Virtual Testing of Aircraft Structures

ORIGINAL PAPER

Virtual testing of aircraft structures

Morten G. Ostergaard • Andrew R. Ibbotson •

Olivier Le Roux • Alan M. Prior

Received: 28 April 2010 / Revised: 23 March 2011 / Accepted: 30 May 2011 / Published online: 26 July 2011

� Deutsches Zentrum fur Luft- und Raumfahrt e.V. 2011

Abstract This paper will focus on the prediction of air-

craft structural strength using virtual testing analysis

methods. Virtual testing is a concept with several attributes

and is to be understood as the simulation of aircraft

structure using advanced nonlinear finite element analysis.

It will involve the combination of analysis software,

methods, people skills and experience to predict the actual

aircraft structural strength with a high level of confidence.

This is achieved through the creation and execution of a

detailed nonlinear finite element analysis model of an air-

craft structure, which represents as accurately as possible

the actual physical behaviour when subjected to a wide

range of loading scenarios. Creating a virtual representa-

tion of an aircraft structure presents the analysts with

several significant challenges, including the creation of the

complex finite element model that accurately represents the

global aircraft structure, and then adding the significant

detail in terms of material and construction required to

make accurate failure predictions with confidence. An

overview will be provided of the general principles used in

the process of virtual testing of both metallic and com-

posite aircraft structures. The paper will focus on the key

challenges and enablers for future successful virtual testing

demonstrations in an industrial context.

Keywords Virtual testing � Aircraft structures �Non-linear analysis � Strength predictions � Industrial

requirements � The wishbone analysis framework

1 Introduction

Historically, the use of structural analysis in commercial

aircraft design and certification has been focussed on linear

finite element analysis for the calculation of internal load

distributions and on the use of analytical stressing methods,

both for initial sizing and then more detailed calculations

for final certification. This stressing approach, when com-

bined with structural testing both to demonstrate the air-

craft structure integrity and to demonstrate the adequacy of

stressing methods, has proven itself to be highly reliable in

the development of safe aircraft structures.

The above approach is based on demonstrating the

adequate strength of the aircraft structure, which is ensured

through conservative assumptions in both the methods and

material properties used.

In recent years, advanced nonlinear analysis methods

have been used increasingly to obtain more accurate

assessments of the actual strength of aircraft test structures,

both for risk mitigation prior to test and subsequent to a

failure event [1]. Nonlinear finite element analysis has been

employed with great effect to increase confidence in the

large-scale and expensive structural tests that are required

before certification, as well as to understand in more detail

the likelihood, causes and consequences of structural failure.

There is an important distinction between predicting

actual and adequate structural strength. For the design and

M. G. Ostergaard (&) � A. R. Ibbotson

Airbus in the UK, Bristol BS997AR, UK

e-mail: [email protected]

A. R. Ibbotson


O. L. Roux

Airbus in France, 31060 Toulouse Cedex 9, France


A. M. Prior

Dassault Systemes Simulia Limited, Warrington WA3 7PB, UK


123

CEAS Aeronaut J (2011) 1:83–103

DOI 10.1007/s13272-011-0004-x

certification of aircraft structures, adequate and conserva-

tive strength assumptions must be employed, irrespective

of the methods used; whereas, for predictions of the actual

strength of an aircraft structure, the analyst must make use

of methods that are as accurate as possible.

Due to the highly competitive nature of the aircraft

manufacturing industry and the need to meet customer

expectations in terms of efficiency, aircraft structures are

highly optimised for weight and strength.

Most of an aircraft structure is typically constructed of

thin-walled stiffened panels. Predicting the strength and

failure mode of such structures which, especially for

metallic structures, are often designed to allow buckling,

presents the analyst with many challenges. Failure can

occur due to buckling alone, but it is usually the conse-

quences of buckling that can lead to critical failure modes in

joints and materials and interactions between these failures.

In addition to the complex design and nonlinear defor-

mation behaviour of the aircraft structure, the analyst is also

faced with the problem of understanding and analysing both

metallic and composite aircraft constructions, where each

new type of material presents new and different challenges

with respect to detailed failure predictions [2, 3].

The increased use of composite materials has presented

the analyst with a raft of new difficulties, largely due to the

highly complex failure modes of composite materials and

associated adhesive joints [4]. The analysis of composite

materials has undoubtedly also increased awareness of the

many uncertainties that can exist in component manufac-

ture, uncertainties which may significantly affect the reli-

ability of actual strength predictions based on analysis

methods. It is inevitable therefore that today composite

structures are designed with more conservatism than

metallic aircraft structures.

Advanced nonlinear analysis has in recent years been

used very successfully to predict the actual strength of

metallic and composite aircraft structures in Airbus.

Examples of detailed nonlinear finite element models of

composite fuselage and wing box structures are shown in

Figs. 1 and 2.

To provide a structured overview of virtual testing, the

following topics will be discussed in the following

sections:

(a) Best practice in virtual testing

(b) Analysis software

(c) Multi-scale analysis

(d) Composites

(e) Modelling details and structural idealisations

(f) Detailed failure predictions

(g) Analysis framework for virtual testing using nonlin-

ear analysis

(h) Implicit and explicit finite element methods

(i) Robust analysis

(j) A380 wing certification

(k) Summary

The principles outlined in this paper will be illustrated

using the A380 wing certification experience, where

advanced nonlinear finite element analysis was used suc-

cessfully in the process to certify the wing structure. More

recent models used to support Airbus aircraft programmes

will illustrate today’s best practice in Airbus and the rapid

and organic evolution in the nonlinear analysis technology

made possible through innovative approaches and

improved software and hardware capabilities.

2 Best practice in virtual testing

Finite element models used for virtual testing can be

extremely complex. The application of best practice is

therefore paramount in order to instil confidence at all

levels. The analyst must be confident in the methods and

software being used; the principal FEA engineer must be

confident in the skills, expertise and experience of the

analysts; and the aircraft manufacturer (and ultimately the

Airworthiness Authorities) must be confident that the vir-

tual testing approach is valid and safe and therefore can be

used for the purpose of demonstrating the actual strength of

the aircraft structure.

In principle, confidence must be ensured in all of the

following three areas:

1. analysis software,

2. methods and analysis processes,

3. people skills and experience.

It might be argued that the most important of these

confidence factors is the skills, expertise and experience of

people, without which the process would not work and the

detailed analysis understanding could not be gained.

However, the functionality of the analysis software is also

critical and confidence must exist in the methods and

analysis processes used.

