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Mechanics of Air-Inflated Drop-Stitch Fabric Panels Subject to Bending Loads

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Rapid deployment and mobility of lightweight structures, namely inflatable structures, are of growing significance to the military and space communities. When deployment and rigidity are driven by pressure (for example, air or fluid) and materials such as textiles, elastomers and flexible composites are used, significant load carrying capacity per unit weight (or per-unit stowed volume) can be uniquely achieved. Specifically, the pressurized air directly provides the stiffness to support structural loads, thus eliminating the requirement for heavy metal stiffeners that are used in conventional rigid structures. However, the material and system behaviors are not sufficiently understood. Furthermore, predictive-performance analysis methods and test standards are not adequately established because the behaviors of inflatable fabric structures often involve coupled effects from inflation pressure such as fluid-structure interactions (FSI’s), thermo-mechanical coupling and nonlinear constitutive responses of the materials. These effects can restrict the use of conventional design, analysis and test methods. This research explores the mechanics of air-inflated drop-stitch fabric panels subject to bending loads using analytical and experimental methods. Results of experimental four-point bend tests conducted at various inflation pressures are used to validate the analytical method. The predicted and experimental deflections, wrinkling onset moments, ultimate loads, pressure changes, etc. are compared and discussed.
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MECHANICS OF AIR-INFLATED DROP-STITCH FABRIC PANELS
SUBJECT TO BENDING LOADS
Paul V. Cavallaro
Naval Undersea Warfare Center, Division Newport
Newport, RI
Christopher J. Hart
Navatek, Ltd.
Baltimore, MD
Ali M. Sadegh
The City College of the City University
New York, NY
ABSTRACT
Rapid deployment and mobility of lightweight structures,
namely inflatable structures, are of growing significance to the
military and space communities. When deployment and
rigidity are driven by pressure (for example, air or fluid) and
materials such as textiles, elastomers and flexible composites
are used, significant load carrying capacity per unit weight (or
per-unit stowed volume) can be uniquely achieved.
Specifically, the pressurized air directly provides the stiffness
to support structural loads, thus eliminating the requirement
for heavy metal stiffeners that are used in conventional rigid
structures. However, the material and system behaviors are
not sufficiently understood. Furthermore, predictive-
performance analysis methods and test standards are not
adequately established because the behaviors of inflatable
fabric structures often involve coupled effects from inflation
pressure such as fluid-structure interactions (FSI’s), thermo-
mechanical coupling and nonlinear constitutive responses of
the materials. These effects can restrict the use of
conventional design, analysis and test methods.
This research explores the mechanics of air-inflated drop-
stitch fabric panels subject to bending loads using analytical
and experimental methods. Results of experimental four-point
bend tests conducted at various inflation pressures are used to
validate the analytical method. The predicted and
experimental deflections, wrinkling onset moments, ultimate
loads, pressure changes, etc. are compared and discussed.
Keywords: inflatable structures, drop-stitch fabrics, analytical
mechanics, experimental methods, technical textiles.
INTRODUCTION
Air-inflated drop-stitch fabric panels fall within the category
of pretensioned structures and are particularly suited for use in
structural applications requiring flat (planar) shapes. Recently,
these lightweight panels have become an important complement
to the military’s dominantly used inflatable shapes such as
cylindrical beams, arches and spheres and they now extend the
range of geometries for inflatable structures. Like the other
inflatable shapes, air-inflated drop-stitch panels provide a fail-
safe mechanism during overload conditions. Unlike traditional
structures that can buckle and fracture, inflatable drop-stitch
fabric structures simply wrinkle and collapse without damage to
the fabric. Once the overload is removed, the structure regains
its design shape and structural performance.
To date, most research performed on inflatable fabric
structures has focused on beam and arch-like structures and the
development of particular analytical, numerical and
experimental methods[1-8] for these shapes. Except for the
recently published findings on three-point bending tests
conducted on inflatable drop-stitch panels[9-10], very little
research addresses the use of drop-stitch fabrics for use in
inflatable structures.
