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Proceedings ArticleDOI

A multi-stable spanwise twist morphing trailing edge

09 Jan 2017-
About: The article was published on 2017-01-09 and is currently open access. It has received 1 citations till now. The article focuses on the topics: Trailing edge.

Summary (3 min read)

Introduction

  • A multi-stable spanwise twist morphing trailing edge.
  • This document is made available in accordance with publisher policies.

A Multi-stable Spanwise Twist Morphing Trailing Edge

  • Qing Ai∗, Paul M.Weaver† University of Bristol, Bristol, United Kingdom, BS8 1TR Comparison with a flap transition design from the literature indicates that further optimization of the profile can lead to improved aerodynamic performance.
  • The proposed morphing transition control surface constitutes a series of stacked ribs with skewed corrugations along the wing span exploiting material and geometric compliance with bend-twist coupling.
  • A proof-of-concept demonstrator was manufactured and investigated with an analytical model, finite element method (FEM) and also experiments.
  • A novel spanwise twist morphing trailing edge (SMTE) concept is developed using prestressed composite laminate spar strips.

II. The spanwise morphing trailing edge concept

  • Over recent decades, several aeroplane wing flap transition devices have been proposed [14–16], most of which use mechanical systems to provide the desired spanwise trailing edge deformed shape.
  • One significant challenge remaining is the actuation requirement for such devices.
  • To address this issue, a multistable SMTE concept is proposed, which is able to provide a spanwise trailing edge deformed shape featuring twist/torsion structural behavior with minimum actuation force requirements.
  • Ideally, an aeroelastic approach coupling fluid and structural analyses is desirable in the morphing structure design and a solution that suits a wide range of flow conditions is realistic and viable.
  • Accurate aerodynamic pressure and force calculations in this case require computationally expensive threedimensional computational fluid dynamic simulations and the coupled fluid-structure interaction can significantly complicate the design process.

A. SMTE design

  • The proposed SMTE concept consists of two main components: ribs along chord and spars in the span direction, which are assembled in a grid pattern.
  • The span length, L, is 600 mm and five ribs are evenly arranged along the wing span.
  • Three rows of spar strips are used: the rear, middle and tip spars, as shown in Fig. 1 and the spar strip length, l is 150 mm.
  • The offset between the selected twist axis and the structural shear centre leads to a spanwise bending deformation and such effects can be minimised by optimizing the positions of the middle and tip spar, i.e. R1 and R2, which is not considered in detail in this paper.
  • Rear spar strips are manufactured flat without an initial curvature while the middle and tip spar laminate strips are manufactured in a stress free state with an initial curvature κx,initial along its local x axis (see the coordinate system in dashed line Fig. 1).

1. Strain energy Π

  • The internal grid structure of the SMTE is inspired by the morphing aerofoil device by Daynes et al. [19]: two prestressed spars are held at a distance Ri from the twist axis at the centroid of the rear spar and are subject to twist deformation about the twist axis under applied actuation moment.
  • The inextensible model developed by Daynes et al. [19] is adopted.
  • An assumption is made that the transverse curvature is negligible, which is valid for slender strips where the strain energy from longitudinal curvature and twist are dominant.

2. Energy stable equilibria

  • The stable equilibria of the SMTE can be found by seeking the minimum strain energy state in terms of design parameters, i.e. the laminate ply angle β for all the spar strips, the initial pre-bend curvature κinitial in the middle and tip spars and the twist angle ϕ [19, 25].
  • The stable equilibrium configurations are determined when the first derivative of the strain energy Π is zero and the second derivative of Π is greater than zero.

III. Strain energy tailoring

  • Using current analytical formulations of the strain energy and the stable equilibria conditions developed in the previous section, Eq.3 and 5, a preliminary optimization study is carried out to investigate the stability of the SMTE.
  • Design parameters considered in this study are the initial pre-bend radius of curvature ρ of the middle and tip spar strips, the spar laminate strip stiffness matrix D∗ and the twist angle ϕ applied to the SMTE.
  • In order to simplify the analysis, only symmetric laminates with the same orientation angle β (see Fig. 1) with constant thickness of 1 mm are considered for all spar strips, i.e. a layup of [β8].
  • The twist angle ϕ is selected to change from −30◦ to 30◦, which provides a large deformation capability for the SMTE.

