ed

wa DLR, Institute of Composite Structures and Adaptive Systems, Lilienthalplatz 7, 38108 Braunschweig, Germany

the design process, the consortiums applied state-of-the-art simulation tools and brought in their own design experience. This paper dealswith the design process as performed within both projects and with the applied analysis procedures. It is focused on the DLR experience

to September 2004, and the 4-year follow-up projectCOCOMAT, which started in January 2004 (cf. Fig. 1),

point of the loaddisplacement curve where a sharpdecrease occurs thus limiting the load-carrying capacity.The POSICOSS team developed fast and reliable proce-dures for post-buckling analysis of bre composite stienedpanels, created experimental data bases and derived designguidelines [1,2,517]. Alternative fast methods were

* Corresponding author.E-mail address: richard.degenhardt@dlr.de (R. Degenhardt).

Available online at www.sciencedirect.com

Computers and Structures 86in the design and analysis of stringer-stiened CFRP panels gained within the scope of these two projects. 2007 Elsevier Ltd. All rights reserved.

Keywords: Collapse; Post-buckling; Composites; Simulation tools; Experiments; Degradation

1. Introduction

The European aircraft industry demands reduced devel-opment and operating costs, by 20% and 50% in the shortand long term, respectively. The European Commission(EC) project POSICOSS, which lasted from January 2000

contribute to this aim [14]. Both projects are under theco-ordination of DLR, Institute of Composite Structuresand Adaptive Systems. The main goal is the exploitationof considerable reserves in primary bre composite fuselagestructures through an accurate and reliable simulation ofpost-buckling up to collapse. Collapse is specied by thatb School of Aerospace, Mechanical and Manufacturing Engineering, Royal Melbourne Institute of Technology, GPO Box 2476V,

Melbourne, Vic. 3001, Australiac Cooperative Research Center for Advanced Composite Structures Limited, 506 Lorimer Street, Fishermans Bend, Vic. 3207, Australia

Received 8 March 2007; accepted 30 April 2007Available online 3 July 2007

Abstract

The European aircraft industry demands reduced development and operating costs, by 20% and 50% in the short and long term,respectively. Contributions to this aim are provided by the completed project POSICOSS (5th FP) and the running follow-up projectCOCOMAT (6th FP), both supported by the European Commission. As an important contribution to cost reduction a decrease in struc-tural weight can be reached by exploiting considerable reserves in primary bre composite fuselage structures through an accurate andreliable simulation of post-buckling up to collapse. The POSICOSS team developed fast procedures for the post-buckling analysis ofstiened bre composite panels, created comprehensive experimental data bases and derived suitable design guidelines. COCOMATbuilds up on the POSICOSS results and considers in addition the simulation of collapse by taking degradation into account. The resultscomprise an extended experimental data base, degradation models, and improved certication and design tools as well as extended designguidelines.

One major task of POSICOSS and COCOMAT is the development of improved analysis tools that are validated by experiments per-formed within the framework of the projects. Because the new tools must comprise a wide range of various aspects a considerable num-ber of dierent structures had to be tested. These structures were designed under dierent objectives (e.g. large post-buckling region). ForDesign and analysis of stienpost-buckling

R. Degenhardt a,*, A. Kling a, K. Roh0045-7949/$ - see front matter 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.compstruc.2007.04.022composite panels includingand collapse

er a, A.C. Orici b,c, R.S. Thomson c

www.elsevier.com/locate/compstruc

(2008) 919929

n))

UR

andeveloped also in parallel to the POSICOSS project [1720].The COCOMAT project builds up on the POSICOSSresults and goes beyond by simulation of collapse. Itimproves existing tools for design and analysis, sets updesign guidelines suitable for stiened panels taking skinstringer separation and material degradation into account,and it creates a comprehensive experimental data base[3,4] concerning such structural components. Another pro-ject was carried out by the Action Group 25 of the Groupfor Aeronautical Research and Technology in Europe(GARTEUR) Structures and Materials panel. It investi-gated three dierent benchmarks with well-documentedbuckling tests in order to identify abilities and decienciesof available analysis tools as well as to establish recommen-dations for buckling, post-buckling and collapse analysis ofthin-walled aerospace structures [21,22]. One of the bench-marks investigated in this GARTEUR activity was taken asa start design for the design process in POSICOSS.

