###### Abstract

An idealized 1:2 scale demonstrator and a numerical parameter optimization
algorithm are proposed to closely reproduce the deformation shape and, thus,
spatial strain directions of a real aerodynamically loaded civil aircraft
spoiler using only four concentrated loads. Cost-efficient experimental
studies on demonstrators of increasing complexity are required to transfer
knowledge from coupons to full-scale structures and to build up confidence in
novel structural health monitoring (SHM) technologies. Especially for testing
novel sensor systems that depend on or are affected by mechanical strains,
e.g., strain-based SHM methods, it is essential that the considered lab-scale
structures reflect the strain states of the real structure at operational
loading conditions. Finite element simulations with detailed models were
performed for static strength analysis and for comparison to experimental
measurements. The simulated and measured deformations and spatial strain
directions of the idealized demonstrator correlated well with the numerical
results of the real aircraft spoiler. Thus, using the developed idealized
demonstrator, strain-based SHM systems can be tested under conditions that
reflect operational aerodynamic pressure loads, while the test effort and
costs are significantly reduced. Furthermore, the presented loading
optimization algorithm can be easily adapted to mimic other pressure loads in
plate-like structures to reproduce specific structural conditions.

###### keywords:

aircraft spoiler; demonstrator; experimental strain analysis; quasi-realistic
loading; SHM; composite sandwich; strain-based

8 11 320 Academic Editor: Shijun Guo 13 September 2021 25 October 2021 28
October 2021 https://doi.org/10.3390/aerospace8110320 Development of Aircraft
Spoiler Demonstrators for Cost-Efficient Investigations of SHM Technologies
under Quasi-Realistic Loading Conditions Development of Aircraft Spoiler
Demonstrators for Cost-Efficient Investigations of SHM Technologies under
Quasi-Realistic Loading Conditions Markus Winklberger 1,*, Christoph Kralovec
1 and Martin Schagerl 1,2 Markus Winklberger, Christoph Kralovec and Martin
Schagerl Winklberger, M.; Kralovec, C.; Schagerl, M. Correspondence:
<EMAIL_ADDRESS>
##  1 Introduction

In aircraft engineering, scaled demonstrators are commonly used to represent
parts, assemblies, or full-scale structures to allow cost-efficient testing.
This is particularly true for aerodynamic development Niu (1999); Hermanutz
and Hornung (2020); Rozov et al. (2019). In addition, for many other purposes,
small-scale models are used, e.g., aircraft design and flight testing
demonstrators Jouannet et al. (2008); Jordan et al. (2005), demonstrators to
develop flight-safety-critical systems Bierig et al. (2017), and technology
demonstrators Bergmann et al. (2019); Balaram et al. (2018). All of these
demonstrators are mainly used to bridge the gap between experimental results
of simple structures (e.g., airfoil test specimens, material testing
specimens, test coupons for bonding tests), together with sophisticated models
(numerical models applying the, e.g., finite element method (FEM)) for design
calculations, and the final target structures in real applications Sepe et al.
(2017). Ideally, multiple experiments with such demonstrators in controllable
test environments should then validate the preceding simulation results. In
many cases, it is practical and cost-efficient to use multiple specimens or
demonstrators of increasing complexity, e.g., first an airfoil, then a
complete wing, and finally a full plane model, to validate models and conduct
design studies. In structural aircraft design, a method known as the test
pyramid has proven effective in addressing the rising costs associated with
the constantly increasing size and complexity in aviation industries Caputo et
al. (2021); Rossow et al. (2014); Berger and Hayo (2014). The test pyramid for
aircraft structures typically includes four layers: (I) coupons, (II)
elements, (III) components, and (IV) full-scale airframe, beginning from the
lowest and widest part (coupons; most generic structures; largest number of
required tests) and ending at the tip of the pyramid (full-scale airframe;
most complex structure; lowest number of required tests). A similar building
block approach is the motivation for the present work. Hence, the layers of
the test pyramid, including structural health monitoring (SHM), may have the
following descriptions:

  1. 1.

Coupon and element level (plate or beam-like structures)—development of
sensors and SHM methods;

  2. 2.

Component level (e.g., aircraft spoilers)—application of SHM to real
structural components;

  3. 3.

Full-scale airframe level (complete aircraft)—application of SHM systems to
real aircraft structures.

In this context, an idealized demonstrator is located between the first and
the second levels and should bridge the gap between simple plate- or beam-like
structures and complex aircraft components (e.g., spoilers), which are
expensive and laborious to acquire. Tailoring novel sensor systems and SHM
evaluation methods reliably to structures of high complexity (e.g., a real
aircraft spoiler) requires large and, thus, expensive test campaigns. A
comparatively cheap idealized demonstrator together with an optimization
methodology reflects an arbitrary behavior (and its associated effects, e.g.,
strain states and deformations are connected by the deformed shape of a beam
or plate) of the full-scale component. Thus, a properly designed demonstrator
structure and optimized loading allow one to imitate a specific behavior (and
neglect all other effects) of parts of interest of complex structures and
their loading in cost-efficient experiments. However, this also implies that
the specific behavior of interest needs to be defined prior by a profound
structural analysis. Consequently, experiments with quasi-realistic loads on
structures of increased complexity (i.e., demonstrators) that reflect real
components enable (i) cost-efficient studies of, e.g., damage parameters or
environmental conditions, and (ii), a more reliable transfer of findings from
simpler structures. Therefore, it is expected that this approach will allow
robust and damage-sensitive SHM methods to be developed in a shorter time and
in a more cost-effective manner. Other contributions Berger and Hayo (2014)
readily proposed the implementation of testing sensor systems and SHM methods
in the structural test pyramid. However, the question of how to efficiently
transfer knowledge from low-level tests to higher levels of complexity
remains. The present work proposes a method that enables one to generate
highly transferable test results at a comparatively low level of complexity
and cost.

In the last decades, numerous SHM methods have been proposed and were
successfully tested on simple specimens relevant to aircraft design in
laboratory environments Nyikayaramba and Murmann (2020); Barman et al. (2020);
Philibert et al. (2018); Alzahrani et al. (2018); Winklberger et al. (2021);
Song et al. (2012). Recently, scaled demonstrators equipped with multiple
sensors have also been built to develop and test the applicability of
promising SHM methodologies Gómez González et al. (2013); Scholz et al.
(2016); Martins and Kosmatka (2020). SHM methods that are capable of
monitoring large thin-walled structures, e.g., spoilers, are guided waves
Giurgiutiu and Santoni-Bottai (2011); Dong and Kim (2018); Gschoßmann et al.
(2016); Humer et al. (2019); Yeasin Bhuiyan et al. (2017), electrical
impedance tomography (EIT) through conductive surface layers Zhao et al.
(2015, 2019), and direct measurements of a structure’s electrical impedance
Nonn et al. (2018). Furthermore, strain-based methods with distributed strain
sensors, e.g., fiber optical sensors (FOSs), are expected to efficiently
monitor large thin-walled structures, which are typical for lightweight design
Milanoski and Loutas (2021); Grassia et al. (2019); Ohanian et al. (2020);
Kressel et al. (2017).

