Extra-large space structure such as space solar power system has been studied for a long time, but its realization is not yet in sight. The most severe problem is the budget, and the second is the transportation of the components into the orbit. Even though the budget was unlimited and the transportation capability was improved a whole lot, it is unlealistic at the current moment to transport the material for several kilo-meter square structure into space, to construct it in space, and to continue to operate and maintain it.

If so, what kind of structure can be available at this moment? What size of space structure will be available? In that case, what kind of technology should be developed upto what level? Such a question was the motivation of this research. Supported by KAKENHI, we achieved the following resutls:

Derivation of theoretical solution of self-extension force and deformation of a convex tape and a bi-convex boom that consists of two convex tapes to increase the stiffness

Development of prototype of planar truss consisting of bi-convex booms and evaluation of its deployability

Development of prototype of three dimensional truss consisting of bi-convex booms and evaluation of its deployability

Formulation of design method of de-orbit device that consists of convex tapes and thin membrane and is available for nano-satellite and development of prototype of the de-orbit device

The right movie shows an example of the prototype of the planar truss. Convex tape and bi-convex boom have several merits: they have self-extension force, they are flexible so that they can deploy even if the deployment is not synchronous, which can not be realized by deployable truss with rigid member. We thought to realize parge space structure by using the member that has such self-extension force and has compressive stiffness with light weight, and carried out this research.

There are a lot of problems to enlarge this structure: How many number of division is best for the each side of the truss structure? Is it possible to estimate the friction of the spindle in the node during the extension of the boom, the friction between the guide roller and the boom, the effect of the membrane to disturbe the deployment by the bending rigidity of the fold line, and other anti-deployment effect? If it is possible, how do we use it for the design? (e.g. if the anti-deployment effect is given quantatibly, how do we determine the design parameter of the boom that has enough self-extension force to overcome the anti-deployment effect?) How small can we design the node? (If the hub of the node is too small, we can not wrap the boom arount the hub). In this research, we formulated the theory and the design method that can answer such questions.

As for the de-orbit device that consists of convex tapes and membrane, we found the parameter to determine the success/failure of the deployment, and formulated the condition of the success of the deployment. The point of the success is to avoid the stack of the tape in the storage. Using this formula, we can design the device appropriately without the trial and error or over capacity. The right photo shows an example of the -deoirbit device for 3U CubeSat. In this photo, the membrane does not deploy completely, but the deployment can be complete almost 100% by some elaboration.

The right photo shows the bi-convex boom that we used in this research. The braid covers two convex tapes to avoid the separation of the tapes roughly (This boom was made by Sakase Ad-Tech Co. Ltd.). The most important fature of the bi-convex boom is that each tape can slide on the other tape in axial direction so that the boom can cancell the difference of the arc length between the inner tape and the outer one. Furthermore, the storage efficiency can be improved more by a little ingenuity.

The most important result of this research is that we achieved the comparison of the numerical prediction and the flight data of IKAROS that was launched in May 2010, and discussed about the deployment behavior of the sail membrane of IKAROS. In addition, we progresed the improvement of the membrane finite element and the model reduction of membrane structure that was researched in the former KAKENHI research project
"Structure preserving method of gossamer multi-body dynamics, and we completed the development of the 3D re-configuration of the membrane shape from the camera image with missing data that was researched in the project"Research on Practical On-Orbit Servicing Systems Using Nano-Satellite Technologies. These became important results because they contributed the evolution to the later research. We won the best paper award from AIAA for the collaborative research on IKAROS, which was very surprizing and great pleasure for us.

THe right above figure is an example of the prediction of the deployment before launch, in which the damping of the membrane was assumed somehow. It is better that the damping of the membrane is larger because the attitude stability of the spacecraft can be assured more easily, but in the eral design of IKAROS, the damping was assued to be quite small value to consider the worst case because we can not measure the damping of the membrane on the ground.

After the launch and the deployment, JAXA estimated the damping of the membrane from the flight data, and compared the spin rate during the "second stage deployment" with that of the numerical simulation, they agreed well with each other as in the right figure. The gap between them is mainly caused by the trouble of the deployment (The second stage deployment was asymmetric because of a certain reason). During the deployment, the membrane is not always under tension, i.e. the membrane is wrinkled or slacked almost all time during the deployment. Therefore, we thought the effect of the stress distribution in the membrane did not give the influence to the deployment and the inertia force governs the deployment motion, but JAXA showed in the later research that the stress distribution has important rule in the deployment.

IKAROS aquired various flight data, and the structure specialist group of solar power sail in JAXA discussed about the structural dynamics of IKAROS with the flight data. The discussin result will contribute the research on the exploration to the Jupiter and Torojan asteroid.

The bellow figure illustrates an exam@le of the analysis of wrinkle of a rectangular membrane that is subject to inplane shear. We compared the numerical results obtained by DK shell element, MITC shell element, and simplified theoretical analysis each other, and compared the result by DK shell element and those by various membrane elements. In the result, we proposed new membrane element "Mod-SRM element" and showed the result by Mod-SRM can simulate the stress distribution of the membrane approprietely at both tensile and compression area, which is similar to the result by shell element.

