only way to gain nec-essary thermal data is by analytical or numericalsimulations of the different missions that are re-quired for the certification of airframe structures.

Numerical simulation techniques are alsokey components for a reduction of developmentcosts. So far a high amount of expensive testsand numerical validation analyses was neccesaryfrom small material specimens to full scale struc-tures. But as computer resources and simulationtechniques are improving it is possible to simu-late a great variaty of scenarios –which classi-cally were subject to testing– with such an accu-racy and speed that cost and time expensive testscan be saved. In Fig. 1 there is shown the future

tendency of effort put to testing and simulation independence on the specimen size and complexity.

Testing Simulation

Effort

Full Scale

Specimen and Substructures

Today

Tomorrow

Fig. 1 Test and simulation effort vs. structure size

In order to save development costs by favour-ing simulation tools instead of testing it is envis-aged to validate the numerical methods by meansof small scale material or substructure tests forparameter identification. Therefore high effortshall be put to both experimental testing and val-idation analyses. As the size of structures in-creases the amount of tests shall be reduced andthe structural behavior will mainly be analyzedby means of reliable simulation techniques. Thefuture aim shall be the radical reduction of ex-pensive full-scale experimental testing by simu-lation called virtual testing. The whole processmust be reliable and standardized in a way that itwill get agreement from the certification authori-ties and can be introduced as standard procedurein the design and development process. Fig. 2shows a principle procedure for validation of sim-ulation tools to predict the behavior of the struc-ture to be designed. To allow for a broad fieldof safe application using the above mentionedmaterials and to ensure the abidance to the highaircraft safety standards an accurate an effectivethermal analysis and thermal loads prediction ismandatory [1].

2 Procedure for reliable application of vir-tual testing

As mentioned above the general procedure startswith investigations on material specimen or sub-structure level. Necessary modelling assump-

2

THERMAL ANALYSIS OF HYBRID COMPOSITE STRUCTURES

Reality

Experiment

Computer

Model

Model

Validation

Model

Qualification

Model

Verification

Computer

Simulation

Analysis

Programming

Conceptual

Model

Fig. 2 Simulation tools validation procedure

tions and parameters will be identified and ver-ified by test correlation analyses. On basis ofthe determined information the simulation of thenext lower dicretization level can be conducted.A principle procedure for the evaluation of makroscale behavior by means of micro scale results isdepicted in the flow chart in Fig. 3. The thermalinvestigation of a FML fuselage section will begiven as a practical example in the following sec-tion.

Substructure/coupon test prediction

validation tests

test correlation, validation

full scale prediction analysis

Fig. 3 Virtual testing process flow-chart

First step in a general procedure is to definethe lowest unit which has to be investigated tobe able of simulating the structure of interest. Inmany cases this part can also be called unit cellsince mostly it resembles a regularly or periodi-cally recuring part. A test prediction analysis onthis unit gives necessary information for the de-sign of an adequate test set-up for the subsequent

verification tests. Based on the results gainedfrom the experiments, test correlation analyseswill be performed in order to get a parameter setthat allows for an exact reproduction of the struc-tural behavior. This step can be realized withdifferent approaches which can also be based onhomogenization strategies. The following threepossible strategies are common in thermal engi-neering but do not cover all possibilities:

(a) geometrically and physically unchangedVerification analyses are conducted on ageometrically and physically detailed unitcell model under consideration of possi-ble symmetric boundary conditions. Un-changed usage in the global analysis wherethe global model is mainly composed fromduplicated unit cells.

(b) geometrically unchanged, physically ho-mogenizedVerifcation analyses are conducted on a ge-ometrically detailed unit cell model. Phys-ical properties are homogenized like equiv-alent thermal properties of laminated com-posites. The global model will be mod-elized from duplicated unit cells [2].

(c) geometrically and physically homoge-nizedVerification analyses are conducted on ageometrically and physically detailed unitcell model. After homogenization of ge-ometrical (e.g. modelling of pourous me-dia as solids) and physical properties ap-plication to a simplified global model byduplicating the unit cells. Ideally the re-sults from the homogenized model shouldbe equal to the detailed analysis. [3]

From the list above it becomes already clearhow the results from the unit cell investigationcan be used for the analysis of a global structure.The choise of the applied procedures and the ac-curacy of the verification analysis are decisivefor the quality of the global results. Especiallythe application of a homogenization requires agood knowing about the structural characteristics

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and in most cases it also requires a high numberof parameter studies and validation tests. How-ever it enables the thermal analysis of full scalestructures with reasonable effort in modelling andcomputational resources.