A. Ply angles

  • 2 presents the contour plot of strain energy Π, twisting moment M and torsional stiffness GJ of the SMTE as a function of the ply angle β of the laminate spar strips for a zero initial curvature in the middle and tip spars (see Fig. 1).
  • Without the prestress effects in the spars, the strain energy Π increases with the twist angle ϕ for all ply angles and peaks are found at ply angles β = ±45◦ and twist angle ϕ = ±30◦.
  • It is worth noting that the stable neutral position of the SMTE proposed can now be predefined over a wide range of twist angles ϕ (in this case, ϕstable = ±0.524 is achievable) by selectively designing the ply angle and the initial curvature in the middle and tip spar laminates.
  • The ZTS SMTE case is also observed in Fig. 6 and marked by the dotted line in the plots.
  • For a ply angle β of 45◦, the increased initial curvature leads to a stable equilibrium position at positive twist angles shown by the red line marking zero twisting moment in Fig. 7a.

A. Finite element method

  • The ZTS SMTE design found in Section III was modelled using the commercial software package ABAQUS/CAE (ABAQUS 6.12, Dassault Systems Inc., VV, France), which has a layup of [08] for all the spar strips with 0◦ along the spanwise direction and a layup of [04] for all ribs with with 0◦ along the chordwise direction.
  • 1 were used and the laminates were modelled with Composite Layups section in Abaqus.
  • 9 shows that the developed analytical model provides accurate predictions of twist moment for the SMTE compared to FEM.
  • Furthermore, the stress concentration and redistribution caused by the prestress at the corners between spar strips and ribs are not modelled in the analytical model, which leads to discrepancies as well.
  • Significant spanwise trailing edge deformation difference is observed and such spanwise geometrical changes significantly affect the aerodynamic and aeroacoustic performance of the wing fitted 9 of 13 American Institute of Aeronautics and Astronautics with the proposed devices.

B. Morphing skins

  • In order to comprehensively investigate effects of the prestressed composite laminate spars on the stability of the SMTE, morphing skins were not considered in previous sections.
  • Ideally, skin materials must meet a series of requirements for a viable, realistic morphing structure: [27] flexibility in the morphing direction to reduce actuation force; stiff in the non-morphing direction for structural integrity; 10 of 13 American Institute of Aeronautics and Astronautics high strain capability and recovery rate; resistance to fatigue, weather, abrasion and chemical.
  • Flexible matrix composites are one of the promising candidates studied [27, 28] that suit the developed SMTE design.
  • Thorough studies have been carried out to assess the mechanical properties and processability and results showed that the proposed “ePreg” suits application in morphing structures.
  • Increased stiffness of the morphing skin does not change effects of pre-stressed spars on the SMTE and materials selection of the skin also broadens the tailorability of the whole structure.

V. Conclusions

  • A novel spanwise twist morphing trailing edge device consisting of CFRP ribs and spars has been proposed in this paper and preliminary optimization studies were carried out.
  • Investigations using an analytical model are carried out and thorough parametric studies show that by selectively changing the spar laminate layups and the initial curvature in the prestressed spar strips, stable neutral position of the SMTE can be pre-defined over a wide range of twist angles (a twist angle change of ±30◦ has been achieved in the current design).
  • The analytical model is verified using commercial FEM and good correlation was found.
  • Morphing skin options are briefly discussed in this paper with emphases on elastomeric matrix composites.