The analysis software must be both capable and feature

rich to enable the analyst to predict actual strength for a

wide range of potential failure modes. In addition, the

solver must be highly efficient, given the tendency in

recent years towards increasingly large analysis models.

Computations running over several days on high-perfor-

mance computing platforms are now commonplace.

It is of fundamental importance, and an airworthiness

authority requirement [5], that the analysis methods and

processes used have been fully validated against test data

from similar aircraft structures and materials. As for con-

ventional stressing techniques, the methods used for virtual

84 M. G. Ostergaard et al.

123

testing based on nonlinear analysis must also be demon-

strated to provide accurate predictions of actual behaviour

for various levels of structural testing, from component or

system level (e.g. wing or fuselage sections), to detailed

coupon level (e.g. material specimens and fasteners).

In order to build confidence, the nonlinear finite element

methods must be fully validated against test data at all

levels of the testing pyramid. For virtual testing purposes,

where actual strength predictions are considered, a close

correlation between methods and test data must be

demonstrated.

It should be noted that virtual testing is and always will

be an approximation to reality. Actual aircraft structures

will always have imperfections in materials, variations in

manufacturing processes, and a range of assembly toler-

ances that will give rise to built-in stresses and variability

in stiffness and strength. Composite materials, in particular,

can exhibit significant variability in the actual lay-up and

Fig. 1 Detailed nonlinear FE

model of composite fuselage

structure

Fig. 2 Detailed nonlinear FE

model of composite wing box

structure

Virtual testing of aircraft structures 85

123

quality of the laminate. These variabilities lead to uncer-

tainty regarding the actual response of the structure. Tests

on several identical physical structures would not result in

identical results.

In a virtual testing program, however, uncertainty and

variability need to be added—they do not arise naturally.

For virtual testing of a baseline structure, such as a Type

Certificate Aircraft, the analysis model would normally be

constructed to the nominal geometry and property; sub-

sequent strength assessments should then take into account

the likely variation in properties and construction.

Analytical or conventional stress analysis methods are

usually based on a set of assumptions with respect to

structural behaviour, loading and constraint systems. These

assumptions make conventional methods less flexible, and

less able to reflect the details of the actual structural design.

They also require that the results are treated as approxi-

mations with a degree of conservatism.

The progression to detailed and advanced nonlinear

finite element methods has allowed some of that conser-

vatism to be addressed. Modern finite element analysis

methods are general-purpose and highly flexible.

By validating the fundamental modelling and analysis

methods, (i.e. the idealisation principles and the models for

materials and joints), these ‘building blocks’ can be used to

construct full models of most types of aircraft structure. The

validation of numerical models of materials and structures

at detailed structural levels is more efficient and less costly

than validating against more complex structural tests.

This means that less validation against actual test data will

be required at complex and large-scale structural levels than

is the case for analytical methods. This is one of the most

important advantages of advanced nonlinear finite element

analysis compared to conventional stressing methods.

A significant challenge in the coming years will be to

validate all aspects of virtual testing methods against all

levels of structural testing, from coupon to component and

full aircraft scales. This validation will need to address the

increased levels of structural complexity and the full range

of materials in use today and in the near future.

The objective should be to increase progressively the

level of confidence in virtual testing methods, to the extent

that they can be used for reliable up-front predictions of

structural testing and, ultimately, can be considered for use

in the certification of aircraft structures.

This will only be possible through the continued appli-

cation of best practice principles.

3 Analysis tools

The virtual testing methods and simulations discussed and

presented in this paper are carried out using the Abaqus

products (Abaqus software, Dassault Systemes SIMULIA,

Providence, USA). The tools allow for a wide range of

nonlinear finite element analysis, which means that simu-

lations can include nonlinear material responses (plasticity,

damage and failure), nonlinear boundary conditions (con-

tact), and nonlinear geometric effects (stress-stiffening,

large rotations and displacements).

The majority of analyses are carried out using the

implicit FE method, which provides an incremental-itera-

tive solution to a quasi-static loading problem. There are

some applications where explicit solutions are appropriate,

such as transient dynamic events, including birdstrike,

debris impact and crash, though these are carried out less

frequently. There are advantages in offering both implicit

and explicit solvers with the same model definition used for

both analysis techniques for complex failure simulations of

static test structures.

The direct solver technology provided with Abaqus/

Standard has improved significantly in recent versions and,

today, the direct sparse solver remains the standard solution

for this type of finite element model. The thin-walled,

stiffened structure common to modern aircraft is prone to

buckling and also exhibits highly nonlinear material

behaviour together with rapid changes in both geometry

and boundary condition due to mechanical contact. Direct

solvers have proven to be more effective than iterative

solvers for the solution of this type of ill-conditioned

system.

4 Multi-scale analysis

In the context of virtual testing of aircraft structures, the

term multi-scale analysis describes the process of sequen-

tially coupling different analysis models at different scales

and levels of fidelity.

This multi-scale approach requires a Level 1 prediction

of the behaviour of the complete structure through a non-

linear finite element model. This is then used to define the

driving boundary conditions for the next models at the

more refined modelling scales, as illustrated in Fig. 3.

Modelling detail is increased as successive analyses

‘zoom in’ on structural regions, identified as being poten-

tially strength-critical. At each level of model refinement,

different modelling idealisation principles, element types

and even material and joint models might be employed.

However, the underlying principle is to maintain a con-

sistent interface and link between the different modelling

scales used. All modelling and analysis methods used must

be fully validated against structural testing. It is important

to understand that, unlike traditional modelling techniques,

where direct links between model scales are provided using

built-in detail meshes or super-elements, the multi-scale


123

analysis process discussed in this article are based on sub-

modelling technology available in the Abaqus software.

This technology enables model data to be transferred

between modelling scales through a parent–child type

relationship, enabling far-reaching future opportunities for

integration of CAD and CAE processes.

It is important that the Level 1 model is nonlinear.

Previous work using a linear Level 1 model has shown that

the assumptions and approximations inherent in the linear

approach will not provide a sufficiently accurate base level

from which to launch more detailed nonlinear analysis

models.

In principle two different approaches exist:

(a) The analysis zooms in on predetermined structural

zones that are then modelled to the required detail

(such as in the A380 wing example). The purpose of

the global model is purely to provide the definition of

boundary conditions for lower scale models.

(b) The high level analysis results, using the Level 1

model, are used to predict zones of interest for more

detailed analysis, so that at each modelling scale the

results are screened in order to identify regions for

subsequent strength analysis.