Drop-stitch fabrics, also known as spacer fabrics, are
examples of 3-D woven pre-forms as shown in Figure (1). They
consist of 2 skins (deck layers) that are simultaneously woven
and spaced apart by a distance governed by the length of the
drop yarns (also known as pile yarns). The drop yarns, which
are a second family of warp yarns woven within the skins, are
periodically “dropped” from one skin to the other skin and
repeated in an alternating manner as shown in Figure (1). For
use in air-inflated structures, the skins are made impermeable by
laminating layers of an elastomeric material (rubber, PVC,
urethane, neoprene, etc) to fully contain a volume of air with
their edges seamed. The skins consist of a base fabric that is
plain-woven using 2 orthogonal yarn directions referred to as the
warp and weft directions and, as previously mentioned, a second
warp yarn family is included for the drop yarns. The weft
direction corresponds to the width direction and is limited by the
1
Copyright © 2013 by ASME
Proceedings of the ASME 2013 International Mechanical Engineering Congress and Exposition
IMECE2013
November 15-21, 2013, San Diego, California, USA
IMECE2013-63839
This work is in part a work of the U.S. Government. ASME disclaims all interest in the U.S. Government’s contributions.
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size of the loom beam. The warp direction, referred to as the
direction of weaving, is virtually unlimited in length.
By analogy, the load carrying behavior of air-inflated drop-
stitch panels is similar to that of sandwich panels in which air
acts as the foam (or honeycomb) core of a traditional sandwich
panel and provides the through-thickness normal and transverse
shearing stiffnesses.
Figure 1 Example of a polyester drop-stitch fabric with
laminated rubber skins.
Load-carrying capacities and stability of inflatable drop-
stitch panels depend upon their shapes, fabric architectures,
material properties, inflation pressures, mechanical loads and
temperature. Additionally, pressure relief valves and
manifolding of inflation ports can be used to control the
deployment and performance of drop-stitch panels used in
inflatable structures.
During inflation of a drop-stitch panel, the air volume
increases with pressure and a developable shape is produced.
The skins become biaxially pretensioned and the drop yarns
become pretensioned to maintain the panel’s flat shape. These
pretensions produce the stiffnesses necessary for the panel to
resist axial, bending, shear and torsion loads.
The role of biaxial pretensioning is critical to the panel’s
ability to support loads. In general, sufficient bending stiffness
can only exist along a particular direction provided that the
pretension stresses from inflation in that direction have not been
fully relaxed by opposing (compressive) stresses. Many
researchers have invoked the assumption that the skins are thin
compared to their planar dimensions and that they behave as
tension-only membranes, that is, the skins are incapable of
resisting in-plane compressive forces. Similarly and by
extension of the previous assumption, the skins are incapable of
developing bending strain energies. However, due to the biaxial
nature of the stress distributions from inflation, the geometry of
the structure and the ratio of orthogonal stresses, the theoretical
maximum bending moment, Multimate, is approximately double
the bending moment corresponding to the theoretical wrinkling
onset moment, Monset [1].
Air can be treated in accordance with the Ideal Gas Law
which is given as:
RTPV
(1)
where P is the absolute pressure, V is the volume of air, R is the
Ideal Gas Constant and T is the absolute temperature (°K).
Additionally, for a polytropic thermodynamic process[11], the
pressure-volume relationship for the compression cycle of a gas
as shown in Figure (2) can be described by:
CPV n (2)
where C = constant and n = ratio of specific heats (n = 1.4 for
air).
Figure 2 Compression cycle for a gas from state-1 to state-2.
Therefore, two states of a polytropic compression (or expansion)
process can be described by:
nn VPVP 2211 (3)
Fluid-structure interactions (FSI’s) occur when the enclosed
air (fluid) experiences pressure and volume changes resulting
from panel deformations due to applied mechanical and thermal
loads. Additionally, tensile strains can develop in the membrane
material which will, for a closed system, contribute to volume
increases. This type of fluid-structure coupling, which is unique
to inflated structures, is a source of nonlinear behavior. This
coupling increases the complexity of the governing mechanics.
When FSI’s are significant, air compressibility must be included
in the energy balance because, in addition to the strain energy
developed in the membrane materials, the thermodynamic work
done on the air, known as PV-work, must be accounted for.