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Ai, Q., & Weaver, P. M. (2017). A multi-stable spanwise twist
morphing trailing edge. In
25th AIAA/AHS Adaptive Structures
Conference, 2017
[AIAA 2017-0055] American Institute of Aeronautics
and Astronautics Inc. (AIAA). https://doi.org/10.2514/6.2017-0055
Peer reviewed version
Link to published version (if available):
10.2514/6.2017-0055
Link to publication record in Explore Bristol Research
PDF-document
This is the author accepted manuscript (AAM). The final published version (version of record) is available online
via AIAA at https://arc.aiaa.org/doi/10.2514/6.2017-0055. Please refer to any applicable terms of use of the
publisher.
University of Bristol - Explore Bristol Research
General rights
This document is made available in accordance with publisher policies. Please cite only the
published version using the reference above. Full terms of use are available:
http://www.bristol.ac.uk/red/research-policy/pure/user-guides/ebr-terms/

A Multi-stable Spanwise Twist Morphing Trailing Edge
Qing Ai
, Paul M.Weaver
University of Bristol, Bristol, United Kingdom, BS8 1TR
A spanwise morphing trailing edge design utilizing structural multistability with minimised actuation
requirements is introduced in this paper. The proposed morphing device consists of composite lami-
nate spars and ribs assembled in a grid pattern. The composite laminate spar strips are manufactured
in a stress free state with a predefined curvature and are prestressed by flattening before assembly.
In this way, initial strain energy is stored in structural components that can later be released during
structural deformations. With an analytical model, design parameters including laminate layups of
spars and the initial curvature in spar strips are investigated. Results show that by selectively chang-
ing the structural design, the stable equilibria configuration of the morphing device can be set over
a wide range of twist angles. Particularly, a zero torsional stiffness spanwise morphing trailing edge
design has been observed. Finite element method results are provided to verify the analytical model
and good correlation is found. The spanwise trailing edge deformed shape of the novel device features
a desirable torsion behavior, providing structural conformality and a constant torsion angle variation
along the span. Comparison with a flap transition design from the literature indicates that further
optimization of the profile can lead to improved aerodynamic performance.
Nomenclature
b = trailing edge chord length
c = aerofoil chord length
E = Young’s modulus
G = shear modulus
M = twist moment
GJ = torsional stiffness
l = spar rib length
L = trailing edge span length
Π = strain energy
D
= laminate reduced flexural stiffness matrix
R = distance between spar and the twist axis
ρ = radius of curvature of the pre-bend spar strips
δ = ratio of l to ρ,
l
ρ
β = laminate ply angle
ν = Poisson’s ratio
κ = curvature
PhD Student, Advanced Composites Centre for Innovation and Science (ACCIS), University of Bristol. qing.ai@bristol.ac.uk
Professor in Lightweight Structures, Advanced Composites Centre for Innovation and Science (ACCIS), University of Bristol,
Paul.Weaver@bristol.ac.uk