Both approaches have advantages and disadvantages.

The first (predetermined) multi-scale analysis approach

can be used only where the critical area of interest is fairly

well known, but can benefit from a relatively coarse Level

1 model. However, the coarser the Level 1 model, the

bigger the lower scale sub-models must be to ensure that

the correct loading is applied to the area of interest. This

approach is also of use when the Level 1 model is used to

define input data to other simulation techniques such as

parametric modelling or analytical methods.

However, from a virtual testing point of view, it is the

second approach that has by far the most significance.

For this approach, it is not necessary to have a prede-

termined understanding of the critical structural response;

instead, screening methods are applied to the analysis

results in a systematic process in order to identify the

critical structural regions to be analysed subsequently in

more detail.

A fundamental requirement for this analysis approach is

that the Level 1 model must be capable of predicting the

overall nonlinear behaviour and have sufficient detail to

calculate the local nonlinear behaviour, such as panel

buckling, nonlinear deformation due to structural eccen-

tricities, and locations of joint failure. The geometrical size

of a family of sequentially refined sub-models used within

the multi-scale analysis process is directly linked to the

accuracy of the Level 1 model. As a general guideline, the

structural domain covered by these must ensure that

the interfaces between the Level 1 model and subsequent

sub-models are sufficiently away to avoid influencing the

accuracy of analysis predictions. This is a particular con-

cern where the analysis objective is to predict the propa-

gation of structural damage and failure. Here the analyst

must ensure that local stiffness change due to local damage

and failure propagation does not invalidate the sub-mod-

elling analysis process.

This presents a very significant challenge to the analyst,

the analysis software, and the computational resources.

Fig. 3 Multi-scale analysis

processes


123

5 Composites

For composite aircraft structures in particular, it is impor-

tant to consider the uncertainties introduced as a result of

manufacturing processes. Many of the failure mechanisms

that occur in composites are so localised that it is not

possible to capture them at a global model scale. Engi-

neering judgement and best practice is therefore required.

In addition, the manufacturing processes used today will

introduce variability in the composite lay-ups in terms of

resin/fibre volume fractions, ply waviness, resin pockets,

inconsistent adhesive layer thicknesses, etc. Such factors

must be considered in the analysis either through the

imposition of conservative assumptions or the use of

‘robust analysis’ methods. These particular aspects of

composite construction methods mean that the accurate

prediction of the strength of composite structures will

remain a significant challenge for many years to come.

New advanced constitutive models for laminated com-

posites which include coupled damage and failure capa-

bilities are being developed and may provide a framework

for the screening process for material failure at global

model scale.

Material models available today that are based on

physical composite failure modes and fracture mechanics

principles are computationally too expensive for use at

most model scales, but are necessary for the accurate

simulation of complex failure modes at lower scale levels,

where they can be used to consider through- thickness

failure and in-plane interaction modes.

The maturity of reliable composite failure modes for all

modelling scales and, in particular, for detailed failure

predictions, is still to be demonstrated.

The following example (Fig. 4) illustrates the use of

screening processes to check for interfacial forces in

adhesive joints between stringers and skins in a detailed

virtual testing process applied to a composite wing struc-

ture. This enables areas with high interface forces in the

adhesive joints to be identified so that more refined analysis

can be carried out. The adhesive joints are modelled using

the cohesive contact capability and the fasteners are

modelled using the mesh-independent fastener feature

available in Abaqus/Standard.

6 Modelling details and structural idealisations

The importance of the detailed modelling techniques to be

used, even at the Level 1 modelling scale, must not be

underestimated: successful simulation in a virtual testing

framework is entirely dependent on the way the structure is

modelled and how the interactions between structural parts

are represented.

The finite element model must represent as closely as

possible the actual structure being investigated, and all

approximations and idealisations must be carefully

considered.

For example, it is not sufficient to make an accurate

representation of the in-plane stiffness of an aircraft panel:

the local and global torsion and bending stiffness of the

panel must also be represented accurately. For local

buckling to be predicted, it is essential that the support

provided by stringers to suppress skin buckling is modelled

accurately. For metallic aircraft structures, it is therefore

necessary to include fasteners (including pre-tension) and

mechanical contact in order to accurately simulate

Fig. 4 Use of Abaqus cohesive

contact modelling


123

buckling. To some extent, composite structures that are

adhesively bonded are easier to model and to analyse,

because the bonds can be represented using geometrical

constraints or cohesive contact models.

It is the responsibility of the analyst to fully understand the

level of certainty associated with a given strategy to be used

for the idealisation and modelling of an aircraft structure.

Existing constraints on solvers and high-performance

computing mean that there is always a compromise

between model refinement and analysis efficiency. At one

extreme the mesh might be too coarse to capture any useful

response, and at the other the model may be too large to run

on even the largest computers.

The analyst must therefore deploy a consistent and well-

understood strategy for meshing and modelling all the

standard aircraft structures that will be encountered, so that

the solution of the large-scale and multi-scale analysis

program can be completed effectively.

Numerous studies must be carried out to fully define the

best practice for modelling these structures. The best

practice will define the types of element to be used, the use

of element off-sets, the use of structure mid-planes for

meshing, the number of elements in part segments such as

stringer webs, flanges and between stringers.

For virtual testing of large-scale aircraft structures it is

essential to ensure that such best practice is followed pre-

cisely and consistently, particularly where many individu-

als in several teams and even external suppliers are

involved.

In such cases, the adherence to best practice for meshing

and modelling quality can only be controlled through the

rigorous application of detailed specifications and stringent

quality checks.

Although the final assembly and execution of the large-

scale models will typically be carried out by highly expe-

rienced analysts, it will not be possible to assign any level

of confidence to the final results unless the modelling

approach for all the systems, subassemblies and compo-

nents has been consistently checked against the best prac-

tice guidelines.

Figures 5 and 6 illustrate the above principle, through

the example of a composite wing top cover. It is important

to note the highly consistent meshing approach, which is

applied irrespective of who built the particular model

components.

6.1 Elements

Another challenge facing the analyst is the choice of ele-

ment to use for a given analysis problem. The principal

choice is between beam, shell and solid elements.

For most virtual testing purposes, where the objective is

to determine the accurate strength of the aircraft structures,

beam elements are of less practical importance, even at

global model scales.

Shell elements have many different formulations and not

all are suitable for nonlinear calculations. The Abaqus

software includes efficient and robust element types such

as S4 and S4R which are recommended for most applica-

tions of nonlinear analysis on aircraft structures.