The idealized form of the energy balance for an air-inflated
fabric structure is:
edissipativkineticstrainernal EEEEFd
int
VdPPdV (4)
2
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where: F is an externally applied force,
is the deflection at
point of loading, Einternal is the internal energy of the system,
Estrain is the sum of the elastic (recoverable) and plastic
(irrecoverable) strain energies, Ekinetic is the kinetic energy of the
system mass, Edissipative is the dissipated energy through damping
and viscous effects. The symbol is used to denote differences
between inflated and bending states.
The key to developing a specific load carrying capacity and
wrinkling stability level is through balancing of the applied
stresses from external loading against the pretension stresses
from inflation. The theoretical wrinkling moment onset, Monset,
occurs when a region of applied in-plane compressive stress
completely relaxes the pretension stress in a given direction.
Although full load carrying capacity is available when the
applied stresses have not fully relaxed the pretension stresses,
the post-wrinkled load carrying capacity becomes reduced. This
reduction depends upon further loss of active cross section and
eventual structural instabilities including buckling. However, as
previously mentioned, the skins are capable of resisting in-plane
compression provided that the orthogonal direction remains
under tension and therefore the maximum moment, Multimate, is
approximately double Monset. The relationship between Monset
and Multimate is further discussed in a subsequent section.
Wrinkling failures, which are a form of fail-safe collapse in
air-inflated fabric structures, are preferred over yielding and
fracture failures associated with materials used in conventional
rigid structures. Wrinkling deformations can be readily and
visually detected unlike plasticity and crack growth which may
require other detection techniques. Today’s inflatable structures
are capable of achieving safe and reliable operating pressures
that are significantly high through the use of continuous textile
processing methods (which eliminates/reduces the number of
seams) and high performance fibers.
SHEARING DEFORMATIONS AS A SOURCE OF PV-
WORK
The key source of volume change during four-point bending
of an inflated drop-stitch panel prior to wrinkling and the loss of
stability is the transverse shearing deformations of the cross
section. Consider a panel constructed with inextensible skins
that is subject to four-point bending as shown in Figure (3)
where
is defined as the angle between the neutral surface and a
line initially perpendicular to the neutral surface. Region (1) is a
region of pure bending in which no transverse shearing strain,
,
is present. Note that plane sections remain plane within this
region. The volume within Region (1) remains constant during
bending and no PV-work is produced in this region. However,
Region (2) is subjected to a uniform transverse shearing strain
that deforms the cross section causing the plane sections to not
remain plane such that
is no longer equal to /2. The volume
change due to
in Region (2) is equilibrated by a corresponding
change in pressure which leads to PV-work. Therefore, the
effective shear modulus of the structure, Geff , is a function of
inflation pressure and
. For the case of shear-deformable skins,
Geff is a function of inflation pressure and the shear modulus of
the skins, Gskins.
Figure 3 Superposition of skin stresses and shearing
deformations.
MATERIAL DESCRIPTIONS
The drop-stitch skins were constructed of a plain-woven
polyester fabric laminated with rubber layers on each surface.
The warp, weft and drop yarns were all constructed of the same
polyester fibers. Figure (2) shows the base and laminated fabric
construction details. The reinforcing effects of rubber coatings
on woven fabrics were investigated using experimental methods
by Farboodmanesh et-al. [12].
Figure 4 Construction details of rubber laminated polyester
fabric reinforced drop-stitch skins.
DROP-STITCH PANEL GEOMETRY
The current air-inflated drop-stitch panel geometry is a
nominally flat enclosed volume with rounded edges as shown in
Figure (5). The overall panel length was Lo, the overall panel
width was wo, and the overall panel thickness was h. The edges
3
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Figure 10 Instantaneous elastic modulus, Einst, vs. strain curves
for drop-stitch skin uniaxial tensile test specimens.
Figure 11 Instantaneous elastic modulus, Einst, and effective
elastic modulus, Eeff , vs. inflation pressure for drop-stitch panel
test specimen.
An average elastic modulus of the skins was established from
the instantaneous modulus versus strain curves and was used to
represent the elastic modulus for both the warp and weft
directions. If the elastic moduli of the skins are different along
the warp and weft directions, then the material should be treated
as orthotropic and the appropriate elastic moduli be used in their
corresponding directions. The average elastic modulus is
justified for use in analytical solutions when the applied bending
stresses can be considered as a perturbation about the inflated
stress state. However, numerical solutions can readily
incorporate a hyperelastic strain energy potential (i.e.; Ogden,
Marlow, Mooney-Rivlin, etc.) to characterize any highly
nonlinear constitutive behaviors over a larger range of bending
stresses.