The necessity of using homogenization tech-niques in thermal analysis is caused by a great va-riety of different problems. It can be performedto simplify certain heat transfer mechanisms butit can also be done to use specific simulationtools. Throughout the present work the thermalanalysis is conducted by using the FEM. There-fore all problems concerning simulation matterswill be related to this method. Some homoge-nization applications and the origin of their ne-cessity will be described hereafter.

Considering the combination of mechanicaland thermal analysis in the design process bymeans of the FEM, it would be very helpfull touse only one FE model for both. For thin-walledstructures the mechanical analysis is usually per-formed using 2D shell elements. In thermal anal-ysis however these elements do not allow to cal-culate the transverse temperature gradient. Thiscan be a fatal neglection especially when appliedto thermally bad conductors or sandwich struc-tures. Therefore solid elements are normally usedfor such applications where every single layer hasto be dicretized by at least one element. Thisnecessarily leads to very large numerical mod-els and hence requires very much computationaltime. By applying a homogenization to the ther-mal material properties it is possible to predictthe temperature profile of such a structure withonly one or two solid elements in thickness direc-tion as will be shown in the industrial applicationexample. This corresponds to point (b) of the listabove. The explained problem can also be over-come by using new FE formulations where shellelements can predict the transverse heat conduc-tion problem as will be shown in section 4.

Another field of application is the homog-enization of geometrically complex structureswhich regularly or periodically recure. Theyneed a high modelling and computational effortwhen applied to large structures. In order to re-duce necessary resources the structure can be ho-

mogenized in a way that it can be resembled bysimple formulations whithout loosing to much in-formation. This corresponds to point (c) of thelist above.

At last it shall be mentioned that for specificapplications, like aircrafts which have tremen-dous amounts of rivited joints, the joints can betreated best when homogenized. This field can ofcourse be enlarge to spot welded or glued jointsor other kinds of thermal contact zones.

Having dealt with all these problems the val-idation of the simplified model can be conductedand the results can directly be applied to a struc-ture of the next higher or even full scale level.

3 Industrial application example

3.1 Basic concept for thermal analysis offuselage structures

This work aimed at the predicition of temperaturefields in the skin-stringer-frame system of an air-craft fuselage section made from FML (GLARE).Herein the take-off with its high mechanicalloads after a heating phase (parking, taxiing, andhold) is considered to be a critical mission part.For an exact prediction it will be focused on heattransfer between skin, stringer and frames whichhave a crucial influence on the global thermal be-havior. These parameters have so far been treatedvery conservatively and may give opportunitiesfor a further structural optimization. All investi-gations to gain knowledge about the thermal be-havior will be performed on panel level and willsubsequently be applied to a fuselage section un-der take-off environmental conditions.

3.2 Test prediction and homogenization

Based on the test panel geometry, thermal loads,and the way of the load application, test predic-tion analyses were performed by means of theFEM. The results are important input for the finaldesign of the test facility e.g. position of thermo-couples. In Fig. 4 there is shown an illustrationof a typical aircraft panel which is to be inves-tigated. It consists of a GLARE skin as well asaluminum frames and stringers. All interfaces are

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glued and the frames are connected to the skin us-ing binders and rivited joints. The GLARE skinitself is composed of 5 layers of aluminum and 4layers of glas-fibre reinforced polymer (GFRP) inan alternating lay-up. Each GFRP layer consistsof a 0◦ and 90◦ sublayer, forming an orthotropicmaterial.

Fig. 4 Test panel

In order to keep the modelling effort as smallas possible symmetry characteristics were con-sidered. The smalest unit from geometrical pointof view as shown in Fig. 4 is an eighth of thepanel. Taking into account the relative size of testspecimen and infrared radiator, as can be seen inFig. 5, it could be proven by means of FE anal-yses that the panel is not homogeneously illumi-nated on its complete surface. This is due to thefinite dimensions of the radiator leading to differ-ing heat flux densities which decrease from thecenter to the outside edges of the test specimen.Therefore a quarter panel was used for all subse-quent analyses.