I. Introduction
Aviation industries are driven by ongoing economic and environmental considerations for aeroplanes of high effi-
ciency and low gas and noise emission [1]. Of particular importance is to maintain aeroplane performance based on
varying flight regimes. As such, shape changing structures that have excellent performance characteristics, low system
complexity and potential light-weight have received growing interest from the engineering community. These intel-
ligently responsive structures are increasingly known as morphing structures and have been considered as promising
candidates for the next generation of high-lift systems for aeroplane wings. [24]
Conventional multi-element aeroplane wings including ailerons and flaps use discrete rigid structural parts that
are articulated around hinges and linkages to provide required geometrical changes for flow control purposes. Such a
design philosophy leads to a heavy system and a high mechanism complexity. On the contrary, morphing structures
enable wing surface geometrical changes to happen through conformal structural deformations including bending
and twisting, reducing system complexity and weight [2, 3, 58]. Furthermore, the intrinsic continuous geometrical
changes and smooth structural surfaces in morphing structures significantly reduce drag forces and noise emission due
to structural discontinuities [5].
Aerofoil morphing concepts are primarily classified into two main categories: in-plane morphing and out-of-plane
morphing with chordwise, spanwise profile change and twist being three different ways for enabling out-of-plane mor-
phing structures [3]. Chordwise morphing structures have received significant interest in recent decades. Campanile et
al. [9] developed a chordwise morphing aerofoil concept, the Belt-Rib, consisting of a closed belt and spokes. Exper-
imental studies have successfully confirmed the feasibility of the concept for aerofoil flow control purposes. Results
showed that tailoring of the structural stiffness of the Belt-Rib can lead to significant aerodynamic and aeroelastic
amplification effects, minimising the external actuation requirement. Furthermore, variable stiffness materials have
also been studied for application in morphing structures due to efficiency and performance considerations [10, 11].
Ai et al. [11] introduced material stiffness variations into a chordwise morphing trailing edge design that facilitated
tailoring of morphing profiles of the deformed trailing edge. Studies of aerofoils fitted with such morphing trailing
edges showed that the aerofoil performance envelope including lift and drag coefficients and noise emission can be
effectively extended [12,13]. However, even though a continuous aerofoil camber change is achieved with the morph-
ing trailing edge concepts, spanwise end gaps remain between adjacent trailing edge flaps that could lead to increased
noise emission and drags. To address this issue, different flap transitions linking flaps in a spanwise fashion have been
proposed in recent decades [1417]. Woods et al. [17] proposed an elastically lofted transition control surface for
wings which covers the gaps between spanwise ends of adjacent control surfaces. The proposed morphing transition
control surface constitutes a series of stacked ribs with skewed corrugations along the wing span exploiting material
and geometric compliance with bend-twist coupling. Desired spanwise nominal deformation shapes can be obtained
with carefully selected corrugated skewed rib angles.
Similar to spanwise flap transitions, wing twisting also provides continuous spanwise profile change and several
concepts have been proposed and studied [3, 18, 19]. Lachenal et al. [18] proposed a zero torsional stiffness (ZTS)
twist morphing blade structure which consisted of pre-stressed flanges and a warping skin as actuation method. A
proof-of-concept demonstrator was manufactured and investigated with an analytical model, finite element method
(FEM) and also experiments. Results showed that by tailoring the prestress in the flanges, a twist morphing blade with
zero torsional stiffness about its rotation axis can be obtained. However, discrepancies between the analytical results
and experimental measurements were observed for large twist angles, owing to the simplicity of the analytical model.
Following this study, Daynes et al. [19] developed a zero torsional stiffness morphing aerofoil which is made of pre-
curved carbon fibre reinforced plastic (CFRP) laminate spar strips and CFRP ribs. The multistable twisting structure
was studied with an analytical model and then validated against FEM and experimental results. Good agreement
was found between results from the analytical model and that from FEM. The study showed that the combination of
geometry nonlinearity, material properties and pre-stress effects in the morphing structure can lead to a significant
reduction in actuation energy requirements and a zero torsional stiffness design case was also observed.
In this paper, a novel spanwise twist morphing trailing edge (SMTE) concept is developed using prestressed com-
posite laminate spar strips. Prestress effects in structures have been used previously to adaptively change the structural
stiffness [20] and the proposed SMTE concept extends on previous research work by Lachenal [18] and Daynes [19].
It is observed that in recent morphing wings [18, 19], geometrical changes were achieved by twisting the whole wing
about an axis, which leads to coupled deformation in both the leading edge and trailing edge parts. The developed
SMTE herein can be attached to a wing leading edge part that decouples the deformation in the trailing edge and lead-
ing edge parts. This paper is organized as follows: the SMTE design is introduced firstly with geometric parameters
given and then a simple analytical model of the SMTE structure is described in detail; preliminary investigations on ef-
fects of changing laminate ply angles and initial curvatures are then discussed to study the stability of the SMTE; finite
element method is used to validate a zero torsional stiffness SMTE design case and the paper finishes by discussing
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American Institute of Aeronautics and Astronautics