This contribution presents the development of an idealized demonstrator on a
1:2 scale together with a concentrated load optimization methodology to mimic
the deformation and strain states (with respect to strain directions) of a
large civil aircraft spoiler under a specific aerodynamic load case. A similar
algorithm was reported in Sepe et al. (2017) to define the loading for
strength tests of a horizontal stabilizer, where the load amplitudes at a
number of fixed introduction points were optimized to reflect a considered
load case. However, the load optimization algorithm presented in this work
enables one to find the best locations of a specific number of load
introduction points. Furthermore, the presented methodology reduces high
stresses in critical regions to allow high loads and, thus, high strain values
to increase the signal-to-noise ratio (SNR) in further investigations (if
required). In addition to optimizing concentrated loads for demonstrators, a
wide variety of optimization methodologies are used in aircraft design to
optimize composite structures for weight reduction Guo et al. (2012); Narayana
Naik et al. (2008), the shape of aircraft parts to reduce gas leakage Zhao and
Wang (2021) and noise impact on the ground Song and Keane (2007), or sensor
positions for SHM applications Gomes et al. (2019); Ostachowicz et al. (2019),
to name just a few examples.

The idealized spoiler demonstrator is needed to further develop and validate
novel sensor systems and SHM methods to, e.g., detect and identify sandwich
face-layer debondings and delaminations under realistic loading conditions
Bergmayr et al. (2020, 2021). Nowadays, spoilers of large civil aircraft are
typically built as composite sandwich structures composed of glass-fiber-
reinforced polymer (GFRP) face layers, a honeycomb core, and monolithic hinges
for mounting and actuation Niu (1999). Impact damages in monolithic composite
structures caused by, e.g., dropping of a tool or a bird strike, as well as
manufacturing defects, are usually difficult to detect through visual
inspection. The same can be said for sandwich structures, where, in addition,
debonding of the core and skin and deteriorations of the sandwich core are
possible failure modes. A secure and common procedure for detecting structural
damages that are not detectable through visual inspection in composite
structures is through more sophisticated non-destructive testing (NDT)
methods, e.g., ultrasonic testing, radiographic testing, vibration/modal
analysis, etc. Staszewski et al. (2009). However, inspections of large areas
using advanced NDT are labor expensive, and hence, they increase down time and
maintenance costs. Using similar damage detection methods, SHM promises to
overcome these issues by monitoring the aircraft structure continuously during
operation with structurally integrated systems of sensors Song et al. (2012).
Furthermore, lightweight structures such as aircraft are highly optimized for
specific loading scenarios. Hence, in the case of manufacturing defects, which
most probably decrease structural strength, or in the case of overloads, such
structures are especially vulnerable to failure.

The typical overall dimensions for spoilers of large civil aircraft depend on
the specific aircraft type and location on the wing; e.g., Airbus A340 spoiler
number 2 (highlighted in Figure 1) has dimensions of approximately
$2400\text{\,}\mathrm{m}\mathrm{m}$ × $800\text{\,}\mathrm{m}\mathrm{m}$ ×
$150\text{\,}\mathrm{m}\mathrm{m}$.

spoilersflapsaileronsslats0.90.80.70.60.50.40.30.20.10.01.0$w/w_{\max}$actuator
lugstrailing edge of spoilerupper skin$x$$y$$z$inboard hinge bracketoutboard
hinge brackethinge lugshinge line

Figure 1: Location and deformation of the considered aircraft spoiler of an
Airbus A340 aircraft, overview of control surfaces (cf. Meindlhumer et al.
(2019)), and out-of-plane deformation of the spoiler’s upper skin according to
considered load case.

2 Consequently, the acquisition of such spoilers and test rigs for mechanical
loading is cost-intensive, and they are often not available in academic
research, where SHM methods are currently developed. Furthermore, an adequate
deformation and strain state (with respect to strain directions) can only be
achieved with high loads, resulting in high potential strain energy, which can
be a safety issue. A small-scale idealized demonstrator is expected to
overcome these difficulties. Obvious advantages are the lower manufacturing
costs, fast assembly, simple introduction of idealized artificial damages,
easier handling, and smaller deformation forces due to reduced dimensions and
a simplified geometry. However, such demonstrators need to be tailored very
well to the objectives of the scheduled investigation. This is of particular
importance when the complexity of the considered structure, its loads, and the
effects provoked by potential damage increase. Aerodynamic loads are always a
challenge to realistically reproduce in mechanical tests. This is also true
for the reconstruction of loaded states for SHM evaluations, as required by
strain-based methods in general Kesavan et al. (2008); Grassia et al. (2019);
Milanoski and Loutas (2021) and the zero-strain trajectory method Schagerl et
al. (2015); Schaberger (2016); Riedl (2018); Kralovec and Schagerl (2020) in
particular. The experimental validation of the latter for the identification
of sandwich-face-layer debonding and delamination is the long-term objective
for the present work.

The reference considered for the development of a scaled demonstrator is a
spoiler of an Airbus A340 wing. This specific control surface is a sandwich
structure with a wedge-shaped honeycomb core. The upper skin and lower skin
are fiber-reinforced polymer (FRP) lamina. The considered spoiler and an
overview of the control surfaces of an Airbus A340 aircraft wing Meindlhumer
et al. (2019) are given in Figure 1. A design load case is considered as the
reference load, where the spoiler has to withstand the aerodynamic pressure
during landing. In this scenario, immediately after touchdown, the spoiler is
extended $35\text{\,}\mathrm{\SIUnitSymbolDegree}$ using a hydraulic cylinder
attached to the actuator lugs. The given loading results in the out-of-plane
displacement $w$ of the upper skin, which is depicted in Figure 1. The largest
displacement $w_{\max}$ occurs at the out-board side of the trailing edge of
the spoiler.

##  2 Materials and Methods

An idealized spoiler demonstrator should be developed to test SHM methods in
laboratory experiments, which simulate spatial strain states comparable to
strain states present on the upper skin of the real aircraft spoiler during
landing. These strain states do not have to match in their absolute numbers,
but the strain directions—i.e., strain trajectories along the, e.g., major
principal strains—need to be reproduced. Furthermore, the test setup effort
should be minimal to perform experiments at low costs and in a short time.