In a similar fashion, it was necessary to characterize the
tensile properties of the drop yarns including their failure modes,
failure strengths, elongations at break and elastic moduli.
Tensile properties of the drop yarns were established using two
methods. The first method conducted tensile tests directly on
individual yarns in both pre-woven and post-woven states (for
the latter, yarns were extracted from the drop-stitch fabric prior
to lamination) as shown in Figure (12a). This was necessary to
establish the effects of yarn damage from weaving on their
strength and stiffness.
A second method was developed to obtain the tensile
strengths of the drop yarns while incorporating the drop-stitch as
a complete, 3-D woven laminated system. The purpose was to
determine if the woven architecture of the drop-stitch skins and
the lamination layers had any influence on the tensile strengths
and failure modes of the drop-stitch yarns. If the drop yarns
failed remotely from the skins (i.e.; at the mid-length of the drop
yarn), then the skins had no effect on the drop yarn tensile
strengths and failure modes. However, if the drop yarns failed at
the region of egress from the skins, then their tensile properties
could be influenced by the woven architecture of the skins (i.e.;
yarn counts per unit length of skin, crimp contents, etc.) and the
ability of the skins to prevent pull-through of the drop yarns
from the skins. This test required the design of a novel test
fixture for use in a conventional strength of materials test
machine. The device, shown in Figure (12b), incorporated a 6-
inch by 6-inch swatch of the drop-stitch fabric which was
adhesively bonded to a pair of steel backing plates. A series of
1-inch wide plates was used to form picture frame assemblies
that were bolted around the perimeter of each skin. The picture
frames were necessary to eliminate peel stress failures of the
adhesive bond layers and to promote uniformity of the drop yarn
tensions across the 6-inch by 6-inch region.
Figure 12 (a) Tensile testing of individual drop yarns. (b)
tensile testing of drop yarns in woven state.
Figure 13 Load vs. strain curves from uniaxial testing of
individual polyester drop yarns extracted from the fabric.
7
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  
dx
APG
xV
FSdx
IPE
xM
PU
ss L
ieff
L
iskin
itotal
0
2
0
2
2)(
2)( (5)
where:
x = position along the supported span length,
Eskin(Pi) = skin elastic modulus at current inflation pressure,
Geff (Pi) effective transverse shearing modulus at current
inflation pressure,
I = second area moment of inertia of the cross section as
defined by the skins with respect to the neutral axis,
FS = shear strain correction factor.
The total pressure-dependent, mid-span deflection,
total(Pi ),
resulting from the total applied four-point bending load, Fapplied,
is derived by minimizing Utotal(Pi ) with respect to x which leads
to the following SDBT solution:
   

3
3
2
2
2
2
3
skinoiskin
arm
s
armapplied
itotal thhwPE
L
L
LF
P
 
skinoieff
armapplied
thwPG
LF
25
3
(6)
in which the first and second terms in Equation (6) represent the
bending and shearing components, respectively, of the total mid-
span deflection.
MECHANICS OF DROP-STITCH PANELS SUBJECT TO
FOUR-POINT BENDING
Four-point bending loads applied to an air-inflated drop-
stitch panel of the geometry previously described will produce
longitudinal tensile stresses in the lower skin and longitudinal
compressive stresses in the upper skin as shown in Figure (3).
From this figure, the balance of pretension and applied bending
stresses is demonstrated by consideration of an infinitesimal
element length as shown in Figure (3).