The improved tools, developed within the POSICOSS[814] and COCOMAT project, have to be validated bytest results. Since appropriate test data was not available,

GARTEUR SM-AG-25GARTEUR SM-AG-25

Improved POstbuckling SImulatiofor Design of Fibre COmposite Stiffened Fuselage Structures

Postbuckling and Collapse Analysis

2003200220012000 2003200220012000

POSICOSS (EU, 5th FPPOSICOSS (EU, 5th FP

Fig. 1. Timetable of the EU projects GARTE

920 R. Degenhardt et al. / Computersboth projects were forced to create new experimental databases for curved stringer-stiened carbon bre reinforcedplastic (CFRP) panels as well as for complete cylindricalshells. To that end suitable panels and cylindrical shellswere designed under own project objectives. Some of thetest structures are already manufactured, inspected andtested. Both projects dierentiate between shell structuresfor validation and for industrial application. The valida-tion structures are designed as to specic limiting applica-tion aspects of the software to be validated, e.g. small orlarge stiness reduction in the post-buckling regime. Theindustrial structures were designed with regard to indus-trial applications, mainly by existing procedures used inday-to-day industrial design practice.

For the design and analysis the partners brought in theirown experience and they utilised dierent available soft-ware tools. Two dierent kinds of tools were applied: fasttools suitable for an economic design process and veryaccurate but necessarily slow tools required for the nalcertication. Geometrical nonlinear computations up tocollapse were performed while the material was assumedlinear elastic. The onset of degradation of the structureand of the skinstringer separation was determined usingdierent failure criteria.

This paper is focused on the experience in design andanalysis of stringer-stiened CFRP panels DLR gainedwithin the scope of the POSICOSS and COCOMAT pro-jects. In [3,6,21,23], the authors have already publishedpartly some results presented here. However, this paperadds new data and gives a useful comparative studybetween the outcomes obtained within the dierent projectsGARTEUR SM-AG-25, POSICOSS and COCOMAT.

2. Design of composite panels

2.1. Introduction

Designing a structure always involves some kind of opti-misation. Regardless of the material, kind of structure orapplication, the objective function in this optimisation pro-

COCOMAT (EU,6th FP, STREP)

Improved MATerial Exploitationat Safe Design of COmposite Airframe Structures by Accurate Simulation of COllapse

COCOMAT (EU,6th FP, STREP)COCOMAT (EU,6th FP, STREP)

Improved MATerial Exploitationat Safe Design of COmposite Airframe Structures by Accurate Simulation of COllapse

2007200620052004 2007200620052004

SM-AG-25, POSICOSS and COCOMAT.

d Structures 86 (2008) 919929cess depends on the purpose of the structure. In general,one can distinguish between industrial structures and vali-dation structures. The validation structures are designedas to specic limiting aspects of application of the softwareto be validated, e.g. type of shell theory (design going intothe limits of the theory), type of buckling before post-buck-ling (local or global), mild or strong stiness reduction inthe post-buckling regime, or multiple or single modes ofbuckling before post-buckling. Industrial structures aredesigned with regard to industrial applications, mainly byexisting procedures and requirements used in day-to-dayindustrial design practice. For these structures, there existusually multi-objective requirements concerning weight,load-carrying capacity and costs.