The real aircraft spoiler has a nonuniform cross-sectional shape (see Figures
1 and 2) and a heterogenous upper skin (thickness is not constant, multiple
FRP lamina with different layups). Hence, the exact stress and strain
amplitudes resulting from the nonuniform aerodynamic load can not be
represented locally by, e.g., a simple sandwich panel with uniform thickness.
However, to yield strain directions (and stress directions considering linear
elastic material properties) similar to the real aircraft spoiler, it is
sufficient for the idealized spoiler demonstrator to represent a similar
deformation shape. More precisely, a similar out-of-plane deformation shape
$w(x,y)$, i.e., for $w^{S}(x,y)=k\,w^{D}(x,y)$, where $k$ is a scaling factor,
will result in a comparable curvature, e.g., $\partial^{2}w(x,y)/\partial
x^{2}$, of the sandwich plates (aircraft spoiler and idealized demonstrator;
indicated by superscripts $S$ and $D$, respectively). Hence, a deformation,
equally scaled on the whole spoiler surface, generates similar strain
states—particularly with respect to the strain directions (amplitudes might
deviate)—on the upper skins. This is true if all fractions
($\varepsilon_{xx}/\varepsilon_{yy}$, $\varepsilon_{xx}/\varepsilon_{xy}$,
$\varepsilon_{yy}/\varepsilon_{xy}$ in the two-dimensional case) of two
different strain tensors (aircraft spoiler and idealized demonstrator) are
identical in every point of the upper skin, which is visualized by a simple
scaling of Mohr’s circle Schagerl et al. (2015); Schaberger (2016) and easily
shown by opposing the bending strains of the plate elements ($S$ and $D$) in,
e.g., the $x$ and $y$ directions.

$\frac{\varepsilon_{xx}^{S}(x,y)}{\varepsilon_{yy}^{S}(x,y)}=\frac{-\frac{\partial^{2}w^{S}(x,y)}{\partial
x^{2}}\cancel{\frac{h^{S}(x,y)}{2}}}{-\frac{\partial^{2}w^{S}(x,y)}{\partial
y^{2}}\cancel{\frac{h^{S}(x,y)}{2}}}\overset{\scalebox{0.5}{$\overset{w^{S}(x,y)=k\,w^{D}(x,y)}{\downarrow}$}}{=}\frac{-\frac{\partial^{2}w^{D}(x,y)}{\partial
x^{2}}\cancel{\frac{h^{D}(x,y)}{2}}}{-\frac{\partial^{2}w^{D}(x,y)}{\partial
y^{2}}\cancel{\frac{h^{D}(x,y)}{2}}}=\frac{\varepsilon_{xx}^{D}(x,y)}{\varepsilon_{yy}^{D}(x,y)},$
(1)

where $h^{S}(x,y)$ and $h^{D}(x,y)$ are the thicknesses of the aircraft
spoiler and the idealized demonstrator, respectively.

Beyond that, the equivalent stresses in all individual parts of the idealized
spoiler demonstrator should stay within the elastic regime during loading to
avoid the plastic deformation or even fracture of any component.

1000380$y$$x$B-BBB2400A2100A760A-Aupper skinleading edgea) Spoiler of
A330/A340 aircraftb) Idealized demonstratorhinge brackethinge lughinge
lugupper skincenter hinge brackethinge brackethinge bracketactuator
lugshoneycombcorehoneycombcore$y$$x$hinge brackethinge linehinge lineconnector
rodupper skintrailing edgeupper skinlower skinupper skinlower skinball
bearingupper skinsandwich plate

Figure 2: Shape and dimensions of (a) the real aircraft spoiler considered in
comparison to (b) the developed idealized spoiler demonstrator.

2

###  2.1 Structural Definition

In general, to establish a proper demonstrator, necessary simplifications must
be well considered to fit the corresponding application. To realize a cost-
efficient idealized demonstrator of the considered aircraft spoiler (shape and
dimensions depicted in Figure 2a), which is feasible for applying novel SHM
methods, three simplifications were made. First, the idealized spoiler
demonstrator was scaled to fit a size smaller than
$$1\text{\,}\mathrm{m}$\times$1\text{\,}\mathrm{m}$$. A demonstrator of this
size fits well into the available test rig and can be set up and operated by a
single person. Second, a rectangular shape and symmetric loading is considered
in order to obtain an efficient simulation model. Additionally, the chosen
symmetry allows one to perform comparative measurements on both sides of the
idealized spoiler demonstrator and reduce manufacturing costs. Third, the
cross-section of the idealized spoiler demonstrator should be homogeneous to
keep the manufacturing costs low. In this way, commercially available sandwich
panels can be used for the idealized spoiler demonstrator. Therefore, the
inhomogeneous triangular sandwich design of the real aircraft spoiler is
replaced by the standard sandwich plate with a homogeneous cross-section, as
depicted in Figure 2b. The center hinge bracket (CHB), which incorporates two
hinge lugs and the actuator lugs, is replaced by two aluminum parts adhesively
bonded to the upper and lower skin of the sandwich panel and a support block
that connects these two parts. In addition, three aluminum blocks for each
hinge bracket at the corners are used as additional supports for the idealized
spoiler demonstrator. A connector rod (simple beam with circular cross-
section) along the hinge line connects all supports. Although the CHB is
rigidly mounted to the test rig, the two hinge brackets at both ends of the
connector rod can rotate around the $x$-axis. The rotational degree of freedom
is provided using ball bearings between support blocks and the connector rod.

###  2.2 Loading Definition and Optimization

The distributed aerodynamic load, which acts on the real aircraft spoiler,
should be represented by a small number of concentrated loads (modeled on
single nodes) at the idealized spoiler demonstrator to allow load application
with a simple whiffle tree; see Section 3. Obviously, this simplification of
loading (distributed load is replaced by a small number of concentrated loads)
is not feasible for representing the full structural behavior (internal
forces, local strain, and stress amplitudes can be fundamentally different).
However, in this case example, the reproduction of the out-of-plane
deformation shape and, hence, the strain directions of the structure under
investigation should be reproduced; see Equation (1). Based on a previous
study, it is assumed that five concentrated loads should be sufficient to
generate the desired deformation shape of the idealized spoiler demonstrator
Hofer (2017). However, the exact optimal locations and amplitudes of these
loads to reproduce the out-of-plane deformation shape of the real spoiler are
unknown. Therefore, a multidimensional non-linear minimization with bound
constraints by transformation was implemented in the numeric computing
environment of Matlab® The MathWorks, Inc. . The algorithm was designed to
identify the optimal locations and amplitudes of three concentrated loads
acting on a symmetrical half model of the spoiler demonstrator based on
parametric simulations by incorporating a simple finite element (FE) shell
model that was solved in Abaqus/Standard Dassault Systèmes Simulia Corp.  .