Convergence studies wrt. the discretizationlevel were conducted aiming on a further reduc-tion of the model size. At this instance sim-plified boundary conditions were applied to thestructure. They merely consist of radiation ex-change between the panel exterior and radiatoras well as the environment and forced convectiondue to the convectional cooling of the radiatorbulbs. The radiator is modelled as an ideal blackemitter with ε = 1, which emits 1000W/m2.This is an approximate heat flux q on zero alti-

xz

y

Panel

StrahlerInfrared Radiator

Fig. 5 Test panel unit structure

tude near the equator [4]. From this the radiatortemperature can be calculated using the Stefan-Boltzman-Law as follows:

Tradiator = 4√

q/σ · ε (1)

For the consideration of the convection a friction-less fluid on a parallel blown plate is taken intoaccount. With Equ. (2) it is possible to roughlyestimate the forced convection coefficient [4].

α = 2 ·λ√

vπ ·a ·L

(2)

Since the fluid stream impinges the specimen onthe whole surface and flows off to all four edgesthe characteristic length L is chosen to be half thetotal specimen length. All remaining surfaces onthe test specimen are considered to be adiabatic.

The discretization level in transversal and lat-eral direction of the skin, which is composed oflayered material, was closely investigated on astrip model of a part of the panel. In lateral di-rection three exact 3D models with either 1, 2or 4 solid elements per layer were compared tothree homogenized models with either 4, 2 or 1element over the whole laminate thickness in or-der to enable a reduction of elements in materialthickness direction. Aim of the lateral discretiza-tion investigation is the reduction of elements inradiation exchange analysis which is in generala very time-consuming process. In this case thefinest 3D model with 9 elements per layer was

5


compared to two reduced models with 4 or 2 el-ements over the whole laminate thickness. In or-der to do so a homogenization of material proper-ties was necessary. The conductivity in transver-sal direction is dealt as a series connection asshown in Equ. (3) and in lateral direction as par-allel connection which can be seen in Equ. (4).

λtransvers =n

∑i=1

ti

/n

∑i=1

ti/λi,tansvers (3)

λlateral =n

∑i=1

λi,lateral · ti

/n

∑i=1

ti (4)

Additionally for transient studies the density andthe heat capacity have to be homogenized. Incase of the density the averaging is made in de-pendence on the layer thicknesses:

ρ =n

∑i=1

ρi · ti

/n

∑i=1

ti (5)

and in case of capacity in dependence on arealmasses:

c =n

∑i=1

ci ·ρi · ti

/n

∑i=1

ρi · ti (6)

where i is a control variable and n is the num-ber of layers in the material. As a result Fig. 6shows the transversal temperature distributions inthe skin for the finest 3D model with 4 elementsper single layer and the homogeneous model with2 elements over the laminate thickness. This ho-mogeneous model still shows slight deviations tothe exact panel. The accuracy is in the same orderof magnitude as for the model with 4 elementsover the laminate thickness. The maximum errorcan be estimated to be in the range of 3− 4K inthe most critical part near the stringer foot. Byusing only one element over the laminate thick-ness the accuracy is not satisfactory so that for allfurther analysis the skin is modelled with 2 ele-ments over the thickness. The results in lateral di-rection do not show a high dependence on the dis-cretization level such that it can be varied slightlyaround the once investigated in this study.

345

350

355

360

365

370

375

380

-2.70

Thickness-Coordinate of skin [mm]

Te

mp

era

ture

[K]

layered skin

smeared homogenous skin

Fig. 6 Transversal temperature profile for differ-ent discretization levels

Based on all the above mentioned studies sta-tionary and transient thermal analyses were per-formed on the quarter panel in order to under-stand the thermal behavior of the panel while test-ing. Hereby the calculations were conducted withall variations of the following parameter values:

ε = 0.7, 0.85, 0.99,

Tradiator = 370K, 390K, 410K and

α = (0.0, 5.0, 10, 100)W/m2K.