Fig. 2 illustrates a realistic (experimentally measured)load-shortening curve of an axially compressed stienedCFRP panel representing a stringer dominant design. Itexplains the terminology of three marked load levels. Thelowest one usually provokes the rst local buckling where

Realistic curve

Simplified curve

glob

s and Structures 86 (2008) 919929 921the buckling mode is restricted to local skin bucklesbetween the stringers. The second level causes the rst glo-bal buckling which is stringer based-buckling. The highestload level is reached at collapse. The thicker red curve is asimplied representation of the real load-shortening curvewith knees at these characteristic load levels. COCOMATaims at improving design capabilities by accounting forthe complete load-shortening behaviour up to collapse.This paper concentrates on the description of the designprocess as performed within the EC projects POSICOSSand COCOMAT. The structures considered are curvedstringer-stiened panels and cylinders made of CFRPmaterial. Within each project a large number of structureswere designed. Because the maximum number of tests waslimited only designs appropriate under the manufacturing

1st global (stringer-based) buckling

1st local buckling

Collapse load Loa

d

1st global (stringer-based) buckling

1st local buckling

Collapse load Loa

d

Fig. 2. Denition of rst local and

R. Degenhardt et al. / Computerand testing conditions were selected. The new test resultsbuild a large experimental data base, which is necessaryfor the validation of the new tools developed to simulatethe buckling and post-buckling behaviour up to collapse.Two kinds of tools are considered: reliable fast tools reduc-ing design and analysis time by an order of magnitude,which allow an economic design process, whereas veryaccurate but in most cases necessarily slow tools arerequired for the nal certication. For the industrial appli-cability, these tools must be on the one hand validated byappropriate experiments and on the other hand their appli-cability must be proven on real industrial panels.

Sections 2.3, 2.4 and 2.5 describe the design process ofDLR as partner within the projects POSICOSS and COC-OMAT. It starts with a description of a benchmark fromthe GARTEUR Action Group 25 which was taken as astart design for the POSICOSS structures. Then the designprocess within the POSICOSS project is described. Thepanel design within COCOMAT builds up on the experi-ence on POSICOSS and is described nally. Section 2.2gives a comparison of the material properties and geomet-rical data used for all panel designs.2.2. Geometrical and material data of the panel designs

This section comprises the material properties andgeometrical data used for all panel designs described inSection 2. Table 1 contains material properties for the pre-preg material IM7/8552 UD, which was used throughout,Table 2 gives material properties for the adhesive, whichconnects the skin with the stringers, Table 3 comparesnominal geometrical data, Fig. 3 shows the dierent strin-ger types used in the test and their nite element (FE) mod-elling with the connection to the skin and Fig. 4 gives theassumed boundary conditions.

2.3. Start design

ShorteningShortening

al buckling load and collapse load.The design of the POSICOSS structures started outfrom the results of a pre-damaged benchmark, which wasformerly tested at DLR. This benchmark was intensivelyinvestigated within the GARTEUR SM Action Group 25Postbuckling and Collapse Analysis [21,22] and at the

Table 1Material properties for CFRP prepreg IM7/8552 UD

Stiness Unit GARTEUR AG25(start design)

POSICOSS COCOMAT

0 tensilemodulus

GPa 192.3 164.1

90 tensilemodulus

GPa 10.6 8.7

0 compressionmodulus

GPa 141 146.5 146.5

90compressionmodulus

GPa 11 9.7 9.7

In plane shearmodulus

GPa 6.3 6.1 5.1

Poisson ratio 0.3 0.31 0.28

beginning of the POSICOSS project and will be subse-quently detailed.

As depicted in Fig. 5, the benchmark represents an axi-ally compressed CFRP panel consisting of a skin withnominally cylindrical shape and stiened by T-shapedstringers. The stringers were partially separated from the

skin by impacting prior to the tests. The damaged areaswere measured by ultrasonic inspection to introduce theminto the FE model for an accurate numerical simulation.Finally, the panel was axially compressed until collapse.