Continuum solid elements, such as C3D8, C3D8I,

C3D10M and C3D10I are used mostly at the lower mod-

elling scales.

An element that is of particular interest for modelling

composite structures from CAD geometry data is the

continuum shell element (SC8R). This element is based on

standard shell theory but has the 3D topology of a solid

hexahedral element. This offers certain advantages when

checking and visualising complex assemblies of aircraft

structure parts, in particular when defining and checking

contact interactions.

The continuum shell has been shown to be efficient when

modelling composite parts from CAD geometry (CATIA

V5) as this data contains all the lay-up information defined

from the tooling surface, which can be assigned to the

continuum shell element properties using the element

thickness direction vector orientation (stack direction).

Fig. 5 Wing box—lower cover removed, ribs and stringers

Fig. 6 Stringers and skin mesh


123

Another notable advantage with the continuum shell

element is that it makes the transition between shell-like

structures and continuum solid elements relatively

straightforward. This is advantageous when using Abaqus/

Standard sub-modelling methods for multi-scale analysis.

Figures 7 and 8 show the usage of continuum shell

elements for modelling of composite aircraft structures.

There is a substantial time, effort and cost involved in

creating fit-for-purpose virtual testing models. A future

challenge to both the aircraft manufacturers and the sup-

pliers of the analysis software is to make such processes as

automatic as possible. This requires much more than just

automatic mesh generation, which is in any case available

in most commercial modelling packages today. The suc-

cessful implementation of best practice principles also

requires modelling of CAD parts based on appropriate

idealisations, which are consistently applied.

7 Detailed failure predictions

As outlined in the previous sections, the purpose of the

virtual testing and multi-scale analysis processes is to

enable reliable strength assessments to be made, and this

requires accurate, reliable and robust failure models for

materials and joints.

It is accepted that currently some modelling techniques

are more mature than others and that more confidence exist

in those failure models used with metallic components than

those in composite aircraft structures where significant

development and research still is to be carried out.

For most static strength analyses, predicting the initia-

tion of failure is adequate. However, more recent failure

modelling capabilities like the X-FEM method is allowing

for more accurate simulation of the propagation of failure

within a material [13, 18–20]. In addition, this capability is

potentially providing a bridging capability across different

types of materials and failure modes.

This section will discuss the usage of material and joint

failure models.

7.1 Material damage—metals

The modelling of the elastic–plastic behaviour of metals is

well established and most modern simulation tools offer a

variety of plasticity models for specific applications. For

example, some components made of high-strength alu-

minium may have orthotropic properties because they are

milled from rolled billets which have an orientated grain

structure within the material. This processing method,

which is used for aluminium wing spars, can lead to a

variation in yield stress in the principal material directions

that can be accounted for using Hill’s plasticity model

(a non-cylindrical 3D yield surface) rather than a standard

von Mises plasticity model that is based on the assumption

of isotropic material properties.

Capabilities to model material behaviour beyond initial

yield, taking into account ductile or brittle damage and

failure, have progressed in recent years. A generalized

framework for damage and failure modelling is built into

the Abaqus tools (Fig. 9), and provides a relatively

straightforward approach.

It allows the definition of a damage initiation state,

followed by some form of degradation in the yield stress

which is accompanied by a reduction in elastic modulus,

down to a failure state where the material can carry no

further load. This approach is an approximation to the

physical response of the material, but allows for relatively

straightforward fitting to test data and can be implemented

in such a way as to minimize mesh dependence.

More complex physically based material models are

available, for example those that include a consideration of

Fig. 7 Stringers on panel

Fig. 8 Continuum shell stringer detail


123

void nucleation and coalescence for ductile failure. How-

ever, it is inevitable that the more complex the model

becomes, the more parameters are required and the more

difficult it is to obtain the necessary data from material

coupon tests.

7.2 Material damage—non-metals

For aerospace applications, the majority of non-metallic

materials are laminated composites of carbon-fibre and the

modelling of such materials is still very much an area of

development.

Analysis models of laminated composites are usually

built-up in modern pre-processing tools that are capable of

constructing complex lay-ups with different thicknesses,

materials and orientations at each ply. These can either be

condensed into a single equivalent anisotropic elastic

behaviour, or kept as a distinct set of ply properties. The

latter approach aids ply-based post-processing and also

offers the extension of ply-by-ply damage modelling dur-

ing a nonlinear solution.

The initiation and evolution of material damage in

laminated composites is highly complex. It depends not

only on the behaviour of the individual constituents but

also the interfaces between them. Damage can occur in the

fibres themselves, either in a compressive buckling mode

or as a tensile failure. Compressive or tensile damage can

also occur in the matrix surrounding the fibres, leaving the

fibres intact and able to carry tensile load, but likely to

buckle under compressive load. Additional failure mecha-

nisms include the fracture of the bond between the fibre

and the matrix, as well as the delamination of adjacent

plies.

This complex set of potential damage and failure

mechanisms could in theory occur simultaneously in any

number of combinations. This makes it very difficult to

produce a constitutive model that is capable of simulating

the overall behaviour, and very difficult to test the material

in order to derive suitable parameters for the constitutive

model. A result of these difficulties is that the development

of comprehensive constitutive models for laminated com-

posites continues to attract significant effort in academia.

Currently, constitutive models can include most of the

fibre and matrix failure modes [10–12, 14, 15, 17]. How-

ever, because many structural models employ plane stress

shell theory, the delamination effect has to be taken into

account separately. This means that the inter-laminar bond

strength must be modelled explicitly, either with cohesive-

type elements [6, 16], a cohesive contact formulation, or

fracture mechanics techniques such as the virtual crack

closure technique (VCCT) [7–9]. Again, it is difficult and

expensive to derive appropriate parameters for a delami-

nation model from a suitable test; however, obtaining

accurate test data can lead to a more sophisticated and

accurate model enabling reliable failure assessments to be

made.

7.3 Joint damage—fasteners

For metallic airframe structures, the most common fastener

is the rivet. Rivets are relatively straightforward to model

in a finite element analysis: they are often idealized to a

simple constraint between two plates, with no preload, no

stiffness of their own, and no potential for damage or

failure. Similar techniques have been used for many years

in the automotive industry for the simulation of spot-welds.

A natural extension to this approach is to model the rivet

as a point-to-point constraint but to augment the behaviour

with some elastic stiffness, a plasticity response and, ulti-

mately, damage initiation and damage evolution to failure.

A combination of axial, shear and bending loads can be

included in the failure envelope for this type of constraint.