Now consider the inflation step. As air fills the volume
enclosed by the skins, the biaxial pretension stresses develop
along the length and width directions such that static equilibrium
is achieved and the panel attains its developable shape. Once
pressurized, the longitudinal force, Flongitudinal, is computed as the
product of inflation pressure and longitudinal projected area:
]
4
)[( 2
h
hhwPF oiallongitudin
(7)
Similarly, the hoop force, Fhoop, is computed as the product of
pressure and hoop projected area:
]
4
)[( 2
h
hhLPF oihoop
(8)
The longitudinal and hoop pretension stress resultants Nx and
Ny, respectively, reported in conventional textile force-per-unit-
length notation are:
])(2[/ hhwFN oallongitudinx
(9)
])(2[/ hhLFN ohoopy
(10)
where x and y are orthogonally aligned along the longitudinal
and width directions, respectively. The denominators of
equations (9) and (10) represent the perimeters of the
longitudinal and hoop cross sections, respectively. The stress
resultants are of particular importance as they can be directly
compared to strengths obtained through tensile tests (also
reported in force-per-unit-length notation) performed on the skin
materials to establish Factors of Safety (FOS) on tensile rupture.
Equations (9) and (10) can be easily converted to obtain
engineering stresses σx and σy with units in force-per-unit-area by
simply dividing each by tskin:
]))(2[(// skinoallongitudinskinxx thhwFtN
(11)
]))(2[(// skinohoopskinyy thhLFtN
(12)
The shape of the inflated structure affects the ratio of biaxial
tensile forces per unit length, Nratio, developed during
pressurization and is expressed as:
x
y
ratio N
N
N (13)
For a right circular cylinder Nratio, = 2.0. For the drop-stitch
panel of the present dimensions (Lo = 100”, wo = 24”, h =4.0”
and tskin = 0.096” ) Nratio = 1.1.
Volume changes due to inflation of drop-stitch panels arise
from the extensibility of the skins and drop yarns. If the elastic
moduli are known for the skins and drop yarns, then the volume
change upon inflation, which is simply due to the strains
developed in the skins and drop yarns, can be readily computed.
Strains in the skins increase the longitudinal and hoop perimeters
of the skins. Similarly, strains in the drop yarns increase the
drop yarn lengths which also increase the panel thickness and
volume.
The present analytical solution assumes that the spatial
density of the drop yarns, defined as the number of drop yarns
per unit area, is sufficient, so that localized skin bowing
deformations between adjacent drop yarns have a negligible
5
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effect on volume changes. Note that volume changes increase
with decreasing drop-yarn densities for a given pressure.
Furthermore, the present analysis provides a total solution by
considering (1) pressure and volume changes with respect to
inflation and (2) pressure and volume changes with respect to
applied loads
MATERIAL PROPERTY TESTS
The analytical models require material property data as input.
Skin strains due to inflation are computed using elastic moduli
obtained through experimental tensile tests. Biaxial tension
testing is the preferred method for characterizing the strength
and elastic moduli of membrane skins used in inflatable
structures due to their biaxial pretensioning from pressure. A
fixture[15] of the type shown in Figure (7) is recommended for
its capacity to independently apply different tensile stress ratios
with combined shearing but was not available for use at the time
of this research.
Figure 7 Advanced biaxial tension and combined shear test
fixture with proportional tension controls[15].
(U.S. Patent 7,204,160)
Ideally, the ratio of biaxial tension stresses used in the test
should match the ratio of biaxial tension stresses, Nratio, produced
in the actual structure from inflation. The ratio of biaxial tension
stresses is dependent upon the geometry of the inflated structure.
In the absence of biaxial testing capability, uniaxial tensile tests
can be performed and stress stiffening effects from biaxial
loading can be established for an isotropic material having an
effective elastic modulus, Eeff and Poisson’s ratio,
, as shown in
equation (14). This is done by combining equations (11-13) with
the plane stress form of Hooke’s Law shown in equation (15).

ratio
skin
eff N
E
E
1 (14)
where Eskin is the elastic modulus of the skins obtained from
uniaxial tension tests,
x is the axial strain.
yx
skin
xE
1 (15)
The uniaxial tensile test method was used in the present
research in which the rubber laminated polyester skin specimens
were cut from as-fabricated drop-stitch panels and tested using
an Instron® machine as shown in Figure (8). Note that the
polyester drop yarns were cut at their mid-length and were
allowed to hang freely as shown. The resulting stress,
instantaneous elastic modulus, Einst, and effective elastic
modulus, Eeff , versus strain curves are shown in Figures (9-11) .
Figure (11) exhibits the pressure stiffening effect on Eeff and was
determined through consideration of Eskin,
x and Nratio. When
uniaxial tensile testing is used to characterize the elastic modulus
of the drop-stitch skins, Eeff should be substituted for Eskin in
equations (5-6) to account for the influence of biaxial tension.