Dierent commercial and self-developed nite elementtools were applied to simulate the behaviour of this panelduring loading up to collapse. Linear and nonlinear analy-ses as well as buckling analyses were performed in order toobserve the axial stiness in the pre-buckling region, thebuckling loads of the panel and the structural behaviourin the post-buckling region. A major challenge of thisbenchmark was the simulation of the damaged regionthrough contact elements. Furthermore, a considerablenumber of parameters like skinstringer connection, strin-ger ange modelling, number of nite elements, damping,

Table 2Material properties of the adhesive Redux 312 [24]

Stiness/strength Unit Value

E1 MPa 3000m12 0.4Max. compressive stress MPa 48Max. shear stress MPa 38Max. normal stress MPa 8.3

Table 3Nominal geometrical data and lay-up for the panel designs

Nominal geometry/lay-up GARTEUR AG25 (start design) POSICOSS COCOMAT

Panel 1/3 Panel 2/4

Panel length (mm) l = 800 l = 780 l = 780Free length (buckling length) (mm) lf = 620 lf = 740 lf = 660Radius (mm) r = 400 r = 400 (1000) r = 1000Arc length (mm) a = 419 a = 420 a = 560Number of stringers n = 6 n = 3 n = 4 n = 5Distance stringer to stringer d = a/6 d = a/6 d = a/8 d = 132 mmDistance stringer to longitudinal edge e = d/2 e = d/2 e = f/2 = 16 mmLaminate set-up of skin [90,+45,45,0]s [+45,45,0]s [90,+45,45,0]sLaminate set-up of stringers (cf. Fig. 3)Blade [(+45,45)3,06]sFlange cf. Fig. 3 [(45,45)3,06]

Ply thickness (mm) t = 0.125Stringer height (mm) h = 14 h = 14Stringer width (mm) f = 37.9 f = 32

3 mmTest

922 R. Degenhardt et al. / Computers and Structures 86 (2008) 919929

FE-model with skin-stringer connection

GARTEUR AG 25 / POSICOSS

Fig. 3. Stringer types o

COCOMAT

12.5 mm 14 mm

32 mm f the panel designs.

rs anGeneral

Lateral edges

Edge support

Fille

Gliding plane

Test panel

clamped

R. Degenhardt et al. / Computerimperfections, loading velocity, boundary conditions,numerical method or kind of nite elements were investi-gated. Fig. 5 illustrates some load-shortening curvesobtained by numerical simulations of the undamagedpanel. As a main result it turned out that all FE softwaretools considered were suitable in general for the simulationof buckling, post-buckling or collapse behaviour of suchpanels. Specic abilities and deciencies of the nite ele-ment tools were evaluated. Recommendations with respectto the inuence of parameters, the initial buckling load, theconvergence behaviour, the simulation of load introductionand boundary conditions as well as the imperfection sensi-tivity were derived.

In order to check the inuence of the pre-damage thisbenchmark was also analysed with damage ignored. Itturned out that this undamaged panel has almost noreserve capacity in the post-buckling region because itslocal skin buckling load is very close to the global stringer

GARTEUR AG 25 / POSICOSS

Fig. 4. Boundary conditions. (For interpretation of the references to colour in

0

20

40

60

80

100

120

140

160

180

0.0 0.5 1.0 1.5

Shorten

Load

[kN]

Fig. 5. Finite element analyses of the undamaged

25 mm

Detail

Blue: Rigid body (loaded edge) Green: Fully fixed

Red: Party fixed (free in axial direction) Yellow: (see row below)

free

d Structures 86 (2008) 919929 923buckling load. This is due to a rather skin-dominantdesign. Since under the design objective large post-buck-ling region such a design represents a highly undesirablecase this undamaged panel was taken as a start designfor the POSICOSS project.

2.4. Design process within POSICOSS

The main design objective within POSICOSS was toobtain a signicant post-buckling area before collapse.DLR aimed to design four panels and two complete cylin-drical shells that should be suitable for software validationpurposes. The undamaged benchmark described in the pre-vious section has almost no post-buckling region and inthat sense represents a highly undesirable design. It wastherefore taken as a start design, which was then modiedin the following way in order to increase the load-carryingcapacity in the post-buckling range (cf. Fig. 2):

COCOMAT

this gure legend, the reader is referred to the web version of this article.)