At a high level, therefore, the rivet can be modelled as a

point-to-point connection with relatively complex behav-

iour. The overall behaviour can be implemented through

the generalized framework of damage initiation and evo-

lution to failure as described above. This is useful for

models that might contain many thousands of rivets, where

it is important to consider the state of the connection as the

load increases, but where it is not possible to model every

rivet as a 3D component.

For some types of fastener, a point-based connection

may not be sufficient, so some form of coupling is needed

to simulate the effect of the ends of the fastener (bolt head

or nut) on the surrounding material. Modern analysis tools

include capabilities to construct large numbers of fasteners

Fig. 9 Abaqus damage and failure framework


123

at varying levels of complexity, based on the fastener

‘map’ for the structure, and including the coupling between

the bolt head and plate material where appropriate.

At a more detailed level, full 3D continuum models of

riveted joints, including the rivet, the plates, the holes and

perhaps even the tools used in the riveting process itself

can be used to simulate the local behaviour under various

loading conditions. Ideally, the study of the fastener

behaviour should include pure shear, pure tension and

various combinations of loading angle in between. Such

models are important for correlating the fastener failure

envelope described previously with physical test results.

An important consideration is the degree to which the

high-level constraint method can take into account the local

behaviour of the joint. In general, it is not possible to

include effects such as pre-load, hole-deformation, fastener

rotation, pull-through etc., unless the specific combination

of fastener and plates is correlated carefully with test. For

complex fasteners which might have countersunk heads,

inserts and pre-loads, even this level of correlation is

unlikely to be sufficient. The combination of the fastener,

the hole and the parent material is a complex system. The

behaviour can depend on the relative strengths of the fas-

tener and the surrounding material, as well as on the form

of the loading. It is not uncommon to see a transition in the

failure mode of a joint as the angle of loading varies from

normal to pure shear, leading to fastener failure in tension

through to failure of the local material around the hole.

The complexity is increased yet further if a single fas-

tener is used to join more than two plates, because addi-

tional failure modes can arise.

Much has been achieved in recent years, with notable

success in several large scale simulations. However, the

detailed modelling of fastener failure continues to evolve,

with aircraft manufacturers carrying out more extensive

investigations into the correlation with test and software

developers seeking more efficient ways to replicate the

physical behaviour.

7.4 Joint damage—adhesives

Adhesive joints are becoming more common in aerospace

structures because of the increasing use of laminated

composites. In some cases the joint is made entirely with

adhesive, while in others the adhesive is used to augment a

joint fastened with bolts. As with other forms of fastening,

the analyst can employ a range of techniques to model the

effect of the adhesive bond, depending on the level of

fidelity required in the particular simulation.

At its simplest, an adhesive joint might be considered as

a tied surface constraint with zero thickness between the

tied surfaces. In general this is adequate for all but the most

detailed analyses, since the elastic stiffness of a thin

adhesive layer is unlikely to be a key variable in the overall

structural response.

For more complex cases, it is important to consider the

possible failure of adhesive joints, particularly in areas

where ‘peeling’ can be initiated. A common area for

attention is at stringer run-outs where failure may also be

driven by high interfacial shear stresses in the adhesive

joint.

The failure of the adhesive bond requires a modification

of the standard tied constraint, either via an extension to a

basic contact algorithm, or through the use of some kind of

zero-thickness cohesive-type element, so that the bond

between the surfaces can be progressively weakened under

increasing load. The most straightforward approach is to

use another form of the generalized damage framework

described previously: the bond has an elastic stiffness

which is applicable up to a limit value of stress or strain, at

which point the properties are degraded down to ultimate

failure. In general, for zero-thickness adhesive bonds, these

properties are defined through a traction–separation law

with a damage phase evolving into failure.

Such approaches can be correlated to peel tests, but it is

not always straightforward to separate the normal and shear

responses, which in the physical bond are very closely

coupled.

The adhesive joint might also be modelled as a layer of

material which has a finite thickness and which has its own

constitutive law that includes an elastic–plastic response

with failure. The layer is then modelled as a 3D continuum

using conventional solid finite elements. This can be

effective, but has several potential difficulties. The ele-

ments are 3D continuum, but may need to be thin in

comparison to other structural dimensions, which presents

problems both in meshing and in obtaining a converged

finite element solution. Also the material behaviour of the

adhesive layer can be extremely complex—the strength

properties of the adhesive may vary significantly with the

thickness of the layer and may also be highly dependent on

the curing process. As a consequence, it is not easy to

develop an analysis approach that can produce reliable

results for a finite thickness adhesive modelled with con-

tinuum elements and a full constitutive model.

Another analysis method available in Abaqus for anal-

ysis of failure propagation in adhesive joints is the VCCT.

This methodology is based on linear fracture mechanics

theory and can be used to predict the stability of existing

cracks in adhesive joints and for simulation of crack

propagation but will not cope with more complex failure

propagation like crack ply-jumping or complex failure

interaction between adhesive joints and adjacent adherents.

Notably, the method can be used with significantly larger

element sizes at the crack front compared to cohesive

element methods typically requiring much smaller element


123

sizes to provide accurate results but cannot be used to

predict the initiation of failure.

For an accurate assessment of adhesive joint damage

and failure, the interaction between failure modes, or mode

openings I, II and III must be included in the analysis.

Again, such interactions must be well correlated against

test data. Several types of interaction models are available

in Abaqus for both cohesive contact and VCCT analysis

methods, where the Benzeggagh–Kenane (BK) mixed

mode fracture criterion is often used [21].

8 Analysis framework for virtual testing using

nonlinear analysis

The preceding discussion on detailed methods leads to the

requirement to ensure that the modelling and analysis

methods are fit-for-purpose and validated against test.

The topic can therefore be addressed through the fol-

lowing three nonlinear analysis building blocks:

1. material modelling (metallic and composite),

2. fastener modelling,

3. adhesive joint modelling.

To build confidence in each of these analysis categories,

a range of structural coupon tests with increased com-

plexity must be carried out and close correlation with

analysis models must be demonstrated. This implies using

exactly the same type of element types, mesh topology and

density, methods and properties at each level of coupon

test/analysis correlation.

This methods validation framework is illustrated in

Fig. 10, using the example of adhesive joint modelling.

The process starts with simple coupon tests where the

actual loading and crack opening mode is well understood;

extends to a more complex 7-point bend test where the

initial flaw in the bondline is subjected to complex loading

and mixed mode crack behaviour; and concludes with a

coupon test of an actual aircraft structure. A fundamental

requirement is to demonstrate that the detailed analysis and

modelling methods employed will provide consistent

accuracy and correlation with test results at all three levels

of structural complexity.