3.3 Experimental testing

All validation tests were conducted on thethermo-mechanical test facility THERMEX ofthe Institute of Composite Structures and Adap-tive Systems of the DLR in Braunschweig. Inprinciple it allows for a simultaneous applicationof thermal and mechanical loads. It is there-fore well suited for investigations of thermallyinduced stresses with or without additional me-chanical load cases. Even thermal buckling phe-nomena are a field of application for this kindof test facility. Fig. 7 gives an impression of aTHERMEX test set-up as used for the FML panelexperiments. In this case the heater is mountedabove the test specimen and a water basin for theapplication of boundary conditions is located be-low the panel. For better understanding a draw-ing of the principle test set-up is depicted inFig. 8. On the left side the two different inves-tigated boundary conditions on the back side ofthe panel are shown. One is completely insulated

6


Fig. 7 THERMEX - thermo-mechanical test facility

leading to almost adiabatic conditions. In the se-cond set-up the ends of the frames are in con-tact with permanently stirred water. In this way itrepresents a very good conductor and a high ther-mal capacity. The right side of Fig. 8 shows thefour investigated different illumination schemes,which are realized by covering the to be protectedareas with insulation plates.

Fig. 8 Test set-up and illumination scheme

In order to investigate the heat transferthrough the panel and heat transfer resistances atcontact zones between FML and aluminum partsthe full illuminated test specimen would be ap-propriate. For the investigation of inplane heattransfer of the panel, the partially heated surfacesare better suited. A test panel without insula-

tion blankets is shown in Fig. 9. All test data arerecorded with the DIADEM 10.0 data acquisitionsoftware. It includes 39 thermocouples on skin,stringer and frames as well as 1 heat flux sensoron the skin.

Fig. 9 Glare test panel with stringers and frames

3.4 Test correlation analysis

Based on the test prediction with its convergencestudies and test results a validation is conductedin order to validate the panel FE model for aglobal analysis on fuselage level. For this reasonthe so far used model needs to be refined. Thediscretization itself will be unchanged but in thecontact zones between skin-stringer, skin-binderand frame-binder additional solid elements wereintroduced to account for the adhesive layer be-tween these structural parts. This layer resem-bles a thermal insulator and must therefore betaken into account. From experience it can besaid that such contact zones are decisive for theglobal thermal behavior of such structures. De-pending on the adhesive layer and the existenceof rivets at the connections different heat transfercoefficients Λ were derived for a constant adhe-sive element thickness of 0.5mm. They are in therange of 2.0W/mK ≤ Λ ≤ 12.3W/mK.

The validation analysis was conducted usingone specific test which gives best opportunitiesfor a proper derivation of all crucial parameters.Boundary conditions to be considered were cho-sen as in the test:

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1. radiation heat flux between radiator andtest specimen is estimated from the elec-trical power of the radiator:

Tradiator = 4

√η ·Pel

ε ·σ ·Aradiator(7)

2. measured heat flux through insulation pan-els for illumination control

3. radiation heat flux between specimen backside and water surface by using an effectiveemissivity of the back surface:

1/εe f f = 1/εwater +1/εback (8)

4. fixed temperature boundary conditions onthe contact between stringer ends and wa-ter surface

In the validation analyses the following pa-rameters have been varried: contact resistances,thermo-optical properties of the test panel, radi-ator heat flux and homogenized thermal conduc-tivity of the skin. At the end a set of parameterswas determined that in global gives very promiss-ing results. The deviations to the measured re-sults are ≈ 6K at maximum. For three measure-ment points the corralation curves are shown inFig. 10. Attention was paid that all results in hotareas are conservative in the sence that they over-predict the measured data. The influence of thecontact resistances was checked by varying theirvalues by one order of magnitude. This showedmoderate changes in the overall thermal behav-ior. However the neglection of the contact zoneswould lead to temperature deviations of morethan 40K.

3.5 Full scale analysis

After having developed a validated FE model ona representative FML panel, the aim of this taskwas to analyse the thermal characteristics of acomplete fuselage section during parking, taxi-ing and take-off. Since the heat fluxes within thestructure along the airplane longitudinal axis are

20

30

40

50

60

70

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Zeit (sec)

Tem

pera

tur

(°C

)

MP43 Measured

MP43 Simulated

MP34 Measured

MP34 Simulated

MP24 Simulated

MP24_RF1

Fig. 10 Comparison of validation tests againsttest correlation results

considered to be negligible the problem can be re-duced to a representative sector. This sector con-sists of one frame with the two half correspond-ing skin sections and the stringers over the fullcircumference. The boundary conditions on thesector edges are adiabatic.

