EXPERIMENTAL STUDIES ON WRINKLING BEHAVIORS OF
GOSSAMER SPACE STRUCTURES
C.G. Wang, X.W. Du and Z.M. Wan
Center for Composite Materials and Structures
Harbin Institute of Technology 150001
ABSTRACT
Ultra-large and ultra-lightweight gossamer space structures have received the widest attention due to their small packaging
volume and low launching cost. Wrinkles are the common deformation status and the main failure mode of such structures.
Experimental test is a main part of wrinkling analysis on gossamer space structures. The contact test can’t be used to
accurately determine the wrinkling behaviors because of the characteristics of lightweight and flexibility. A novel non-contact
Dot-Printing Photogrammetry (DPP) based on the technology of the printed-dot targets is presented to test the out-of-plane
wrinkle deformation. The rules of wrinkling development of gossamer space structures are obtained by incorporating the DPP
method and a Tension Wrinkling (TW) test. Results reveal that wrinkles are the bifurcation deformation from the in-plane
displacement. The obvious five deformation phases can be obtained by plotting the tension-amplitude figure. The wrinkling
mechanisms corresponding to the deformation phase are studied by associating the characteristic curve and experimental
results of key nodes. A numerical simulation analysis based on nonlinear buckling finite element method is performed to verify
the wrinkling experimental results. The predictions show good agreement with the experiments.
Introduction
The primary reason to perform wrinkling measurements and experiments on gossamer structures is to validate computational
models. Once these models are validated, they become reliable design tools for future spacecraft systems. Non-contact
instrumentation is preferred because gossamer structures are thin and ultra-lightweight; and typically transparent or specularly
reflective. These restrict the use of contact measurement techniques because interference with the membrane material can
have a significant effect on the structure and interfere with the measurement being attempted. Furthermore, there is also
significant risk of damaging the membrane during contact.
There are several non-contact measurement technologies and instruments available to quantify the shape, fine details such as
wrinkling, and membrane dynamics. These include projection moiré interferometry[1], light detection and ranging systems[2],
capacitive-type displacement sensors[3] and photogrammetry[4-7]. Each exhibits their own advantages and disadvantages.
The complete overview and survey of such non-contact measurement methods were given by Jenkins[8].
During the last decade, photogrammetry has found an increasing number of applications in industrial and aerospace
engineering due to the advancement of video technology. At present, non-contact photogrammetry has been successfully
applied to the test of deformation of gossamer space structures[4,5]. Pappa[6] did the test on wrinkle deformation based on the
dot-projecting photogrammetry, the out-of-plane wrinkle amplitude was obtained. By now, the accurate test on the small
amplitude wrinkle in small scale structures is a key problem of wrinkling experiment. Choosing and forming targets that do not
alter the desired parameter, including some aspect of membrane shape, is critical. There are three types targets, including
diffuse, retro-reflective, and projected targets, are currently available[7,8]. Diffuse materials, such as common white paper,
reflect light in all directions. Retro-reflective materials, such as highway road signs or markers, reflect light mostly back in the
direction of its source, significantly increasing visibility in that direction alone. These targets give excellent contrast and
produce exceptional results, but do add mass and localized stiffness. Projected targets, typically white dots from a standard
slide projector, are an attractive alternative for static-shape measurements of delicate Gossamer structures, but are not as
useful as attached targets for dynamic measurements because they do not move with the structure.
In the present work, we presented a novel non-contact Dot-Printing Photogrammetry (DPP) based on the technology of the
printed-dot targets. Based on such measurement technique, we can obtain the fine wrinkle configuration and the out-of-plane
deformation in the small scale (less then 500mm×500mm) delicate gossamer structures. The Tension Wrinkling (TW) test
associated with the DPP measurement was performed to analyze the rules of wrinkling development and evolution of
gossamer structure. The experimental results are compared with the numerical simulation based on nonlinear buckling finite
element method.
DPP Measurement and TW Test
The photogrammetry is a three-dimensional measurement technique based on the analysis of two-dimensional photographs
and the principles of triangulation. It is relatively inexpensive and can be used to obtain data on the static shape as well as the
dynamic behavior of membrane structures. The internal photogrammetric processes of image analysis, triangulation, and
three-dimensional data reconstructions is summarized in detail in Ref[8].
The DPP measurement is based upon photogrammetry, where the targets are the printed-dot targets. Such targets produced
with the Dot-Printing technique of the membrane have several outstanding characteristics available in wrinkling measurement,
such as the little mass, the good contrast to the membrane, flexible/variable scale, and accompany movement.
The square specimen with the printed-dot targets is shown in Fig.1. Such specimen is fixed onto the INSTRAN5569 tension
test instrument (as shown in Fig.2) along the left-top and right down edges. The TW test is performed by moving slowly the
clamp at speed 0.02mm/min. A square polyimide membrane (100 mm×100 mm) with 50mm thickness is chosen as the test
specimen. And the image analytical software within DPP measurement is PhotoModeler Pro 5[9].
Figure 1. Specimen with printed-dot targets
Figure 2. TW test instrument
Experimental Results and Discussion
DPP method associated with TW tests are used to obtain the out-of-plane wrinkle deformation and the rules of wrinkling
occurrence and development. The load is smoothly and slowly applied to make the membrane wrinkle, and the loading
process will end until the wrinkling configuration keeps stable.