Combining the multi-scale analysis process as shown in

Fig. 3 with the methods validation framework in Fig. 10

provides a general analysis framework for advanced non-

linear analysis of aircraft structures, as depicted in Fig. 11.

The analysis framework is named after the shape of the

wishbone found in common birds.

It is vital to ensure that at the point of confluence

between the upper and lower arms of the wishbone analysis

framework there is a consistent set of analysis and mod-

elling methods and processes that are used. In practice this

means that for detailed failure predictions in the multi-scale

analysis framework, validated methods from the lower arm

of the wishbone must be used. By ‘validated’ we mean that

the methods have been demonstrated to provide accurate

results at different structure complexity levels.

Fig. 10 Methods validation

framework


123

In order to enable this integrated analysis framework to

be developed and deployed, there is a requirement for it to

be based on the consistent use of a common, feature-rich

analysis tool that in turn creates the opportunity for future

analysis developments and wide collaboration with exter-

nal partners to Airbus.

The wishbone analysis concept has proven to provide a

robust analysis framework for the development and

deployment of advanced nonlinear analysis methods and

processes. Furthermore, and perhaps more importantly, the

analysis framework provides a structured, logical and

unified basis for exploitation and deployment of the virtual

testing technology in an industrial context.

9 Implicit and explicit finite element methods

Implicit nonlinear finite element analysis methods are

currently the standard for static virtual testing simulations.

Explicit methods are normally too expensive computa-

tionally for use in quasi-static type analysis problems. If

dynamic effects and numerical noise are to be eliminated

then run times become unmanageable.

There are, however, certain cases where explicit finite

element analysis methods are of significant importance in

static type calculations and where implicit and explicit

methods can be used together. The Abaqus software has

interfaces between the implicit and explicit solvers that

enable the same analysis model to be used for both types

and analysis. Examples include:

(a) manufacturing process simulations,

(b) residual strength calculations where the static strength

of impact damage initially can be assessed using

Abaqus/Explicit for impact damage and subsequently

using Abaqus/Standard for residual strength,

(c) simulation of failure propagation and assessment of

local failure.

Abaqus/Explicit can be used to understand the likely

failure sequence and final result after the initial failure

has been predicted using Abaqus/Standard. It is possible

to simulate the structural failure by taking the implicit

solution close to the predicted failure load level and,

using compatible material, fastener and contact models

in both solvers, to import the solution to Abaqus/

Explicit in order to complete the ultimate failure pre-

diction. This is illustrated in Fig. 12 for a metallic box

beam structure used for the testing of wing compression

panels [22].

It can be difficult to use implicit solvers to model the

progressive damage and failure of both materials and

joints, because of the instabilities and bifurcations that can

occur in the solution. Some form of damping or stabilisa-

tion is frequently required. Explicit solvers, on the other

hand, do not have any such instability issues.

In the near future, explicit finite element methods are

likely to play an increasingly important role in the simu-

lation of progressive structural failure events. The explicit

technique provides an improved understanding of the effect

of initial local failures which might result only in local load

Fig. 11 General analysis

framework—the wishbone


123

redistribution effects rather than catastrophic failure of the

aircraft structure.

10 Robust analysis

It is important to understand that increasing the complexity

of material models by adding capabilities to simulate

plasticity, damage and failure, does not necessarily by itself

improve the accuracy of the simulation; nor does increas-

ing the precision of the input data.

Improved simulations arise through careful construction

of a realistic analysis model that represents as closely as

possible the real structure under real-world conditions. The

preceding sections have highlighted the importance of

using appropriate test data, appropriate levels of abstrac-

tion, and correlating models against experiment before

embarking on predictive virtual tests.

Another major consideration for the analyst is the level

of uncertainty in the model. Uncertainty arises because

many aspects of the real structure, including material

properties, dimensions, and the initial ‘state’ of the

assembly, cannot be known with absolute certainty, and

also because the physical structure will have some vari-

ability in both properties and state, from location to loca-

tion within the structure, and from batch to batch.

It is unlikely that an analysis model could be constructed

that replicates the true property and state of the physical

structure at every point, even if that data could be measured

in the first place. Therefore, it is important for the analyst

to take account of uncertainty and variability in the simu-

lation work. This is usually achieved by running several

analyses to explore the effects of uncertainty, rather than

running one single deterministic analysis.

Unfortunately, in some cases, small variations in mate-

rial properties can have a significant effect on the response

of the model as well as the actual structure, particularly if

the effects of plasticity, damage and failure are included.

This high level of sensitivity to key failure parameters

means it is very important to carry out a range of analyses

to fully explore the effect of variability.

Simulation of a structural test up to and including

damage and failure requires extensive modelling of the

behaviour of both materials and joints. The more complex

the model, the more data is required to represent the

complexity and the more correlation work is needed.

Another consequence of the addition of more complex

failure behaviour is that the initial state of the structure

becomes more important. There is little benefit in model-

ling the failure of fastened joint more accurately, if the

starting point of the analysis differs markedly from the

initial state of the real structure. Therefore, when increas-

ing the accuracy of analysis models it is necessary, as far as

is practical, to take into account initial stresses arising from

component manufacture and assembly, together with the

dimensional tolerances, variation in material properties and

imperfections arising from the assembly process.

Simple sensitivity studies can be used to gain adequate

insight into the likely sensitivity of the structural response

and failure mode to variations in properties and geometric

imperfections. However, it is important to note that before

considering any type of robust analysis, be it based on

stochastic or other types of probabilistic methods or simple

sensitivity studies, best practice principles must be fol-

lowed in the modelling process. The baseline analysis

model should be constructed to nominal, or if fully known,

actual geometry data and actual measured material and

fastener properties. If the baseline analysis model is not fit

Fig. 12 Box-beam test and

analysis


123

for purpose, then not even the most advanced probabilistic

methods will deliver adequate results.

11 A380 wing certification

Advanced nonlinear finite element analysis methods were

used to solve several issues during A380 certification. The

most significant was to identify the root cause of the wing

structural failure during the final ultimate static test trial in

Toulouse in 2006. The aircraft wing test structure is shown

in Fig. 13.

In order to illustrate the scales of deformation involved

in this test, it is interesting to note that the maximum

deflection of the wing tip at ultimate load level is

approximately 8 m.