####  2.2.1 Simple FE Shell Model

The search algorithm for the optimal load introduction uses a highly
simplified FE model. Due to the symmetry in the $x$-plane and the $z$-plane of
the idealized spoiler demonstrator, it is implemented as half model with
planar shell elements; see Figure 3. The sandwich panel is modeled using a
composite layup with an isotropic linear elastic material for the skin
(thickness of $1\text{\,}\mathrm{m}\mathrm{m}$,
$E_{\mathrm{Al}}=$70\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$$,
$\nu_{\mathrm{Al}}=0.33$) and an orthotropic material definition for the core
(thickness of $1\text{\,}\mathrm{m}\mathrm{m}$,
$E_{1}=$1\text{\,}\mathrm{M}\mathrm{P}\mathrm{a}$$,
$E_{2}=$1\text{\,}\mathrm{M}\mathrm{P}\mathrm{a}$$,
$E_{3}=$630\text{\,}\mathrm{M}\mathrm{P}\mathrm{a}$$,
$\nu_{12}=\nu_{13}=\nu_{23}=0$,
$G_{12}=$1\text{\,}\mathrm{M}\mathrm{P}\mathrm{a}$$,
$G_{13}=$280\text{\,}\mathrm{M}\mathrm{P}\mathrm{a}$$,
$G_{23}=$140\text{\,}\mathrm{M}\mathrm{P}\mathrm{a}$$; see HEXCEL COMPOSITES
(2000)). In the area of the hinge brackets (small black rectangles in Figure
3), the honeycomb core is replaced by an isotropic and linear elastic material
model of steel
($E_{\mathrm{St}}=$210\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$$,
$\nu_{\mathrm{St}}=0.3$). The boundary conditions of this simplified FE model
are chosen to represent the boundaries of the real aircraft spoiler. All nodes
of the CHB (black area in the center) are fixed in all degrees of freedom
(DOFs). To allow a rotation and axial translation of the small hinge bracket
at the corner, the nodes of its back edge are not restrained in the DOFs
related to the $x$-direction. The FE model is loaded with one single
concentrated unit force in the negative $z$-direction. This load is located at
any single node in one of the highlighted regions, $\mathcal{J,K}$, and
$\mathcal{L}$, in Figure 3. The out-of-plane deformation ($z$-direction) of
the shell model is simulated for every node position of the concentrated unit
load.

$\mathcal{K}$$\mathcal{L}$$\mathcal{J}$symmetrical half model$x$$y$ Figure 3:
FE shell model with three predefined node sets, $\mathcal{J,K}$, and
$\mathcal{L}$. The 2D shell elements have an exact size of 20 mm × 20 mm.

####  2.2.2 Optimal Locations and Amplitudes of Concentrated Loads

In order to find loads that result in a deformation and, thus, spatial strain
orientation, similarly to the real aircraft spoiler, the developed simple FE
shell model is integrated into a minimization algorithm implemented in
Matlab®. Herein, the out-of-plane deformation in a defined operating condition
of the real aircraft spoiler acts as the target function; see Figure 1. The
main objective is to minimize the difference between the numerically
calculated out-of-plane deformation of the real aircraft spoiler and that of
the spoiler demonstrator FE shell model. The structure of the optimization
algorithm is depicted in Figure 4.

FE shell modelcompliances $\zeta^{D}_{i,j}$, $\zeta^{D}_{i,k}$,
$\zeta^{D}_{i,l}$$m$ load positions in $\mathcal{J,K}$ and
$\mathcal{L}$(fminsearchbnd)Matlab script($m$ simulations)optimized
concentrated load locations ($j,k,l$) and amplitudes
($F_{j},F_{k},F_{l}$)target deformation of aircraft spoiler $w_{i}^{S}$ Figure
4: Flowchart of the proposed concentrated load optimization methodology.

First, the unit load is applied step by step to one node at a time for all
nodes in $\mathcal{J,K}$, and $\mathcal{L}$; see Figure 3. After the
calculation of all FE shell models (with applied unit loads on
$m=|\mathcal{J}|+|\mathcal{K}|+|\mathcal{L}|$ different locations), the
resulting deformation results are exported for further analysis. Second, the
parameter optimization

$\operatorname*{arg\,min}_{\left\\{j\in\mathcal{J},k\in\mathcal{K},l\in\mathcal{L},F_{j},F_{k},F_{l}\right\\}}\left\\{\left(F_{j}+F^{\,}_{k}+F^{\,}_{l}\right)\min_{\left\\{0\leq
F_{j},F_{k},F_{l}\leq
5000\right\\}}\left[\sum_{i=1}^{n}\left(F^{\,}_{j}\zeta_{i,j}^{D}+F^{\,}_{k}\zeta_{i,k}^{D}+F^{\,}_{l}\zeta_{i,l}^{D}-w_{i}^{S}\right)^{2}\right]\right\\}=\left\\{j,k,l,F_{j},F_{k},F_{l}\right\\}$
(2)

2 is executed using the Matlab® function fminsearchbnd D’Errico (2006), where
$\zeta^{D}_{i,j}$, $\zeta^{D}_{i,k}$, and $\zeta^{D}_{i,l}$ are calculated
compliances of node $i$ for each defined unit load at nodes $j\in\mathcal{J}$,
$k\in\mathcal{K}$, and $l\in\mathcal{L}$. The inner minimization of Equation
(2) represents a least-squares search with the superposition of compliances
$\zeta^{D}_{i,j}$, $\zeta^{D}_{i,k}$, and $\zeta^{D}_{i,l}$ multiplied by
unknown $F_{j}$, $F_{k}$, and $F_{l}$ (which yields the displacements of the
demonstrator) and subtracted by the target displacements of the civil aircraft
spoiler $w^{S}_{i}$ for all relevant nodes $n$. The additional constraint of
$0\leq F_{j},F_{k},F_{l}\leq 5000$ ensures forces in the negative
$z$-direction (see Figure 5), as well as a limitation to a maximum load
amplitude of $5000\text{\,}\mathrm{N}$. Subsequently, the sum of the squared
differences between the target deformations and the deformations of the
demonstrator is weighted by the sum of the loads ($F_{j}$, $F_{k}$, and
$F_{l}$) found. This energy-type expression is used to find an optimal
solution that balances the deformation accuracy and required load sizes.

The resulting load amplitudes $F_{j}$, $F_{k}$, and $F_{l}$ and corresponding
positions of nodes $j$,$k$, and $l$ on the upper skin of the idealized spoiler
demonstrator are given in Table 2.2.2.

[H] Optimized concentrated loads and their locations on the idealized spoiler
demonstrator according to Equation (2).

Node |  Load [N] |  $x$ [mm] |  $y$ [mm]
---|---|---|---
$j$ |  1885 |  480 |  120
$k$ |  2705 |  440 |  360
$l$ |  0 |  0 |  120

As, at the symmetry line load $F_{l}$ yields a numerical value close to zero,
the overall result is a four-point loading of the idealized spoiler
demonstrator, which is depicted in Figure 5b. However, with the relatively
large loads given in Table 2.2.2, the stress in the sandwich skin around the
corner of the CHB exceeds the yield stress of the initially considered
aluminum alloy
($R_{p02,\text{Al}}=$130\text{\,}\mathrm{M}\mathrm{P}\mathrm{a}$$). A
proportional reduction of load amplitudes would lead to a decrease in
deformation and straining of the upper skin of the idealized spoiler
demonstrator. In this case, strains in large areas of the upper skin
calculated with the simple FE shell model would then be below
$20\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{m}\mathrm{/}\mathrm{m}$, which
is defined as the minimum strain amplitude measurable with the facilitated
digital image correlation (DIC) system (cf. Section 3). Furthermore,
considerable strain amplitudes are desired in order to yield a large SNR for
newly developed sensor systems.