2.0 2.5 3.0 3.5 4.0

ing [mm]

DLR, ABAQUS/Explicit Karlsruhe, FEAP, 3D elements Karlsruhe, FEAP, 2D elements QinetiQ, LUSAS Samtech, SAMCEF Test 67

DLR benchmark taken as start design [21].

(1) For the rst cylinder design, the number of stringerswas reduced to trigger the local buckling at a lowerlevel and to increase the load-carrying capacity inthe post-buckling region.

(2) In the second cylinder design, in addition to thereduced number of stringers, the 90-layers of theskin were removed in order to increase the sensitivi-ties to torsion loading. The radius of both cylinderswas xed to 400 mm due to testing constraints.

(3) For the purpose of comparison, the panels should beas similar as possible to the cylinders. Therefore, therst two panel designs were taken as 60 sectionsfrom the cylinder designs.

(4) Two additional panel designs were dened that dierfrom the rst two, only by an increase in the radiusfrom 400 mm to 1000 mm in order to examine theinuence of the radius and to get closer to the real air-craft fuselage structures.

This design process resulted in four dierent stienedpanels and two dierent complete cylindrical shells as illus-trated in Fig. 6. Except for one panel, which has the small-est post-buckling region, all designs were manufactured,some of them two or three times each in order to increasethe reliability, and were tested at the DLR buckling testfacility until collapse. Fig. 7 illustrates the comparison ofthe test and simulation of one tested panel. It can be seenthat the panel design has a large post-buckling region asit was planned. There is a good agreement between simula-tion and test up to the rst global buckling. From thatpoint on the dierences become larger. However, becausedegradation is not considered within that simulation a bet-ter agreement in the deep post-buckling region is notexpected. In addition, the modelling of the boundary con-ditions for the clamping of the lateral edges of the panelshowed a large inuence on the axial stiness in the post-buckling region after the rst global stringer buckling.

sig

lize 2

lize 2on (2

924 R. Degenhardt et al. / Computers and Structures 86 (2008) 919929Fig. 6. POSICOSS de

0

20

40

60

80

100

120

0 0.5 1 1.5 2

Axi

al lo

ad [k

N]

Experiment P12

ABAQUS/Standard, Stabi

ABAQUS/Standard, Stabibuckling-mode-imperfecti

First ply failure by Tsai-WuShorte

Fig. 7. (Color online) POSICOSS design panns (DLR, cf. Fig. 3).

2.5 3 3.5 4 4.5

e-6, 20mm boundary

e-6, 20mm boundary, with0%)ning [mm]

el P12 comparison test and simulation.

More details are given in [5]. Considering degradations aswell as additional investigations to applied longitudinaledge conditions are topics of the project COCOMAT.

2.5. Design process within COCOMAT

To simulate accurately the collapse load of stringer-sti-ened CFRP panels the COCOMAT group improves slowcertication tools and fast design tools that are capableof taking degradation into account. The group considersthe following degradation modes: skinstringer separation,delamination in the stringer blade and degradation on thecomposite structure itself. For the validation of the toolsan appropriate experimental data base is not available(the POSICOSS test data base could only be taken as abaseline because degradation was not considered duringthe project). Therefore new curved stringer-stiened CFRPpanels, which shall be manufactured and tested, weredesigned. As in POSICOSS, the group designed two kinds

process the onset of dierent kinds of degradation, suchas skinstringer separation, delamination in the stringerblade and failure in the composite laminate structure havebeen estimated by simple extension of the available soft-ware tool. In order to check the inuence of degradationon collapse the panels with a large post-buckling regionand the indication of skinstringer separation (failure inthe adhesive layer) as early failure mode were favoured.