To create this section, 128 panel models haveto be connected. The size of a single panel, al-though reduced, is still high and would lead toa very big global model. Therefore a furthermodel reduction is necessary. Since the top partsof the fuselage, which are under direct sun illu-mination, are in the focus of the study all otherparts are again simplified. They incorporate skinand stringer conductivity in one effective con-ductivity such that the panels in the bottom sec-tion consist only of the frame and a homogenizedskin definition. Furthermore all relevant bound-ary conditions for such a mission were taken intoaccount. There are:

• direct solar heat flux• convection heat exchange with air• heat exchange with hot runway• reflected solar heat flux from runway• heat flux through insulation into the aircraft

interior

In Fig. 11 there are shown the given profiles ofvelocity, temperature, altitude and convection co-efficient during parking, taxiing and take-off forthe first 480 seconds of a flight mission. Based on

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this input a transient thermal analysis was con-ducted and the temperature histories in the FMLpanels were determined. A typical temperature

Fig. 11 Take-off profiles of velocity v, Tempera-ture T , Altitude H and Convection h

distribution in skin, stringer and frame right be-fore take-off can be seen in Fig. 12. In this con-text it should be noted that the temperatures aredecreasing from the middle of the skin field overthe binder to the top of the frames. After take

Fig. 12 Fuselage temperature profile accross oneframe

off the skin fields are cooled down very rapidlyby forced convection such that the temperaturedistributions will qualitatively be inverted. Thisbecomes clear when looking at the temperature-time history in Fig. 13. The numbering of thenodes in the diagram is in a straight line from the

skin field center over the binder to the frame asalready considered this way above. It should alsobe noticed that the decrease of the temperaturein the panel already starts 60 sec before take-off.Here the change of the airplane orientation be-tween taxiing and take-off has also been consid-ered.

Fig. 13 Temperature distribution in take-off en-vironment

These predictions are valuable input for thedesigners work. They are enabled by the valida-tion of the simulation tools on small scaled struc-tures. By means of this example a conceivableprocedure for virtual testing can be demonstrated.

4 Approaches for effective thermal modelingand analysis

4.1 Efficient thermal analysis

At the present time mechanical FE simulationsof thin walled structures are conducted by meansof 2D elements, which are suitable for most ap-plications. To gain a fully 3D temperature fieldhowever a 3D discretization is necessary so far.This poses one main problem in simulation:The usage of only one FE model for both analy-sis tasks mechanical and thermal is not operable.Very often it demands the modification of the me-chanical mesh and a geometrical and physical ho-mogenization of the model parameters. Further-more an increase of the model size and computa-tional time is often a direct result of these model

9


changes. Up to now this is not automated to anextent that is adequate for current design tasksand needs further development.

With the thermal lamination theory (TLT) oneapproach has been presented by Rolfes [5] withfurther developments by Noack [6, 7]. Appliedto the FEM it allows to analyse hybrid compositestructures as FMLs with layerwize varying ther-mal conductivities.

By assuming a perfect thermal contact at thelayer interfaces the TLT describes a linear orquadratic temperature distribution in each singlelayer depending on the approach. Nonlinear tem-perature distributions are likely to occur in tran-sient problems with rapid heating or cooling, un-der concentrated thermal loads or for large tem-perature gradients in conjunction with tempera-ture dependent material properties.

The application of equilibrium conditions atthe layer interfaces for temperature and heat fluxin transverse direction for linear TLT and addi-tionally the change of heat flux for quadratic TLTmakes the number of functional degrees of free-dom independent of the number of layers. Thetemperature of layer k, T (k), can then be ex-pressed by means of the temperature of a refer-ence layer b, T (b), as shown in Equ. (9) for linearand Equ. (10) for quadratic TLT where z̃k and ˜̃zkare functions of the thickness coordinate z.

T (k) = T (b)0 + z̃k(z)T

(b)0,z (9)

T (k) = T (b)0 + z̃k(z)T

(b)0,z +˜̃zk(z,z2)T b

0,zz (10)

Based on these theories, FE elements are devel-oped using linear shape functions in lateral direc-tion.

To demonstrate the performance of these ele-ments they have been applied to the FML con-vergence studies from section 3.2 with slightlysimplified boundary conditions. The exact 3Dmodel with 4 elements per layer and the homog-enized model with 2 elements over the materialthickness are used for the comparison with onequadratic QLT element. Fig. 14 gives an impres-sion of the effectiveness of this element formula-tion. Although there are slight differences, the re-sults are in very good agreement and the compu-

345

350

355

360

365

370

375

380

-2.70

Thickness-Coordinate of skin [mm]

Te

mp

era

ture

[K]

layered skin

smeared homogenous skin

Thermal Lamination Theory (QLT)

Fig. 14 Comparison of fully 3D and homoge-nized simulation with thermal lamination theory

tational effort can be reduced by orders of mag-nitude. Using these elements would also improvethe mesh compatibility between mechanical andthermal analysis.