$F_{j}$$F_{j}$$F_{k}$$F_{k}$b)a)aerodynamic pressure$\scriptstyle
w/w_{\max}$0.50.01.0$\scriptstyle
w/w_{\max}$0.50.01.0$y$$z$$x$$y$$z$$x$concentrated loads

Figure 5: Result of loading optimization on an idealized spoiler demonstrator.
Schematic sketch of (a) the real aircraft spoiler due to aerodynamic loads and
(b) the idealized spoiler demonstrator under four-point loading (half model
rendered in symmetrical full view for display purposes).

2 Thus, the sandwich panel made out of an aluminum alloy was replaced by a
composite sandwich panel with an aramid honeycomb core and GFRP skins with a
quasi-isotropic layup [0,45,$-$45,0] and a total skin thickness of
$0.5\text{\,}\mathrm{m}\mathrm{m}$. The thickness reduction of the sandwich
skin from $1.0\text{\,}\mathrm{m}\mathrm{m}0.5\text{\,}\mathrm{m}\mathrm{m}$
reduces the bending stiffness significantly and, thus, allows larger
deformation at the same loading. The material parameters of the composite
sandwich panel are given in Table 2.2.2.

[H]Material parameters of the composite sandwich panel of the idealized
spoiler demonstrator HEXCEL COMPOSITES .

|  $E_{11}$ |  $E_{22}$ |  $E_{33}$ |  $\nu_{12}$ |  $\nu_{13}$ |  $\nu_{23}$ |  $G_{12}$ |  $G_{13}$ |  $G_{23}$
---|---|---|---|---|---|---|---|---|---
|  [MPa] |  [MPa] |  [MPa] |  - |  - |  - |  [MPa] |  [MPa] |  [MPa]
Each layer of skin ([0,45,$-$45,0]) |  22,550 |  20,900 |  1 |  0.15 |  0 |  0 |  4500 |  3500 |  3500
Core |  1 |  1 |  500 |  0 |  0 |  0 |  1 |  66 |  34

2 The change in the material brings two additional advantages: First, the
given GFRP sandwich skins have an maximum allowable in-plane stress of
$\sigma_{\max,\text{GFRP}}=$100\text{\,}\mathrm{M}\mathrm{P}\mathrm{a}$$,
which is similar to the yield stress of the initially considered aluminum
sandwich skin, thus allowing loading at similar stresses. Second, due to the
smaller stiffness (more than three times) of the composite sandwich panel (cf.
Table 2.2.2) compared to the stiffness of the aluminum alloy, a larger
deformation and, hence, approximately $2.5$ times larger strain amplitudes
(considering stiffness and maximum allowable in-plane stresses) can be
achieved with the same loading. However, the maximum possible strain
amplitudes are defined by a further detailed analysis of strain states and
stresses in each component using a three-dimensional (3D) FE model.

###  2.3 Stress and Strain Analysis with a Detailed 3D FE Model

The idealized four-point loading found with an optimization with a simplified
FE shell model (cf. Section 2.2.1) is now applied to a more sophisticated
symmetrical 3D FE model. Two concentrated loads are defined at the identified
optimal locations (see Table 2.2.2) on the lower skin of the idealized spoiler
demonstrator. By this measure, the local influence of concentrated loads on
the deformation and strain states of the upper skin around the load
introduction points (single nodes on lower skin) is minimized. The 3D FE model
incorporates the updated composite sandwich geometry and material properties
(cf. Table 2.2.2) and includes many more details than the simple shell model
representation used for the optimization of the loading. The geometry of the
detailed half model of the spoiler demonstrator is depicted in Figure 6.

kinematic couplingbeam† to hold hinge brackethinge bracketmodeled with
aCHBskin∗ ($0.5\text{\,}\mathrm{m}\mathrm{m}$)coresymmetry constraintfixed
supportfixed support702060130$F_{j}$$F_{k}$outline offront edge of CHB of
submodelsubmodelfront edge of CHBadhesive layer
($\geq$0.05\text{\,}\mathrm{m}\mathrm{m}$$)4040optimized
LDLCHB101.01.020100.8core ($15\text{\,}\mathrm{m}\mathrm{m}$)

Figure 6: Detailed 3D FE model (all dimensions in millimeters), ∗ shell
thickness, and † beam cross-section rendered for display purposes.

2 This incorporates multiple parts: The sandwich panel is modeled with a solid
core (8-node linear brick elements with reduced integration, C3D8R in
nomenclature of the used FE program Abaqus Dassault Systèmes Simulia Corp. ,
painted red in Figure 6), and the shell elements as top and lower skins
(4-node linear shell elements with reduced integration, S4R in Abaqus
nomenclature, painted blue in Figure 6) connected by tie constraints. Below
each support block of the CHB (8-node linear brick elements with reduced
integration, painted in gray in Figure 6) lies an adhesive layer with a
thickness of $0.05\text{\,}\mathrm{m}\mathrm{m}$ (8-node linear brick elements
with reduced integration, painted green in Figure 6). Subsequently, to connect
the support blocks of the CHB (painted gray in Figure 6) with the sandwich
skins, tie constraints between the skin and adhesive layer and between the
adhesive layer and support block are used. The connector rod, which holds the
hinge bracket of the idealized spoiler demonstrator, is modeled by a beam with
constant circular cross-section (diameter
$d=$35\text{\,}\mathrm{m}\mathrm{m}$$ and length
$l=$400\text{\,}\mathrm{m}\mathrm{m}$$; 2-node linear beam elements, B31 in
Abaqus nomenclature, painted yellow in Figure 6), as well as a linear elastic
material model of steel
($E_{\mathrm{St}}=$210\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$$,
$\nu_{\mathrm{St}}=0.3$). The support blocks for the CHB and the hinge
brackets are modeled with linear elastic material behavior and parameters for
aluminum ($E_{\mathrm{Al}}=$70\text{\,}\mathrm{G}\mathrm{P}\mathrm{a}$$,
$\nu_{\mathrm{Al}}=0.33$). The parameters for the linear elastic material
model of the adhesive layer (3M DP490 Epoxy,
$E_{\mathrm{Ad}}=$660\text{\,}\mathrm{M}\mathrm{P}\mathrm{a}$$,
$\nu_{\mathrm{Ad}}=0.38$) are taken from Nhamoinesu and Overend (2012). The
boundary conditions for the detailed 3D FE model are highlighted in orange in
Figure 6. Both CHBs are fixed in all DOFs at nodes in rectangular areas of
size $$20$\times$60\text{\,}\mathrm{m}\mathrm{m}^{2}$$, which represents the
cross-section of the remaining CHB (cf. Figure 2b). A symmetry constraint is
defined for all nodes of all components touching the $x$-plane. The left end
of the connector rod is fixed in all DOFs. The nodes of the upper and lower
skins of the sandwich panel, which lie in the area of the hinge bracket, are
connected with a kinematic coupling and can only rotate around the bearing
point at the right end of the connector rod; see Figure 6.