Figure 8 Tensile testing of drop-stitch skins.
Figure 9 Stress vs. strain curves for drop-stitch skin tensile test
specimens.
6
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Figure 10 Instantaneous elastic modulus, Einst, vs. strain curves
for drop-stitch skin uniaxial tensile test specimens.
Figure 11 Instantaneous elastic modulus, Einst, and effective
elastic modulus, Eeff , vs. inflation pressure for drop-stitch panel
test specimen.
An average elastic modulus of the skins was established from
the instantaneous modulus versus strain curves and was used to
represent the elastic modulus for both the warp and weft
directions. If the elastic moduli of the skins are different along
the warp and weft directions, then the material should be treated
as orthotropic and the appropriate elastic moduli be used in their
corresponding directions. The average elastic modulus is
justified for use in analytical solutions when the applied bending
stresses can be considered as a perturbation about the inflated
stress state. However, numerical solutions can readily
incorporate a hyperelastic strain energy potential (i.e.; Ogden,
Marlow, Mooney-Rivlin, etc.) to characterize any highly
nonlinear constitutive behaviors over a larger range of bending
stresses.
In a similar fashion, it was necessary to characterize the
tensile properties of the drop yarns including their failure modes,
failure strengths, elongations at break and elastic moduli.
Tensile properties of the drop yarns were established using two
methods. The first method conducted tensile tests directly on
individual yarns in both pre-woven and post-woven states (for
the latter, yarns were extracted from the drop-stitch fabric prior
to lamination) as shown in Figure (12a). This was necessary to
establish the effects of yarn damage from weaving on their
strength and stiffness.
A second method was developed to obtain the tensile
strengths of the drop yarns while incorporating the drop-stitch as
a complete, 3-D woven laminated system. The purpose was to
determine if the woven architecture of the drop-stitch skins and
the lamination layers had any influence on the tensile strengths
and failure modes of the drop-stitch yarns. If the drop yarns
failed remotely from the skins (i.e.; at the mid-length of the drop
yarn), then the skins had no effect on the drop yarn tensile
strengths and failure modes. However, if the drop yarns failed at
the region of egress from the skins, then their tensile properties
could be influenced by the woven architecture of the skins (i.e.;
yarn counts per unit length of skin, crimp contents, etc.) and the
ability of the skins to prevent pull-through of the drop yarns
from the skins. This test required the design of a novel test
fixture for use in a conventional strength of materials test
machine. The device, shown in Figure (12b), incorporated a 6-
inch by 6-inch swatch of the drop-stitch fabric which was
adhesively bonded to a pair of steel backing plates. A series of
1-inch wide plates was used to form picture frame assemblies
that were bolted around the perimeter of each skin. The picture
frames were necessary to eliminate peel stress failures of the
adhesive bond layers and to promote uniformity of the drop yarn
tensions across the 6-inch by 6-inch region.
Figure 12 (a) Tensile testing of individual drop yarns. (b)
tensile testing of drop yarns in woven state.
Figure 13 Load vs. strain curves from uniaxial testing of
individual polyester drop yarns extracted from the fabric.
7
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Figure 14 Fibril fracture mode of individually tested drop yarns.
The polyester drop yarn properties listed in Table (2) were
characterized through measurements performed on scanning
electron microscopy (SEM) images of extracted drop yarns. The
weight density of polyester used to further compute the drop
yarn denier was 0.048 lb/in3.
Table 2 Measured properties of polyester drop yarns.
Polyester Drop Yarn Measured Properties
# Fibers Per Drop Yarn 34
Average Fiber Diameter 25 microns
Average Fiber Area 7.609 E-07 in2
Average Drop Yarn Area 2.587 E-05 in2
Linear Mass Density 200 denier
The resulting stress vs. strain curves for the 3 polyester drop
yarns shown in figure (13) are shown in figure (15). Assuming
linear elastic behavior, the average elastic modulus of the drop
yarns , Edy, was 1.05E+06 psi.
Figure 15 Stress vs. strain curves for 3 polyester drop yarns.