4.2 Heat transfer in joints and interfaces

As already pointed out in the previous sections,thermal interface parameters (rivets, bolts, spotwelds or adhesive) can be decisive for the qual-ity of the analysis predictions. In many casesit is necessary to homogenize the thermal con-tact area since an exact modelling of these zoneswould be very complex and the model size wouldget out of limits very easily. In order to gainmore knowledge, preliminary investigations wereconducted on spot welded and/or glued connec-tions as shown in Fig. 15. In order to limit the

Fig. 15 Thermal contact investigation examples

number of boundary conditions, namely convec-tion, these tests were carried out in the thermal-vacuum investigation facility (see Fig. 16). It issuitable for thermal testing of structures undertechnical vacuum. In this specific case the testresults were also used for the validation of the

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Testbox

Vacuumcontainer

Radiator

Fig. 16 Thermal radiation investigation chamber

numerical methods in order to simulate the tran-sient temperature distribution in manufacturingprocesses of hybrid sheet metal structures.

5 Conclusions and outlook

The paper outlines a general procedure for the es-tablishment of virtual testing in thermal analysisof composite and hybrid structures. It is madeclear by an industrial application example; theanalysis of a fuselage section made from FML,based on experimental testing on panel level. Inthe course of this presentation problems of nu-merical simulation like the necessity of homog-enization, the modelling of interface zones orthe transferability of mechanical and thermal FEmeshes are discussed. An approach for the solv-ing of the latter problem was explained. It isbased on the development of new 2D finite ele-ments which allow the calculation of a 3D tem-perature distribution. Furthermore the work givesan outline on the used test facilities which enablethe investigation of a wide range of thermal trans-fer phenomena.

In the presently used FE software for thermalanalysis the consideration of free and forced con-vection is very rudimentary. Here it should befocused on multi-disziplinary solving of designtasks by incorporating fluid-dynamics solvers.For a better application of the above describedextented 2D finite elements, interface elementsshall be developed in order to easily connect thin-

walled structures to geometrically complex struc-tures.

It seems that although more and more com-posite and hybrid materials are used in aircraftstructures, the dependence of the mechanical be-havior on thermal loadcases is still underesti-mated. A higher sensitivity to the thermal analy-sis problems is recommended in the early designphase.

References

[1] R. Rolfes, J. Tessmer, K. Rohwer. Models andTools for Heat Transfer, Thermal stresses, andStability of Composite Aerospace Structures,Thermal Stresses, Vol. 26, Nr. 6 (2003), pages641–670

[2] J. Tessmer. Thermalanalyse von Rumpf-bauteilen, Internal Report, DLR (2002)

[3] T. Sproewitz, J. Tessmer, R. Rolfes. Thermalhomogenization of perforated sandwich struc-tures for space antennas, in: F. Ziegler, R.Heuer, C. Adam, Proceedings of the 6th Inter-national Congress on Thermal Stresses, Vol. 2,pages 791-794, Vienna (2005)

[4] Baehr, Stephan. Wärme- und Stoffübertragung,3. Edition, Springer 1998

[5] R. Rolfes. Higher order theory and finite el-ement for heat conduction in composites, inR.W. Lewis, J.H. Chin, G.M. Homsy, Numeri-cal methods in thermal problems, Proceedingsof the Seventh International Conference, Vol.VII (1991), pages 880-889

[6] J. Noack. Eine schichtweise Theorie und Nu-merik für Wärmeleitung in Hybridstrukturen,Dissertation, FB Maschinenbau, TU Braun-schweig, Shaker Verlag, Aachen (2000)

[7] J. Noack, R. Rolfes, J. Tessmer. New layerwisetheories and finite elements for efficient thermalanalysis of hybrid structures, Computers andStructures, Vol. 81 (2003), pages 2525–2538

[8] J. Tessmer, S. Waitz, R. Rolfes, J Ackva, T.de Vries. Thermal analysis computation and ex-perimental validation of fiber metal laminates,Proceedings of the 5th International Congress ofThermal Stresses, Blacksburg, USA (2003)

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thermal analysis of hybrid composite structures

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