For the present idealized spoiler demonstrator, the highest stress amplitudes
are calculated in the composite sandwich skin and the adhesive layer in a
small region below the rounded corner of the CHB. A load distribution lip
(LDL) with a cross-section of $$10$\times$1\text{\,}\mathrm{m}\mathrm{m}^{2}$$
is added to the front edge of the CHB in order to reduce these local high
stress amplitudes. Additionally, an FE submodel of the corner region (node-
based submodeling technique with an enforced displacement boundary condition;
outline indicated by a dashed magenta line in Figure 6) was used to improve
the shape of the LDL. With this detailed FE submodel, different LDL types were
tested (various thicknesses of the LDL, different fillet and chamfer types—not
depicted in Figure 6). The best shape found has a large chamfer, which
tangentially reduces the thickness of the LDL from 1.0 to 0.25mm and increases
the thickness of the adhesive layer from 0.05 to 0.8mm (cross-section of the
improved LDL and adapted adhesive layer at the front edge of the CHB are
depicted in the top of Figure 6). This improved LDL shape reduces the local
high stresses in the adhesive layer by $33\text{\,}\mathrm{\char 37\relax}$
and in the upper skin by $28\text{\,}\mathrm{\char 37\relax}$ compared to the
initial straight shape. With these two measures (change from aluminum to
composite sandwich panel and adding an improved LDL), the maximum possible
loads are $F_{j,\max}=$178.6\text{\,}\mathrm{N}$$ and
$F_{k,\max}=$256.4\text{\,}\mathrm{N}$$.

The out-of-plane deformations of the upper skin calculated with the detailed
3D FE model of the idealized spoiler demonstrator and a comparison with
deformations given for the FE model of the real A340 aircraft spoiler are
presented in Figure 7. For better comparability, both contour plots are
normalized to the out-of-plane displacement calculated for the same point
$P_{0}=(x=$500\text{\,}\mathrm{m}\mathrm{m}$,y=$380\text{\,}\mathrm{m}\mathrm{m}$)$.
The white dashed rectangles indicate the outer dimensions of the idealized
spoiler demonstrator. A close correlation between both deformation contours is
shown. The out-of-plane deformation in point $P_{0}$ calculated for the
idealized spoiler demonstrator at maximum loading yields
$w_{\text{FEM}}(P_{0})=$22.93\text{\,}\mathrm{m}\mathrm{m}$$.

$x$$y$$P_{0}$Real aircraft spoiler (mirrored, scale 1:2)$x$$y$$P_{0}$Idealized
spoiler demonstrator$w/w_{P_{0}}$

Figure 7: Out-of-plane displacement contour plots of numerical FE models
(dashed rectangles indicate the size of the idealized spoiler demonstrator).

2

The evaluation of strain states is performed by using strain directions and
strain trajectories. Aside from commonly known principal strain directions
with angles $\alpha_{1,2}$ resulting from

$\varepsilon_{nm}=-\frac{\varepsilon_{xx}-\varepsilon_{yy}}{2}\sin
2\alpha+\varepsilon_{xy}\cos 2\alpha\overset{!}{=}0,$ (3)

the so-called zero-strain directions $\beta_{A,B}$ are calculated with

$\varepsilon_{nn}=\frac{\varepsilon_{xx}+\varepsilon_{yy}}{2}+\frac{\varepsilon_{xx}-\varepsilon_{yy}}{2}\cos
2\beta+\varepsilon_{xy}\sin 2\beta\overset{!}{=}0,$ (4)

where $\varepsilon_{xx}$, $\varepsilon_{yy}$, and $\varepsilon_{xy}$ are
components of the linear strain tensor. The right-hand sides of Equations (3)
and (4), i.e., $\overset{!}{=}0$, indicate that the solutions for angles
$\alpha$ and $\beta$ are found when $\varepsilon_{nm}$ and $\varepsilon_{nn}$
are set to zero, respectively. The normal strain vanishes in both zero-strain
directions $\beta_{A}$ and $\beta_{B}$. Note that, in the zero-strain
directions, the second normal strain component and the shear strain component
of the calculated strain tensor are not zero. Strain trajectories start at an
arbitrary point and are calculated by following a specific strain direction in
an iterative manner Schagerl et al. (2015); Schaberger (2016); Riedl (2018).

A comparison of the numerically calculated strain directions and the three
selected trajectories of the aircraft spoiler with aerodynamic pressure
loading and the idealized spoiler demonstrator with four-point loading is
depicted in Figure 8. In front of the CHB (in the center of the spoiler
surface), no zero-strain directions can be computed because the strains in
both principal directions have positive signs. Therefore, instead of zero-
strain directions, the minor principal strain directions are used in this
area. This area in front of the CHB, where no zero-strain trajectories exist,
is larger for the idealized spoiler demonstrator than for the real aircraft
spoiler. In addition, in the vicinity of the free edges of the real spoiler
surface, the strain directions yield larger deviations than on most of the
spoiler surface around the CHB. However, the overall shapes of trajectories
fit well together. The transitions between zero-strain and principal strain
trajectories are also located at similar locations on the spoiler surfaces.

$x$$y$Real aircraft spoiler (mirrored, scale 1:2)$x$$y$Idealized spoiler
demonstrator$\alpha_{1}$ \-
dir.${\color[rgb]{1,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,0}\alpha_{2}}$
\-
dir.${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\beta_{A}}$
\-
dir.${\color[rgb]{0,1,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,1,0}\beta_{B}}$
\- dir.$\alpha_{1}$ \-
traj.${\color[rgb]{1,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,0}\alpha_{2}}$
\-
traj.${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\beta_{A}}$
\-
traj.${\color[rgb]{0,1,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,1,0}\beta_{B}}$
\- traj.

Figure 8: Comparison of strain directions and trajectories of numerical FE
models (the region around the CHB and the hinge bracket is not considered;
dashed rectangles indicate the size of the idealized spoiler demonstrator).

2

##  3 Experimental Validation of the Developed Idealized Spoiler Demonstrator

The experimental validation of the numerical results of the idealized spoiler
demonstrator is performed by means of mechanical tests and a DIC system. In
this section, first, the assembly steps for building the idealized spoiler
demonstrator are explained. Second, a detailed description of the experimental
setup, including the demonstrator and measurement equipment, is given.
Finally, the last paragraph of this section explains the measurement procedure
performed.

###  3.1 Assembly of the Idealized Spoiler Demonstrator

The assembly of the idealized spoiler demonstrator is depicted in Figures 2b
and 9. The aluminum supports (CHB and hinge brackets) were bonded onto the
sandwich panel using the two-component epoxy adhesive 3M Scotch-Weld DP490 3M™
Scotch-Weld™ . According to the data sheet, at least seven days of curing time
at room temperature were given to achieve full strength of the bonding layer.
After the curing period, filets with $R=$1\text{\,}\mathrm{m}\mathrm{m}$$ at
the edge around the support blocks were carefully machined using a ball-nose
cutter to produce a clean and defined border. All support blocks (2 $\times$
CHB and 4 $\times$ hinge brackets) were mounted with M12 screws to aluminum
blocks, which were themselves combined by the connector rod; see Figure 2b.
The connector rod was rigidly mounted to the aluminum block of the CHB. Both
support blocks for the hinge brackets were mounted with ball bearings onto the
connector rod.