WRINKLING STABILITY
Skin wrinkling is a phenomenon that occurs due to
superposition of the bending stresses with the pretension stresses
from inflation. During bending, as shown in the half-symmetry
view of Figure (16), compressive stresses are applied to the
upper skin (point-A) and tensile stresses are applied to the lower
skin (point-A’). The skin reaction forces create the necessary
force-couple required to resist the bending moment and maintain
static equilibrium. The applied compressive stresses in the
upper skin oppose (relax) the in-plane pretension stresses
developed during inflation as shown in Figure (17). The applied
tensile stresses in the lower skin add to the in-plane pretension
stresses from inflation. The bending moment that completely
relaxes the pretension stress in the upper skin (such that the net
longitudinal stress is zero) is referred to as Monset as shown in
Equation (16) for drop-stitch panels of the specific panel
geometry described previously. Note that Equation (16) is valid
for tskin << h such that higher ordered terms in tskin are negligible.
The inflated values of h and wo are used (i.e.; h(Pi) and wo(Pi) )
to capture the volume changes due to inflation. Skin wrinkling
is fully developed at Multimate 2 Monset, which occurs from a
loss of the effective load-carrying cross section and, unlike in
conventional rigid materials, is reversible in membrane skins.
(a) (b)
Figure 16 Superposition of inflation and bending stresses (a)
prior to wrinkling, (b) at wrinkling onset.
(a) (b) (c) (d)
Figure 17 States of superimposed stresses on an upper skin
element.

)()(2)(2 )()(4)(4
)(
16
2
2
iiio
iiio
i
i
onset PhPhPw
PhPhPw
Ph
P
M
(16)
8
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Wrinkling stability limits the load carrying capacity of
inflated drop-stitch panels when subject to four-point bending
loads. The panel simply loses stiffness once wrinkling develops
and eventual fail-safe collapse will follow when Mult is reached.
A fail-safe collapse will not generally damage the drop-stitch
panel. Upon restoration of the panel to its pre-wrinkling load,
the panel will return to its intended design shape.
FOUR-POINT BEND TESTS
Experimental four-point bend tests were conducted using an
Instron® machine configured with a customized rigid test frame
as shown in Figure (18) on drop-stitch panels as described in
Figure (5) with Lo=100”, Ls=76”, Lp=24”, Larm=26”, and
tskin=0.096”.
Figure 18 Experimental four-point bend test arrangement.
The bend tests were performed in displacement control mode
at a constant crosshead rate of 1.0 inch/minute. The panels were
inflated to each of the prescribed initial inflation pressures and
the air fill valve was then turned off such that the air volume was
a closed volume during the bending event. For safety purposes,
however, a pressure relief valve was connected to the air fill line.
Data recorded during each test included initial inflation
pressure, instantaneous pressure, mid span deflection (using a
displacement wire transducer), instantaneous load, load-point
(crosshead) displacement and temperature.
The panels were subjected to a series of initial bending
cycles for preconditioning purposes to remove any alignment
anomalies such as temporary curvature of the panels. These
cycles consisted of 3 consecutive runs to achieve a 4.0-inch mid
span deflection. The specimens were then flipped over and 3
additional, similarly applied runs were performed.
After preconditioning was completed, 3 bend tests were
conducted at each pressure. Loading ceased once the mid span
deflection reached approximately 6.0 inches. No measurable
changes in air temperature were observed.
Figures (19-24) show graphs of total applied load versus mid
span deflection for initial inflation pressures of 5, 10, 15, 20, 25
and 30 psig. The dotted line represents the analytical SDBT
solution. The white circle designates the SDBT solution at the
onset of wrinkling, Monset; the red circle designates the SDBT
solution at the ultimate wrinkling moment, Mult.
Figure 19 Load vs. mid span deflection for 5.0 psig inflation.
Figure 20 Load vs. mid span deflection at 10.0 psig inflation.
9
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Figure 21 Load vs. mid span deflection for 15.0 psig inflation.
Figure 22 Load vs. mid span deflection for 20.0 psig inflation.
Figure 23 Load vs. mid span deflection for 25.0 psig inflation.
Figure 24 Load vs. mid span deflection for 30.0 psig inflation.