There was another important change of Design 1 incomparison to the POSICOSS design. For Design 1, theclamping boundary conditions of the lateral edges of thepanel, which were applied on all POSICOSS experiments,were released because the modelling of these boundaryconditions showed a signicant inuence on the axial sti-ness in the post-buckling region after the rst global strin-ger buckling (cf. Fig. 7). However, in order to avoid skinbuckling starting in that laterally free area the stringerswere moved in circumferential direction to the lateraledges. In addition, dierent designs were analysed in order

adhe

R. Degenhardt et al. / Computers and Structures 86 (2008) 919929 925of panels: validation panels and industrial panels. Being aresearch establishment DLR concentrated to design onevalidation panel which is called Design 1 in the following.The objective was to accomplish a large post-bucklingregion and an early onset of skinstringer separation.

The design process for Design 1 started with a panelconguration with a radius of 1000 mm tested within POS-ICOSS. The objective was to increase the post-bucklingregion further, especially to have a certain load capacityafter the rst global buckling. The reason is that the inu-ence of skinstringer separation on the collapse loadshould be investigated and this kind of degradation usuallyoccurs after the rst global stringer buckling. Several para-metric studies for the variation of the lay-up of the skin andstringer, number of stringers, stringer geometry and posi-tion of the stringers were performed. During the design

0

20

40

60

80

100

120

140

0 0.5 1 1.5

Load

[kN]

Start desi gn

Design 1

1st failure in the adhesive

POSICOSS panel

First estimated failure in theShorten

Fig. 8. (Color online) Load-shortening curve of the COCOMAT pto ensure that the onset of skinstringer separation starts inthe middle stringers and not in those at the edges.

On the basis of structural and fracture mechanics anal-yses one design (Design 1) was selected as being the mostsuitable for the experimental investigation into degradationand collapse of stiened composite panels. Fig. 8 illustratesthe load-shortening curve of this design in comparison to aPOSICOSS design. Design 1 exhibits a large post-bucklingregion, even after the rst global stringer buckling whichstarts in the center of the panel.

3. Analysis of composite panels

For the design of the panels, described in the previoussection, the FE software ABAQUS/Standard (Abaqus)was applied. Geometrical nonlinear computations with an

2 2.5 3.5 43

Design 1 sive ing [mm]

anel design in comparison to the start design from POSICOSS.

incremental iterative NewtonRaphson method with arti-cial damping (stabilize-method) up to collapse were per-formed. The material is linear elastic. In order to modeldegradation DLR developed Abaqus user subroutines,which consider the skinstringer debonding using stress-based failure criteria.

3.1. Nonlinear nite element analysis without degradation

To analyse the pre- and post-buckling behaviour of thepanels the four-node shell element S4R of Abaqus has beenused. Fig. 9a depicts some details of the FE model (e.g.spring elements, which have been applied to introducethe stiness of the longitudinal edge supports in the com-puter model of the POSICOSS project).

The approach to conduct the FE analysis consists basi-cally of four stages (Fig. 9b): The preprocessing, a lineareigenvalue analysis to extract buckling modes, which aresubsequently used as initial imperfections in the nonlinearanalysis utilising the built-in NewtonRaphson techniquewith adaptive/articial damping, and nally the postpro-cessing. This nonlinear solution method has been provento be relatively stable for the considered stringer-stienedpanels. Figs. 7 and 8 depict the loaddisplacement curves,which have been obtained by utilising the analysis proce-dure described in Fig. 9b with and without initial geometricimperfections.

The validation of the numerical simulation is performedby a comparison with experimental results on the so-calledglobal and local level. On the global level of valida-tion the overall load-shortening as well as the full scaledeformation patterns are compared. Fig. 10 shows such acomparison of buckling patterns obtained by experimentand simulation. The experimental data was obtained usingARAMIS a 3D-optical measurement system based onphotogrammetry. On the local level measurements fromstrain gauges are considered and compared to numericallycalculated strains. Details to this concept can be found in[6]. Fig. 7 shows a comparison of the load-shorteningcurves of simulation and experiment of the POSICOSSpanel P12 [5]. Up to the rst global buckling load a verygood agreement can be observed. From that point the sim-ulation and experiment begin to dier. There are two expla-

926 R. Degenhardt et al. / Computers and Structures 86 (2008) 919929roughestimate

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

Spring-elements

Fig. 9a. Details of the FE model (POSICOSS).Fig. 9b. Analysis procedure in Abaqus.nations for that. Firstly, no degradation is taken intoaccount, so in the deep post-buckling region a good agree-ment cannot be expected. Secondly, the high sensitivity ofthe modelling of the lateral clamping boundary conditionshas most probably caused the starting of divergence shortlybefore global buckling.