LED light sourceDIC camerasHBMDICLaptopvertical clamping platformmount DIC
camerasaluminum bars todisplacement sensorhydraulic cylinderload cellwiffle
treeidealized spoiler demonstratortest rig attachmentball bearingconnector
rodleveling feethinge bracketCHBmeasured area

Figure 9: Test setup for the deformation and strain measurements.

2

###  3.2 Experimental Setup

The test setup, including the spoiler demonstrator and all facilitated
measurement devices, is displayed in Figure 9. The complete assembly of the
idealized spoiler demonstrator was mounted with two M24 screws and slot nuts
to the vertical clamping platform of the test rig. The loading of the spoiler
demonstrator was done with a single manual hydraulic cylinder. The load was
distributed to the defined locations with a whiffle tree, as readily
mentioned. Its arms were adjusted according to the calculated loads and their
locations in Table 2.2.2. Each of the four loads was applied torque-free to
the lower skin of the idealized spoiler demonstrator using steel leveling feet
with a base plate diameter of $38\text{\,}\mathrm{m}\mathrm{m}$.

The facilitated measurement equipment included a load cell (HBM U3:
$F_{\max}=$10\text{\,}\mathrm{k}\mathrm{N}$$) and a displacement sensor (HBM
WA50: $d_{\max}=$50\text{\,}\mathrm{m}\mathrm{m}$$), both connected to the
data acquisition device (HBM QuantumX MX840A: sample rate
$100\text{\,}\mathrm{H}\mathrm{z}$; cf. Hottinger Brüel and Kjaer GmbH (a)).
The load cell was located between the hydraulic cylinder and the whiffle tree.
The displacement sensor was positioned at location
$P_{1}=(x=$480\text{\,}\mathrm{m}\mathrm{m}$,y=$360\text{\,}\mathrm{m}\mathrm{m}$$;
compare Figures 9 and 10. Measurements of HBM sensors were recorded using the
software HBM catman${}^{\text{\textregistered}}$Easy, cf. Hottinger Brüel and
Kjaer GmbH (b). Additionally, a DIC system from Correlated Solutions Inc. with
two synchronized cameras with a resolution of $2448\times 2048$ pixels was
used together with a HEDLER Profilux LED1000 light source Correlated Solutions
Inc. . The evaluation software VIC-3D 8 was used to analyze the DIC pictures
that were taken. A speckle pattern was applied with an airbrush on the
sandwich’s upper surface using white as a background color and black as the
speckle color (mean speckle size was $2.2\text{\,}\mathrm{p}\mathrm{x}$). The
cameras were mounted on the horizontal aluminum bar with a distance from each
other of $l_{\text{cam}}=$995\text{\,}\mathrm{m}\mathrm{m}$$ and a stereo
angle of $\beta_{\text{cam}}=$27.9\text{\,}\mathrm{\SIUnitSymbolDegree}$$. The
aluminum bar was adjusted parallel to the spoiler surface with a normal
distance of $l_{\perp}=$2000\text{\,}\mathrm{m}\mathrm{m}$$. With these camera
positions, the complete left half of the spoiler surface could be measured by
the DIC system (the area of measurement is indicated with a black dashed
polygon in Figure 9).

Before starting the measurement, the whiffle tree was adjusted according to
the calculated positions of the single load points, and all sensor signals
were zeroed. Subsequently, the data acquisition was started, and the loading
was manually increased until a total load of $F=$400\text{\,}\mathrm{N}$$
($F_{j}=$82\text{\,}\mathrm{N}$$, $F_{k}=$118\text{\,}\mathrm{N}$$) was
reached.

##  4 Results and Discussion

The results of measured displacements and strains are compared with the
simulation results of the detailed 3D FE model. A comparison of the simulation
results of the real aircraft spoiler and the 3D FE model has already been
presented in Section 2.3, and will not be repeated here.

###  4.1 Out-of-Plane Displacements

A comparison of the displacements at a loading of
$F=2F_{j}+2F_{k}=$400\text{\,}\mathrm{N}$$ calculated with the FEM simulation
and measured with the DIC system is depicted in Figure 10. The overall shapes
of the contour plots of the simulation and experiment show a very good match.
The extraction of the displacement at point
$P_{2}=(x=-$480\text{\,}\mathrm{m}\mathrm{m}$,y=$360\text{\,}\mathrm{m}\mathrm{m}$)$
from the DIC measurement yields
$w_{\text{DIC}}(P_{2})=$11.19\text{\,}\mathrm{m}\mathrm{m}$$. At the
equivalent location on the opposite side of the idealized spoiler demonstrator
(where no DIC measurements were conducted), the displacement sensor at
position
$P_{1}=(x=+$480\text{\,}\mathrm{m}\mathrm{m}$,y=$360\text{\,}\mathrm{m}\mathrm{m}$)$
measured a similar displacement of
$w_{\text{DS}}(P_{1})=$11.14\text{\,}\mathrm{m}\mathrm{m}$$. The deviation
between the measured displacements at points $P_{1}$ and $P_{2}$ was less than
$0.5\text{\,}\mathrm{\char 37\relax}$. Hence, these measurements at
symmetrical points, as well as the similar displacement shapes, indicated that
the whiffle tree was correctly adjusted and positioned.

$P_{2}$DIC measurement at demonstrator$P_{1}$Numerical results of 3D FE
model$w/w_{P_{1,2}}$$x$$y$

Figure 10: Out-of-plane displacement contour plots at an applied load of
$\bm{F=}$ 400 N.

2

The displacement calculated with the symmetrical 3D FE half model yielded
$w_{\text{FEM}}(P_{1,2})=$9.66\text{\,}\mathrm{m}\mathrm{m}$$. The maximum
deviation between the calculated and measured displacements in the simulation
and experiments was $13.7\text{\,}\mathrm{\char 37\relax}$. This rather large
deviation was expected because the material parameters were taken directly
from data sheets and were not extracted from coupon tests. With a simple
scaling of stiffness parameters, the deviation in amplitudes could be
significantly reduced. However, more important for the development of a
spoiler demonstrator to test SHM systems is a similar displacement shape,
which was achieved with the current idealized spoiler demonstrator and the
optimized four-point loading. Nevertheless, the final aim was to correctly
represent strain states on the spoiler surface in order to test strain-based
SHM methods.

###  4.2 Principal In-Plane Strains

Principal in-plane strains on the surface of the upper skin of the idealized
spoiler demonstrator are depicted in Figure 11 for the DIC measurements and
numerical results of the 3D FE model.

a)

DIC measurement at demonstratorNumerical results of 3D FE
model$\varepsilon_{1}\cdot 10^{-3}$$x$$y$

b)

DIC measurement at demonstratorNumerical results of 3D FE
model$\varepsilon_{2}\cdot 10^{-3}$$x$$y$

Figure 11: Comparison between the experiment and simulation of (a) minor and
(b) major principal in-plane strains at an applied load of $\bm{F=}$ 400 N.