The onset of wrinkling was typically observed during the
bend tests as the formation of a local creasing deformation
extending across the full width of the upper skin adjacent to the
outboard side of the load point as shown in Figure (25).
Figure 25 Example of the wrinkling onset deformations in the
upper skin adjacent to the outboard side of the load point.
Pressure changes during the bending tests were compared
with the SDBT predictions at the wrinkling onset points shown
in Figures (19-24) in Table (3).
Table 3 Pressures at wrinkle onset moment, Monset.
Initial
Pressure, Pi 5 10 15 20 25 30
SDBT
Pressure at
Monset 5.04 10.09 15.14 20.19 25.24 30.29
Experimental
Pressure at
Monset 5.02 10.02 15.02 20.04 25.05 30.07
10
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SUMMARY AND CONCLUSIONS:
The pressure-dependent behavior of inflatable drop-stitch
panels subject to four-point bending loads was investigated
through combined analytical and experimental methods. The
analytical method, developed using SDBT, accounted for
pressure and volume changes due to inflation and pressure and
volume changes due to applied bending loads.
Material level tests on the drop yarns and skins were
performed to characterize their extensibility behaviors. The
biaxial tensile behavior of the skins was established using
Hooke’s law in conjunction with uniaxial tensile test results.
The panel geometry and biaxial tension ratio from inflation were
shown to critically influence the SDBT solution.
Excellent correlation of load-deflection results was obtained
between the SDBT predictions and the experimental results up to
the wrinkling onset level for all inflation pressures. The SDBT
predictions, however, underestimated the ultimate bending
moment for pressures of 10 psig and below. This likely resulted
from the inability to fully develop a symmetric loading state at
such low pressures. The SDBT predicted slightly greater
pressures at the wrinkling onset state than those measured during
testing; however, the measured pressure changes up to the
wrinkling onset were less than 0.4%.
The maximum applied experimental load at 30 psig was
nearly 700 lb with a corresponding ultimate moment of 9,100 in-
lb—clearly demonstrating the significant load-carrying capacity
of inflatable drop stitch fabric panels. However, based upon the
breaking strength of the drop yarns, the analytically-predicted
maximum achievable pressure was approximately 50 psig with a
corresponding ultimate wrinkling moment of 16,152 in-lb and
total applied load of 1,300 lbs. The weight of the experimental
panel was 22 lbs resulting in a theoretical ultimate load carrying
ratio of 59:1. Such a ratio could be easily increased by using
drop yarns of higher deniers (i.e.; increased filament counts) and
higher tenacity fibers.
The panels of the present research were inflated over a
range of safe operating pressures; no testing was performed to
establish their burst pressures. However, assuming that the
strengths of the skins and seamed edges exceeded the tensile
strengths of the drop yarns, the expected mode of initial failure
was drop yarn tension failure. In addition to wrinkling as a fail-
safe phenomenon, drop-stitch inflatable panels provide a unique
margin of safety against total structural failure. In the event that
drop yarn tensile failures occur, the air volume increases, panel
deformations become cylindrical, a simultaneous pressure drop
occurs, and stresses in the skins and remaining active drop yarns
are redistributed.
The scope of this research is being expanded to include
numerical solutions (finite element analysis) for predicting the
post-wrinkled behavior through complete collapse and for
inflatable drop-stitch fabric skins having significant hyperelastic
behavior. Numerical solutions are most appropriate when
nonlinearities due to geometric (large deflections, large strains
and large rotations) and material behavior are present. Such
solutions can readily incorporate hyperelastic strain energy
potentials (for example, Ogden[16] and Marlow[17]) to
characterize their stiffness over a large range of bending stresses
to preclude being restricted to perturbations about the inflated
state. Additionally, the effects of drop yarn tensile failures and
local stress redistributions due to overpressurization are being
investigated.
ACKNOWLEDGEMENTS:
The authors gratefully acknowledge Martin Leff and David
Segala of the Naval Undersea Warfare Center, Newport, RI for
their support in conducting the material level tests and Gary
Proulx and Karen Buehler of the Army Natick Soldier Research,
Development and Engineering Center, Natick, MA for their
support in designing the test frame and performing the inflated
panel bending tests.
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10. Waters, J., Falls, J., “Bending Tests of Inflatable Dropstitch
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12
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