The objective for the design of the panels within COC-OMAT was a large post-buckling region and an early onsetof skinstringer debonding. At that stage of the project notools were available that could take this kind of degrada-tion into account. However, for the design process it is suf-cient to know when degradation starts. As a work-aroundthe available tool Abaqus was utilised in following way. Todetermine the onset of degradation of the composite lam-ina structure itself failure criteria that are available in Aba-qus (e.g. Tsai-Wu and Tsai-Hill) were applied. Theadhesive, which connects the skin with the stringers, wasmodelled with 3D solid elements (cf. Fig. 3). The occur-rence of the maximum allowable stress in the adhesivewas taken as indication for the onset of degradation.Detailed results can be found in [23]. The load-shorteningand failure predictions in Fig. 8 were calculated using thisapproach. One can see that the onset of skinstringer deb-Fig. 10. Out-of-plane deformations of one tested POSICOSS panel atidentical load levels.

the Abaqus analysis with the user subroutines shows agood agreement with the experiment. However, it mustbe noted that it is not sucient to compare only theload-shortening curve, because the global buckling patternof the simulation and experiment are dierent. In addition,the subroutines predicted more damaged adhesive areasthan observed in the experiment. Fig. 14 illustrates thedamaged areas for the connection between skin and string-ers after the collapse test. It was obtained by ultrasonicinspection (left) and the optical lock-in thermographywhich show a good agreement between each other.Fig. 13 shows the numerical simulation of failure propaga-tion of the adhesive layer at four load levels of Fig. 12 [25].The comparison with the experimental result of Fig. 14with the simulation in Fig. 13 shows that within the simu-lation too many adhesive elements failed. This demon-strates that further improved degradation models as

process.

Fig. 12. (Color online) Comparison of experiment and dierent simula-tion tools [23].

s anonding almost coincided with the beginning of global strin-ger buckling. This behaviour is plausible and was expectedbecause the onset of stringer buckling causes also signi-cantly higher stresses in the adhesive layer.

3.2. Nonlinear nite element analysis with degradation

One main task of the COCOMAT project is to improveslow certication tools. Within this task DLR concentrateson the improvement of Abaqus in order to allow for skinstringer separation. To solve this problem the adhesivelayer between skin and stringer is modelled using 3D niteelements. The mechanical behaviour of these elements isdescribed by means of new self-developed Abaqus usersubroutines. Three user subroutines are developed, whichdier in their numerical approach. At this stage they usesimple stress-based failure criteria. However, it is possibleto implement more enhanced and probably more accuratedegradation models in two of the three subroutines. WithinCOCOMAT new degradation models, which are based onexperimental investigations, are currently developed and itis planned to implement them into the subroutines. Thethree subroutines can be described as follows:

(1) User Dened Field (USDFLD): Allows dening onlysimple failure criteria, which reduce selected materialproperties.

(2) UMAT explicit: The stresses are calculated from theprevious increment results explicitly. It has theadvantage to control the failure propagation andthe degradation of the adhesive layer.

(3) UMAT implicit: The stresses are calculated from thecurrent stiness matrix implicitly. This version wasalso extended for nding the rst element failing ineach increment. This increases the analysis timedramatically.