2 In order to measure the depicted area of the idealized spoiler demonstrator,
the DIC cameras had to be positioned with a relatively large normal distance
(see Section 3), which reduced the strain accuracy and resolution. Therefore,
the calculated strain contours of the finite element simulation yielded
smoother strain distributions and showed the load introduction points more
clearly than the strain contours measured with the DIC system. However, in
large areas, the major and minor principal in-plane strains showed similar
results. The major principal strains, which are depicted in Figure 11a, mainly
yielded positive amplitudes in most areas, except for the area in front of the
CHB. In contrast, the minor principal strains exclusively yielded negative
results on the whole surface; see Figure 11b.

The calculated and measured strain directions and resulting trajectories are
depicted in Figure 12, showing the mirrored results of the FEM simulations for
better comparison (otherwise, the notation of strain directions $\beta_{A}$
and $\beta_{B}$ would be interchanged; cf. Figure 8). In the center of the
spoiler in front of the CHB, no zero-strain directions could be computed
because the strains in both principal directions had negative signs; compare
with Figure 11. On the remaining spoiler surface, only zero-strain directions
are printed for better plot clearness. All depicted strain directions yielded
similar orientations for the DIC measurement and the numerical simulation
results. Furthermore, in the simulation and experiment, almost identical
trajectories could be drawn along the zero-strain and major principal strain
directions. It is assumed that distributed strain sensors, e.g., FOSs, applied
along such lines can be used to efficiently monitor the structural integrity
of the spoiler.

DIC measurement at demonstrator

Numerical results of 3D FE model (mirrored)$x$$y$$\alpha_{1}$ \-
direction${\color[rgb]{1,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,0}\alpha_{2}}$
\-
direction${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\beta_{A}}$
\-
direction${\color[rgb]{0,1,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,1,0}\beta_{B}}$
\- direction$\alpha_{1}$ \-
trajectory${\color[rgb]{1,0,0}\definecolor[named]{pgfstrokecolor}{rgb}{1,0,0}\alpha_{2}}$
\-
trajectory${\color[rgb]{0,0,1}\definecolor[named]{pgfstrokecolor}{rgb}{0,0,1}\beta_{A}}$
\-
trajectory${\color[rgb]{0,1,0}\definecolor[named]{pgfstrokecolor}{rgb}{0,1,0}\beta_{B}}$
\- trajectory

Figure 12: Comparison of the strain directions and trajectories for the
experiment and simulation at an applied load of $\bm{F=}$ 400 N.

2

##  5 Conclusions

The calculated deformation shape of a real aircraft spoiler subjected to
aerodynamic pressure could be reproduced by means of a simplified and
idealized spoiler demonstrator (homogeneous sandwich plate with attachments on
a scale of 1:2) and four concentrated loads defined by location and
amplitudes. This was achieved with a numerical FE-parameter-study-based
optimization of the amplitudes and locations of five initially defined unit
loads in order to minimize the out-of-plane deformation differences between a
real aircraft spoiler and an idealized spoiler demonstrator by following a
least-squares approach. Furthermore, the optimal load positions and amplitudes
were weighted with the associated maximum stresses to enable large spatial
strains without the structural failure of the demonstrator. Thus, deformations
resulting from the four-point loading of the idealized spoiler demonstrator
that were large enough to allow a distributed strain analysis of DIC
measurements in mechanical tests were achieved. However, to further maximize
the possible strain values, a composite sandwich with GFRP face layers and an
aramid honeycomb core was used. Thorough stress and strain analyses were
performed using a detailed 3D FE model. In a static strength analysis, special
care was also given to the stresses in the adhesive layer between the sandwich
panel and the CHB in the region around the front corner, where stress
concentrations occurred. Through the design of a load distribution lip, the
maximum stress in the adhesive between the CHB and sandwich face layer was
reduced by $33\text{\,}\mathrm{\char 37\relax}$. A comparison between the
numerical results of the aircraft spoiler and the idealized spoiler
demonstrator showed good agreement of the out-of-plane displacements and
strain states with respect to strain orientations. Hence, for the aerodynamic
pressure load considered, the displacements and spatial strain orientations of
the real aircraft spoiler were adequately reconstructed with only four
concentrated loads in the idealized spoiler demonstrator.

The validation of the simulation results for the idealized spoiler
demonstrator developed here was performed by comparing the numerically
calculated deformations and strain states with measurements gained from a
corresponding experimental setup. The out-of-plane displacements were measured
using a displacement sensor and a DIC system, and they fit well to the
calculated results. Further processing of the measured strain states revealed
that the strain directions and trajectories also correlated well with the FE
results. However, the presented load optimization algorithm is also capable of
quasi-realistically reproducing other loading conditions and strain states of
operated aircraft spoilers. Hence, the idealized spoiler demonstrator and the
load optimization algorithm represent a cost-efficient and adequate platform
for experimental studies of SHM systems under quasi-realistic loading
conditions and strain states.

The next step of this research work is the application of various sensors and
SHM methods to the idealized spoiler demonstrator. In order to identify
damages critical to composite structures (e.g., sandwich debonding,
delamination, impact damage), strain sensors must be applied to the idealized
spoiler demonstrator, and potential strain-based SHM methods must be tailored
to the considered structures and damage cases; they must also be applied and
tested under changing environmental conditions. Finally, the most promising
SHM methods that are the most cost-efficiently developed or have been improved
using the spoiler demonstrator can be validated through applications on a real
aircraft spoiler.

Conceptualization, M.W., C.K., and M.S.; methodology, M.W. and C.K.;
validation, M.W. and C.K.; investigation, M.W. and C.K.; writing—original
draft preparation, M.W.; writing—review and editing, M.W., C.K., and M.S.;
visualization, M.W.; supervision, C.K. and M.S.; funding acquisition, M.S. All
authors have read and agreed to the published version of the manuscript.

This research was funded by the Christian Doppler Research Association, the
Austrian Federal Ministry for Digital and Economic Affairs, and the National
Foundation for Research, Technology, and Development.

Not applicable.

Not applicable.

The data presented in this study are available upon request from the
corresponding author.

###### Acknowledgements.

The authors thank Erich Humer and Reinhold Wartecker for their precise
manufacturing of the idealized spoiler demonstrator for the experimental
tests. Furthermore, the support of Lukas Heinzlmeier in performing the
experimental measurements, as well as that of Thomas Bergmayr and Martin
Meindlhumer in reviewing the manuscript, is gracefully acknowledged. The
authors thank Open Access Funding by the University of Linz. The authors
declare no conflict of interest. Abbreviations The following abbreviations are
used in this manuscript:
SHM | structural health monitoring
---|---
FEM | finite element method
EIT | electrical impedance tomography
FOS | fiber optical sensor
FRP | fiber-reinforced polymer
GFRP | glass-fiber-reinforced polymer
NDT | non-destructive testing
SNR | signal-to-noise ratio
FE | finite element
DOF | degree of freedom
CHB | center hinge bracket
DS | displacement sensor
DIC | digital image correlation
3D | three dimensional
LDL | load distribution lip
Al | aluminum alloy
St | steel
Ad | adhesive
cam | camera of the DIC system
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