The experimental result on the wrinkling configuration and the out-of-plane configuration is plotted in Fig.3. The obvious
wrinkle wave crest and hollow can be observed in the central part from Fig.3.
Figure 3. Wrinkling configuration and out-of-plane deflection
As shown in Fig.3, the mark A is wrinkling region. In this region, the wrinkling direction is parallel to the tension. The mark B is
slack region, in such region, the membrane is free configuration with zero stress. We focus on the wrinkling characteristics in
wrinkled region (mark A). According to the out-of-plane wrinkling deflection, we can determine and obtain the wrinkling
wavelength and amplitude. Where, the average distance between the adjacent wave hollows is defined as the wrinkling
wavelength. And the average value of the largest out-of-plane wrinkling deflection is named as the wrinkling amplitude. In our
experiment, the wrinkling wavelength and amplitude are 12.98mm and 9.07mm, respectively.
The plots of tension-amplitude and tension-wavelength are plotted in Fig.4. The obvious bifurcation of the in-plane
displacement corresponds to the occurrence of the wrinkle, and the critical wrinkling load can be determined at such
bifurcation point.
(a)
(b)
Figure 4. Experimental curves. (a) tension-amplitude curve; (b) tension-wavelength curve
These curves are unusual and we can obtain some important information of wrinkling evolution. The obvious “abrupt jump”
variation can be observed from the Fig.4a and b (especially in Fig.4b). We considered that such variation is related to the
occurrence of wrinkling. Before “abrupt jump”, the amplitude and wavelength are both zero, that is, there is no out-of-plane
deflection in the membrane. After such jump, the out-of-plane deflection increases as the tension. Thus, we defined the point
corresponding to such “abrupt jump” as the critical wrinkling point. The tension load corresponding to wrinkling point is critical
wrinkling load, which is 24.66N. According to the experimental results, we conclude that the occurrence of the wrinkles is the
results of out-of-plane bifurcation of the in-plane displacement. Such bifurcation reveals that the compressive stress in the
membrane reaches the critical wrinkling stress. After the wrinkling point, the amplitude increase unsteadily as the tension, it
indicates the continuous wrinkling evolution. The wrinkling wavelength decreases as the increasing tension. Such variation
reveals that the wrinkles concentrate into the wrinkled region due to the increased tension.
We pick up a tension-amplitude curve at random from the experimental data, and plot it in Fig.5.
Figure 5. Characteristic curve
We can observe clearly the different deformed characteristics from the curve. To understand deeply the wrinkling mechanism
and development, we divide the deformed curve into five characteristic phases: a)in-plane deformation, oa; b)critical
deformation, ab; c)break wrinkling deformation, bc; d)increasing deformation, cd; e)stable deformation, de. The experimental
results corresponding to key nodes (o,a,b,c,d and e) are shown in Fig.5.
(a) key node o
(b) key node a
(c) key node b
(d) key node c
(e) key node d
(f) key node e
Figure 6. Experimental results corresponding to key nodes of characteristic curve
There is only in-plane deformation in oa phase. There is small, inconspicuous and unsteady out-of-plane deformation in the
next phase (critical deformation phase), such case can be observed from Fig.6b to c. After ab phase, an “abrupt jump” occurs.
Thus, we named this phase as break wrinkling deformation phase. In such phase, the obvious wrinkles are formed and such
wrinkles can be observed clearly in Fig.6d. The key node b is the wrinkling point and the wrinkles occur at this point. After the
break wrinkling deformation phase, the wrinkles increase as the increased tension (increasing deformation phase). The
variation of wrinkles (numbers and region) is obvious in the increasing deformation phase, as shown in Fig.6d and e. where,
the obvious fluctuation (c’) indicates the “new” wrinkles born from the “old” wrinkles. At last, the variation of wrinkling amplitude
is not obvious and it tends to stability (stable deformation phase). We can determine the average wrinkling wavelength and
amplitude in such stable deformation phase.
Numerical simulation
Nonlinear buckling finite element method associated with ANSYS shell63 element is chosen to simulate the wrinkles. The
flowchart of the wrinkling numerical analysis is shown in Fig.7. Where, the prestress is applied to stabilize the solution, and the
initial imperfection is introduced to initiate post-wrinkling analysis. The numerical results of out-of-plane wrinkling deformation
are shown in Fig.8. And the comparison between prediction and experiment test is plotted in Fig.9. The numerical predictions
agreed well with the experimental results.
Figure7. Flowchart of wrinkling analysis
a) tension is 28.56N
b) tension is 43.76N
Figure 8. Results of wrinkling prediction
Figure 9. Comparison of prediction and experiment
Conclusions
A study of the wrinkling behavior of gossamer space structure was undertaken using the DPP measurement technique and
TW test. A numerical simulation is performed to compare the experimental test. The main conclusions are summarized in the
following items.
1) The wrinkles are the out-of-plane bifurcation deformation from the in-plane displacement;
2) The wrinkling development is divided into five characteristic phases, and the occurrence of the wrinkles followed by a
“abrupt jump”, and the critical wrinkling load is the load corresponding to the jumping point;
3) In the increasing deformation phase (cd), the obvious fluctuation indicates the “new” wrinkles born from the “old” wrinkles;
4) The DPP measurement and TW test are the effective way to obtain accurately the wrinkling behaviors in small scale
gossamer structures, and the numerical predictions agreed well with the experimental results.
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