The position of the user subroutines within the Abaquscalculation process is given in Fig. 11. The last two usersubroutines allow for monitoring the propagation of thefailure in the adhesive and the implementation of compli-cated user-dened degradation models. As a rst approach,a simple stress-based failure criterion for the adhesive wasimplemented into all three user subroutines. The degrada-tion of the adhesive is simulated by decreasing the Youngsmodulus to a small fraction of the initial value for thosenite elements for which the maximum allowable stress(cf. Table 2) is reached.

All three user subroutines were tested and compared onsmall and large models and showed a good agreementbetween each other. The application of one user subroutineon the COCOMAT panel Design 1 and the comparisonwith the experiment and other software tools without deg-radation is shown in Fig. 12. This gure illustrates theload-shortening curve of Design 1. Up to the rst global

R. Degenhardt et al. / Computerbuckling at about 1 mm shortening, it shows an excellentagreement between all curves. From that point on onlyStart of increment

Calculate

Start of iteration

USDFLD

UMAT explicit / implicit

Calculate integration point field variable from nodal values

Define loads:

Calculate ,

Fig. 11. Position of the user subroutines within the Abaqus calculation

d Structures 86 (2008) 919929 927under current development within COCOMAT areneeded.

an928 R. Degenhardt et al. / Computers4. Summary and conclusions

This paper illustrates the design process and the experi-ence gained at DLR on stringer-stiened panels and cylin-ders through the work done in the nished EU projectPOSICOSS and the running EU project COCOMAT.The FE tool Abaqus was applied for the design processand is extended by means of self-developed user subrou-

Fig. 13. (Color online) Numerical simulation of failure propaga

Fig. 14. (Color online) Ultrasonic aw echo (left) and thermographic (right) intest.d Structures 86 (2008) 919929tines that simulate the order of degradation of the skinstringer separation. The numerical calculations have beensuccessfully validated with experimental data up to the rstglobal buckling. For the simulation of the deep post-buck-ling region degradation must be taken into account. HereAbaqus user subroutines were developed, which considerstringer debonding using simple stress-based failure crite-ria. First application of the Abaqus user subroutines

tion of the adhesive layer at four load level of Fig. 12 [25].

vestigation visualising damages mainly between skin and stringer after the

yielded promising results. However, improved degradationmodels which are currently under development within theCOCOMAT project are needed. It can be expected thatthis design and analysis experience will be of advantagefor the design of future composite fuselage structures.

Acknowledgements

The nished project POSICOSS was supported by theEuropean Commission, Competitive and SustainableGrowth Programme, Contract G4RD-CT-1999-00103.The running project COCOMAT is supported by the Euro-pean Commission, Priority Aeronautics and Space, Con-tract AST3-CT-2003-502723. The information in this

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[11] Rikards R, Abramovich H, Auzins J, Korjakins A, Ozolinsh O,Kalnins K, et al. Compos Struct 2004;63(2):24351.

[12] Gal E, Levy R, Abramovich H, Pavsner P. Buckling analysis ofcomposite panels. Compos Struct 2006;73(2):17985.

[13] Lanzi L, Giavotto V. Postbuckling optimisation of compositestiened panels: computations and experiments. Compos Struct2006;73(2):20820.

[14] Rikards R, Abramovich H, Kalnins K, Auzins J. Surrogate model-ling in design optimisation of stiened composite shells. ComposStruct 2006;73(2):24451.

[15] Rikards R, Abramovich H, Green T, Auzins J, Chate A. Identica-tion of elastic properties of composite laminates. Mech Adv MaterStruct 2003;10(4):33552.

R. Degenhardt et al. / Computers and Structures 86 (2008) 919929 929paper is provided as is and no warranty is given that theinformation is t for any particular purpose. The readerthereof uses the information at its sole risk and liability.

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Design and analysis of stiffened composite panels including post-buckling and collapseIntroductionDesign of composite panelsIntroductionGeometrical and material data of the panel designsStart designDesign process within POSICOSSDesign process within COCOMAT

Analysis of composite panelsNonlinear finite element analysis - without degradationNonlinear finite element analysis - with degradation

Summary and conclusionsAcknowledgementsReferences