Both wings broke simultaneously, at the same location,

at about 3% below the ultimate design load. The ultimate

design load is defined as 1.5 times the maximum load that

the aircraft structure will experience during in-service

flight conditions (in turn defined as the Limit Load).

Despite the fact that the test was so close to demonstrating

the ultimate load strength capability, a large investigation

was launched to identify the reason for the wing failure and

to design a structural modification to achieve the certifi-

cation of the A380 aircraft structure. Amongst other efforts

launched, it was decided to create a detailed nonlinear

finite element model of a section of the A380 wing box,

bounded by both spars and with a span of 7 rib bays.

There was no detailed nonlinear model of the complete

A380 wing structure available, so it was decided to trans-

late a global, but relatively coarse, linear MSC Nastran

model (MSC Nastran, MSC Software Corporation, Santa

Ana, CA, USA) of the wing structure into an Abaqus finite

element model suitable for nonlinear analysis. This was

then used to drive the boundaries of the detailed model at

the in-board and out-board cut-sections.

The Abaqus model of the detailed wing box section is

shown in Fig. 14 and includes all discrete load inputs

(rubber loading pads) within the domain of the wing box

section.

The global analysis process used is illustrated in Fig. 15.

This figure also shows that due to the coarseness of the

global wing model, the detailed model had to include

additional structure away from the zone of interest. This

was required in order to introduce the loading correctly into

the detailed model of the section where the failure was

expected to have initiated (a zone of approximately 3 rib

bays and from rear to front spar). Very little information

was available about likely cause or location of the failure

other than that the failure was unlikely to have occurred in

the lower cover as this was largely intact at the end of the

test.

Every structural part within the zone of the wing box

was modelled from nominal CAD geometry, mostly using

Abaqus shell elements (S4 or S4R). For the top cover about

8,000 fasteners (rivets and bolts) were included in the

model using the Abaqus mesh-independent fastener ele-

ment as depicted in Fig. 16. The mechanical contact

between skins and stringers and between top cover and rib

feet was also modelled.

Significant effort was put into meshing the upper skin

and stringers as consistently as possible using best practice

modelling techniques as illustrated in Fig. 17. Likewise

Figs. 18 and 19 show the meshing details used for spar and

rib panels.

Material and fastener properties were modelled using

actual measured properties for the wing structure. Exten-

sive material coupon testing was carried out to fully

characterise the properties for the upper skin and stringer

materials in particular. Detail coupon tests were machined

from the test structure and used to characterise the stringer

Fig. 13 A380 wing in test structure

Fig. 14 Sub-model with loading pads


123

and rivet properties as shown in Fig. 20. Detailed Abaqus

models were used to correlate the analysis properties

against the coupon test data using the same modelling and

meshing strategy as used in the detailed sub-model of the

wing box structure.

The coupon test programme also allowed the physical

nonlinear shear and tension stiffness characteristics of the

rivets to be determined. These were subsequently included

in the detailed wing box model together with an interaction

to describe the relationship between the shear and tension

failure behaviour.

As explained in previous sections, it is a fundamental

requirement that all analysis methods are fully validated

against test data. Extensive correlations were therefore car-

ried out between measured and calculated wing deflections

Fig. 15 Analysis process—

global and sub-model of wing

Fig. 16 Rivets between skin and stringers

Fig. 17 Mesh of cleat, rib-feet and Stringers

Fig. 18 Spar and detail meshing


123

data, measured strain levels at all strain gauge locations in the

wing box section of interest and other information available

such as known permanent deformation.

Figure 21 shows the correlation between the measured

wing deflections along the wing front spar and the results

of the global nonlinear finite element model that was used

to drive the detailed sub-model. It illustrates that the global

wing model provides an excellent representation of the

global wing stiffness.

All strain gauges used on the test structure were mod-

elled explicitly as depicted in Fig. 22, which enables a

Rib-Web

Stiffeners

Rib-Foot & Boom

Fig. 19 Mesh of rib-foot and beam, rib web and stiffeners

Fig. 20 Rivet shear and tension

coupon modelling, plus photo of

test rig

Front Spar Vertical Deflection

Ver

tica

l Dis

pla

cem

ent

(mm

)2000

1000

8000

7000

6000

5000

3000

4000

ES deflection at 1.45LLAbaqus global FEMNastran global FEM

5000 10000 15000 20000 25000 35000 4000030000

Distance along wing from wing -root (mm)0

0

Fig. 21 Front spar vertical deflection, test and analysis comparison


123

straight forward correlation between measured and calcu-

lated strain levels.

The following two figures (Figs. 23, 24) show an

example of correlation against strain gauges for the global

and detailed model, respectively, located on the outer skin

surface and stringer flange as shown in Fig. 22.

The strain gauge correlation clearly shows that the

global finite element model is capable of calculating the

skin strain levels accurately up to the point where signifi-

cant buckling occurs in the top cover. However, after that

point the model is not capable of capturing the detailed

local post-buckling response.

The detailed sub-model, however, does calculate the

buckling correctly and is able to predict the strain levels

very well in the outer skin surface as well as on the stringer

free flange. It should be noted that due to the highly

complex buckling taking place in the top cover near ulti-

mate load, the detailed strain correlation is sensitive to the

actual location of the strain gauge and some deviation from

intended location is possible during installation.

Overall, all the available evidence verified that the

detailed sub-model and global wing nonlinear finite ele-

ment model represented the actual A380 wing box struc-

ture very well and that the detailed model could be used to

calculate the nonlinear deformation behaviour, including

the effects of post-buckling.

Once it had been established that the detailed wing box

model was fit for purpose, the investigation focussed on the

identification of the root cause of the structural rupture. Every

possible stress concentration in the structure modelled was

identified and investigated using refined meshes and detail. An

example is shown in Fig. 25 for one of the rib panels.

However, all evidence suggested that the rupture had

occurred in the top cover as this was where the highest

stress and plastic strain levels were present. The top cover

was subjected to extensive skin buckling resulting in very

complex post-buckling behaviour. This is shown in Fig. 26

at ultimate load level, i.e. 3% above the actual wing

structural failure load level.

Fig. 22 Modelling method for

strain gauges

Fig. 23 Outer skin strain correlation—global FEM

Fig. 24 Outer skin and stringer strain correlation—detailed sub-

model


123

The buckling calculated is shown in more detail in

Fig. 27 using a scale factor equal to 5. The analysis carried

out confirmed that global panel buckling (from rib to rib)

would occur at ultimate load exactly, which was as pre-

dicted by the conventional stressing methods used for

design of the structure.