results and giving conclusions.
II. The spanwise morphing trailing edge concept
Over recent decades, several aeroplane wing flap transition devices have been proposed [1416], most of which use
mechanical systems to provide the desired spanwise trailing edge deformed shape. However, one significant challenge
remaining is the actuation requirement for such devices. Not only do they have complex driving mechanisms, but
also require large amount of actuation energy. To address this issue, a multistable SMTE concept is proposed, which
is able to provide a spanwise trailing edge deformed shape featuring twist/torsion structural behavior with minimum
actuation force requirements.
A SMTE device can be used as a single function unit for spanwise wing geometrical changes and can also serve as a
smooth transition between different control surfaces. Using such concepts, the drag force and wing noise emission can
be reduced by removing flow vortices around the flap ends from the pressure side to the suction side [5]. In this section,
a SMTE design consisting of composite laminate spars and ribs is introduced and an analytical model is developed
to describe the mechanical behavior of the structure. Ideally, an aeroelastic approach coupling fluid and structural
analyses is desirable in the morphing structure design and a solution that suits a wide range of flow conditions is
realistic and viable. However, in this SMTE concept, the flow field around the trailing edge depends greatly on
the flow velocity, angles of attack and the deformed shape (both spanwise and chordwise) of the morphing trailing
edge. Accurate aerodynamic pressure and force calculations in this case require computationally expensive three-
dimensional computational fluid dynamic simulations and the coupled fluid-structure interaction can significantly
complicate the design process. Thus, the current research only focuses on the concept development and effects of
aerodynamic forces are not considered in this preliminary design study.
Figure 1. Schematic of the spanwise morphing trailing edge design
A. SMTE design
The proposed SMTE concept consists of two main components: ribs along chord and spars in the span direction,
which are assembled in a grid pattern. A NACA 0012 aerofoil is chosen in this study. The wing has a chord of c = 500
mm and a trailing edge length of b = 100 mm (b/c =20%). The span length, L, is 600 mm and five ribs are evenly
arranged along the wing span. Three rows of spar strips are used: the rear, middle and tip spars, as shown in Fig. 1 and
the spar strip length, l is 150 mm. The distances from rear spar to middle spar, R
1
and from the middle spar to the tip
spar, R
2
, are 30 mm and 40 mm, respectively. This paper focuses on describing a generic concept of a twist morphing
trailing edge instead of developing a product for any specific application and as such, geometrical parameters used
are for general purposes and not optimized. All the rib and spar strips are made of composite laminates using Hexcel
8552/IM7 CFRP prepreg [21] with mechanical properties given in Table. 1. All ribs have the same laminate layup
of [0
4
] with 0
along chord and the spar ribs ply angle β is considered as a design parameter for a layup of [β
8
] with
0
along span. It is worth noting that prestress effects are only introduced into the the middle and tip spar strips (see
Fig. 1) with an initially manufactured curvature before assembly.
The twist axis is positioned at the centroid of the rear spar and does not coincide with the shear centre of the
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American Institute of Aeronautics and Astronautics

Table 1. Material properties of prepreg material [21]
Material E
11
(GPa) E
22
(GPa) G
12
(GPa) ν
12
(−−) ν
21
(−−) Thickness (mm)
8552/IM7 135 9.5 5 0.3 0.021 0.125
structure. The offset between the selected twist axis and the structural shear centre leads to a spanwise bending
deformation and such effects can be minimised by optimizing the positions of the middle and tip spar, i.e. R
1
and R
2
,
which is not considered in detail in this paper. Rear spar strips are manufactured flat without an initial curvature while
the middle and tip spar laminate strips are manufactured in a stress free state with an initial curvature κ
x,initial
along its
local x axis (see the coordinate system in dashed line Fig. 1). The grid structure is then built in a heightened energy
state and the pre-stored energy in the flattened spar strips can be released during the twist deformation to reduce the
work done by the actuation force.
B. Analytical model
1. Strain energy Π
The internal grid structure of the SMTE is inspired by the morphing aerofoil device by Daynes et al. [19]: two
prestressed spars are held at a distance R
i
from the twist axis at the centroid of the rear spar and are subject to twist
deformation about the twist axis under applied actuation moment. In this paper, the inextensible model developed
by Daynes et al. [19] is adopted. Key assumptions are: (1) the laminate strip deformation is inextensible and (2) the
curvature is uniform across the mid-surface of the strips. When the SMTE is subject to a twist angle ϕ at the spanwise
end, as shown in Fig. 1, the curvature change κ of a spar strip with respect to its local coordinate (see coordinate
system in dashed line in Fig. 1) is expressed as follows [19]:
κ =
κ
x
κ
y
κ
xy
=
R
i
· ϕ
2
2L
2
κ
x,initial
0
2
ϕ
L
, (1)
where R
1
denotes the distance between the rear spar and middle spar, R
2
refers to the distance between the middle spar
and tip spar, L is the SMTE span length, κ
x,initial
is the initial bend curvature in the middle and tip spar strips, defined
as κ
x,initial
=
1
/ρ with ρ denoting the initial radius of curvature in the pre-bend strips. An assumption is made that the
transverse curvature is negligible, which is valid for slender strips where the strain energy from longitudinal curvature
and twist are dominant. However, a thorough study has been carried out by Lachenal et al. [22] to investigate effects
of the transverse curvature on the stability of helix structures. It was found that membrane stretching occurs when
the transverse curvature is considered and a two-dimensional, extensional model can provide explicit insight into the
mechanical behavior. In the following sections, investigations are carried out with the current analytical formulations
owing to its combined simplicity and sufficient level of accuracy.
The structural strain energy Π is expressed as: [23]
Π =
1
2
N
i=1
l
i
H
i
κ
T
i
D
i
κ
i
, (2)
where N represents the total number of spar strips in the structure, l
i
and H
i
denotes the length and width of the i
th
strip respectively, κ
T
i
refers to the transpose of the curvature change tensor κ
i
, D
i
is the reduced flexural stiffness
matrix of the composite laminate spar strips and is defined as, D
= D BA
1
B, where A, B and D are the in-plane,
coupling and flexural stiffness matrices in classic laminate theory [24].
Combining Eqs. 1 and 2, the strain energy is calculated as:
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American Institute of Aeronautics and Astronautics

Citations
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Book ChapterDOI
01 Jan 2021
TL;DR: This holistic review provides recent advances in the reconfiguration mechanism, fabrication, and design of multistable composite structures and their applications in morphing structures, bioinspired structures, and soft robotics grippers are particularly highlighted with great potential in this promising field.
Abstract: Multistable composites, as a novel class of advanced composites, are characterized by two or more stable configurations that allow to remain in their respective equilibrium states without the continuous action of external loading. Owing to the advantages of lightweight, high mechanical strength, and good reconfigurability, multistable composite structures are widely used in aerospace industries, energy harvesters, robotic industries, etc. Such advanced composite structures have been extensively studied by means of theoretical analysis, experimental investigation, as well as finite element simulation. This holistic review provides recent advances in the reconfiguration mechanism, fabrication, and design of multistable composite structures. In addition, their applications in morphing structures, bioinspired structures, and soft robotics grippers are particularly highlighted with great potential in this promising field.

2 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the authors classify the shape morphing parameters that can be affected by planform alteration (span, sweep, and chord), out-of-plane transformation (twist, dihedral/gull, and span-wise bending), and airfoil adjustment (camber and thickness).
Abstract: Aircraft wings are a compromise that allows the aircraft to fly at a range of flight conditions, but the performance at each condition is sub-optimal. The ability of a wing surface to change its geometry during flight has interested researchers and designers over the years as this reduces the design compromises required. Morphing is the short form for metamorphose; however, there is neither an exact definition nor an agreement between the researchers about the type or the extent of the geometrical changes necessary to qualify an aircraft for the title ‘shape morphing.’ Geometrical parameters that can be affected by morphing solutions can be categorized into: planform alteration (span, sweep, and chord), out-of-plane transformation (twist, dihedral/gull, and span-wise bending), and airfoil adjustment (camber and thickness). Changing the wing shape or geometry is not new. Historically, morphing solutions always led to penalties in terms of cost, complexity, or weight, although in certain circumstances, thes...

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TL;DR: The mechanics of composite materials is universally compatible with any devices to read and is available in the authors' book collection an online access to it is set as public so you can download it instantly.
Abstract: Thank you for downloading mechanics of composite materials. Maybe you have knowledge that, people have look hundreds times for their favorite books like this mechanics of composite materials, but end up in malicious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they are facing with some infectious bugs inside their desktop computer. mechanics of composite materials is available in our book collection an online access to it is set as public so you can download it instantly. Our book servers hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the mechanics of composite materials is universally compatible with any devices to read.