As it was now confirmed that the root cause could not be

explained by material rupture or global buckling, the

attention was now focussed on the rivets and bolts used in

the top cover.

Figure 28 shows that as a consequence of the skin

buckling, very localised separation or gapping occurred

between skin and stringers (shown at 1.449 Limit Load)

and for one zone in the top cover in particular.

Screening all the fasteners in this region for shear and

tension loads, it became evident that the local skin buckling

resulted in additional nonlinear shear and tension forces in

the rivets, as shown in Fig. 29. It can be seen that initially

the shearing force carried by the rivet is increasing linearly

with the load as the rivet resist in-plane shear forces in the

panel (wing torsion) and that the tension force is constant

and equal to the small preload defined in the rivet model.

At the onset of initial skin buckling, the local buckling

results in separation forces between skin and stringers,

which can be seen as a sudden increase in the rivet ten-

sion. Additional shearing forces in the rivets are also

Fig. 25 Local stress

concentration on rib stiffener

Fig. 26 Top cover buckling, sub-model

Fig. 27 Detail of top cover buckling at 1.5 9 LL


123

observed after onset of buckling, which are caused by

the complicated buckle patterns resulting in curvature

changes both span-wise and chord-wise in the top cover

panel. These local changes in curvature will sometimes

increase the rivet shear forces and sometimes reduce

them, depending on the rivet position in relation to the

local buckles in the panel.

Screening all fasteners showed that more than one rivet,

on one stringer, was predicted to fail at about 1.44 to 1.459

Limit Load. This was in good agreement with the actual

wing rupture at 1.459 Limit Load. No other plausible

failure mode was predicted below 1.59 Limit Load and the

root cause of the rupture had therefore been identified as

being caused by rivet failures.

Not only was it possible to identify the cause of the

rupture but it was also possible to fully understand

the underlying issues that had to be considered for the

structural modification to demonstrate adequate strength.

Figure 30 shows the local panel deformation in cross sec-

tion A–A indicated in Fig. 28 and illustrates the level of

detail considered and captured in the analysis.

It clearly shows that the local buckling resulted in

gapping between skin and stringer. A design modification,

using straps along the stringer feet both sides, was therefore

designed to avoid the separation and the rivets were

replaced locally with bolts.

The preceding section provides only a brief description

of the analysis models and processes used to identify the

reason for the A380 wing structural failure. It is not pos-

sible to fully detail, in this paper, the many different

analyses and sensitivity studies carried out during the

intense investigations. However, it is important to state that

advanced nonlinear finite element analysis had been used

successfully to identify and explain an extremely compli-

cated industrial structural analysis problem and to con-

tribute to the process to achieve the certification of the

A380 wing structure.

12 Summary

This paper has provided an overview of the virtual

testing technology of aircraft structures in Airbus sub-

jected to static loading conditions. The importance of

confidence and best practice associated with a virtual

testing approach has been discussed. A general frame-

work—the wishbone—for working with multi-scale

analysis methods and the various challenges facing the

analyst have been presented, with particular focus on

detailed failure prediction methods for materials and

fasteners.

The construction of FE models to include plasticity,

damage initiation, damage evolution and ultimate failure

requires careful consideration of the behaviour of the

underlying materials as well as of the joints and fasteners

between components. Modern FE tools are capable of

Fig. 28 Contact opening in

stringer attached flange

1.01

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Circ

ular

inte

ract

ion

For

ce (

N)

Load (LL)

Tension and shear forces for a failed rivet

Tension

Shear

Circular Interaction

Onset of local skin buckling

Rivet failure at 1.44 X LL

Fig. 29 Tension and shear forces for failed rivet


123

simulating complex damage processes, but increasing the

level of complexity requires additional parameters, which

need to be obtained from tests and correlated against

experimental results.

There are therefore significant trade-offs to be consid-

ered in relation to the expediency of running many rela-

tively simple analyses, the difficulty of obtaining and

correlating complex material behaviour, and the potential

risk of generating misleading results from apparently

advanced simulations that have not been properly validated.

However, there is no doubt that when used carefully,

with due regard to the derivation and validation of model

data and the trade-offs of complexity against efficiency, the

use of nonlinear FE analysis can have a significant impact

on the development and structural strength assessment of

advanced aircraft structures.

A number of key enablers have been identified in order

to improve virtual testing capabilities still further. These

include:

• detailed modelling and meshing methods,

• automatic meshing and modelling methods from CAD

definition based on consistent meshing rules,

• automatic composite property and lay-up capabilities

from CAD to CAE,

• large-scale computations and increased use of detailed

modelling, based on continuous improvements to high-

performance-computing capabilities,

• efficient multi-scale analysis methods and screening

processes to identify critical structures,

• fit-for-purpose detailed failure models for materials and

joints and in particular for composite materials,

• robust quality processes.

Airbus has developed strong partnerships with both

software providers and research institutes, including vari-

ous European universities, in order to make progress on the

above key enablers.

The EU FP7 research project MAAXIMUS (more

affordable aircraft structure through extended, integrated,

and mature numerical sizing) is an example of a major

project designed to make progress on virtual testing

methods, which has both Airbus and Dassault Systemes

SIMULIA as partners [23].

Many of the analysis short-comings discussed in previ-

ous sections are addressed in the frame of MAAXIMUS. It

is expected that within the timeframe of the project, the

size of the models that can be handled in a nonlinear finite

element approach can be increased by between 1 and 2

orders of magnitude. The Giga-DOF model (10^9 DOF) is

the figure being used as a target for the developers in the

project.

In recent years, significant progress has been made in

exploiting virtual testing methods for the solution of

complex industrial structural issues, such as the A380 wing

certification described in this paper. However, it must be

acknowledged that virtual testing methods of composite

aircraft structure are still being developed and will continue

to provide the analyst, the software developers and aca-

demia with significant challenges.

Fig. 30 Cross-section showing

fasteners


123

In addition, it is important that particular attention is

paid to the development of best practice in methods and

processes in order to enable industrial deployment.

The correct combination of skills, tools and processes

used within the wishbone analysis framework can then be

used to maximise the benefit of the virtual testing tech-

nology in an industrial context and to provide a shared

platform for future collaboration between industry, aca-

demic partners and software providers.

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23. FP7 MAAXIMUS—more affordable aircraft through extended,

integrated and mature numerical sizing: http://www.maaximus.eu/


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http://www.maaximus.eu/

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Virtual Testing of Aircraft Structures