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"A multi-stable spanwise twist morph..." refers background in this paper

  • ...The structural strain energy Π is expressed as: [23] Π = 1 2 N ∑ i=1 liHi△κ i Di κi, (2) where N represents the total number of spar strips in the structure, li and Hi denotes the length and width of the ith strip respectively, △κT i refers to the transpose of the curvature change tensor △κi, Di is the reduced flexural stiffness matrix of the composite laminate spar strips and is defined as, D∗ = D − BA−1B, where A, B and D are the in-plane, coupling and flexural stiffness matrices in classic laminate theory [24]....

    [...]

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TL;DR: In this paper, the authors present failure criteria for thin-walled composite beams with shear deformation and cross-sectional properties of thin-wall composite beams, as well as the buckling loads and natural frequencies of orthotropic beams.
Abstract: Preface List of symbols 1. Introduction 2. Displacements, strains, stresses 3. Laminated composites 4. Thin plates 5. Sandwich plates 6. Beams 7. Beams with shear deformation 8. Shells 9. Finite element analysis 10. Failure criteria 11. Micromechanics Appendix A. Cross-sectional properties of thin-walled composite beams Appendix B. Buckling loads and natural frequencies of orthotropic beams with shear deformation Appendix C. Typical material properties Index.

738 citations


"A multi-stable spanwise twist morph..." refers background in this paper

  • ...The structural strain energy Π is expressed as: [23] Π = 1 2 N ∑ i=1 liHi△κ i Di κi, (2) where N represents the total number of spar strips in the structure, li and Hi denotes the length and width of the ith strip respectively, △κT i refers to the transpose of the curvature change tensor △κi, Di is the reduced flexural stiffness matrix of the composite laminate spar strips and is defined as, D∗ = D − BA−1B, where A, B and D are the in-plane, coupling and flexural stiffness matrices in classic laminate theory [24]....

    [...]

Journal ArticleDOI
TL;DR: In this article, the authors provide a concise survey of the achievements in airframe noise source description and reduction over the last 40 years worldwide and provide examples but do not claim to be complete.
Abstract: With the advent of low noise high bypass ratio turbofan engines airframe noise gained significant importance with respect to the overall aircraft noise impact around airports. Already around 1970 airframe noise, originating from flow around the landing gears and high-lift devices, was recognized as a potential “lower aircraft noise barrier” at approach and landing. Since then, the outcome of extensive acoustic flight tests and aeroacoustic wind tunnel experiments enabled a detailed description and ranking of the major airframe noise sources and the development of noise reduction means. In the last decade advances in numerical and experimental tools led to a better understanding of complex noise source mechanisms. Efficient noise reduction technologies were developed for landing gears while the benefits of high-lift noise reduction means were often compensated by a simultaneous degradation in aerodynamic performance. The focus of this paper is not on the historical sequence of airframe noise research but rather aims to provide a concise survey of the achievements in airframe noise source description and reduction over the last 40 years worldwide. Due to the vast amount of work focused on a variety of airframe noise problems, this review can only provide examples but does not claim to be complete.

360 citations


"A multi-stable spanwise twist morph..." refers background in this paper

  • ...Furthermore, the intrinsic continuous geometrical changes and smooth structural surfaces in morphing structures significantly reduce drag forces and noise emission due to structural discontinuities [5]....

    [...]

  • ...Using such concepts, the drag force and wing noise emission can be reduced by removing flow vortices around the flap ends from the pressure side to the suction side [5]....

    [...]

Frequently Asked Questions (2)
Q1. What are the contributions in "A multi-stable spanwise twist morphing trailing edge" ?

In this paper, a spanwise twist morphing trailing edge device consisting of CFRP ribs and spars was proposed and preliminary optimization studies were carried out. 

Future work could include: • experimental studies on the ZTS SMTE design to further investigate the mechanical properties and benchmark the developed analytical model ; • investigations on possible morphing skins and further development of the analytical model to consider skin properties ; • wind tunnel testing on the wing fitted with the developed SMTE device and/or numerical simulations to characterize effects on spanwise morphing profiles on wing performance ; • development of integrated design methods considering both spanwise and camber morphing capabilities for performance enhancement.