The right figure illustrates a numerical example of the model reduction by empirical proper orthogonal decomposition (PDO). Prof. Yamazaki obtained a doctor's degree of engineering by the research of this model reduction method. POD is used in various research field. We think POD is a powerful tool to obtain the valid numerical results of the deployment of membrane efficiently in case of the parametric study which requires long computation time.
Off course it is necessary to show the validity of the results from the model reduction by e.g. comparing with experimental results if POD gets recognition from the scientists in this research field. We try to make POD get recognition and apply it to the efficient design and development of gossamer structures.

The right figure shows an example of imaging measurement for the shape of membrane with 1.2m diameter during the spin deployment. With this research as the first opportunity, we are getting better to re-construct threee dimensional shape of the membrane using empirical proper orthogonal decomposition of experimental image data with deficiency and numerical analysis result.

Hiraku Sakamoto, Yasuyuki Miyazaki, and Osamu Mori, Transient Dynamic Analysis of Gossamer Appendage Deployment Using Nonlinear Finite Element Method, Journal of Spacecraft and Rockets, 48(5), pp.881-890, September 2011, DOI: 10.2514/1.52552

Masahiko Yakazaki and Yasuyuki Miyazaki, Error Estimation of Low-Order Model for Gossamer Muti-body Structure, AIAA-2011-6281 (Proc. AIAA Modeling and Simulation Technologies Conference 2011), pp.1-9, August 2011, DOI:10.2514/6.2011-6281

Masahiko Yakazaki and Yasuyuki Miyazaki, Empirical Model Reduction of Geometrical Constrained Gossamer Structures, Journal of System Design and Dynamics, Special Issue of Asian Conference on Multi-Body Dynamics 2010, 5(3), pp.441-449, April 28, 2011, DOI: 10.1299/jsdd.5.441

Yoji Shirasawa, Osamu Mori, Yasuyuki Miyazaki, Hiraku Sakamoto, M Hasome, Nobukatsu Okuizumi, Horotaka Sawada, Hiroshi Furuya, Saburo Matunaga, and Michihiro Natori, Analysis of Membrane Dynamics using Multi-Particle Method for Solar Sail Demonstrator "IKAROS", AIAA-2011-1890 (Proc. 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference), pp.1-14, April 2011, DOI:10.2514/6.2011-1890

Hirotaka Sawada, Osamu Mori, Nobukatsu Okuizumi, Yoji Shirasawa, Yasuyuki Miyazaki, Michihiro Natori, Saburo Matunaga, Hiroshi Furuya, and Hiraku Sakamoto, Mission Report on The Solar Power Sail Deployment Demonstration of IKAROS, AIAA-2011- 1887 (Proc. 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference), pp.1-11, April 2011, DOI:10.2514/6.2011-1887

Masahiko Yakazaki and Yasuyuki Miyazaki, Low-Order Model of Spin Type Solar Sail Dynamics by Empirical Model Reduction, AIAA-2011-1891 (Proc. 52nd AIAA/ASME/ASCE/ AHS/ASC Structures, Structural Dynamics, and Materials Conference), pp.1-8, April 2011, DOI:10.2514/6.2011-1891

Yasuyuki Miyazaki, Yoji Shirasawa, Osamu Mori, Hirotaka Sawada, Nobukatsu Okuizumi, Hiraku Sakamoto, Saburo Matunaga, Hiroshi Furuya, and Michihiro Natori, Conserving Finite Element Dynamics of Gossamer Structure and Its Application to Spinning Solar Sail "IKAROS", AIAA-2011-2181 (Proceedings of 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference), pp.1-17, April 4-7, 2011, Denver, Colorado, DOI:10.2514/6.2011-2181

The most important result of thie research project is that we developed the analysis code NEDA2.0 that is the updated version of the structure-preserving analysis code NEDA, and we applied it to the development of the solar power sail "IKAROS" by JAXA, e.g. the simulation for the deployment of the sail mmembrane (The evaluation of the result and improvement of NEDA2.0 was follwed by the next KAKENHI project "Solution structure of gossamer muti-body dynamics). In this research, we established the following research procedure: the improvement of the analysis model, correspoinding modification of the code, and validation of the model and code by experiments, and verification by the flight data. The main results are as follows:

The fist one is the analysis of IKAROS. IKAROS deploys square membrane of 14m in its each side, and 7.5 micro-meter in its thickness. The deployment sequence consists of two steps, i.e. "first stage deployment" and "second stage deployment" (You can see the detail of the sequence in youtube movie). In the analysis of IKAROS, we implemented the following effect into NEDA that is unique to membrane or solar sail: 1) spring-back effect at the fold line, 2) re-inforcing tape on the membrane (mesh superposition), 3) self-contact in membrane, 4) constraint to connect the center tether (cable element) to the spacecraft main body (rigid element), 5) connection of trapezoidal membrane and the rectangular "bridge" membrane (mesh superposition), 6) solar radiation pressure considering the optical parameter of the surgace of the membrane.

The mathematical model of the first stage deployment is implemented into Matlab®-based NEDA and Prof. Sakamot analyzed the first stage deployment. We analyzed the second stage deployment using C-based NEDA. The given time for the development of IKAROS was so short that we thought we must reduce the computation time. Therefore, we modified NEDA into the parallel computing code using MPI library, which we call NEDA2.0. The body domain is divided geometrically into several subdonains, and the deformation of each subdomain is calculated in parallel. The geometric constraint between the subdomains are considered by using Lagrange mutiplyers. In case of IKAROS, the domain is divided into (only) six subdomains, i.e. four trapezoidal membran epetals, spacecraft main body, and the center tethers that connect the main body and the membrane petals. The computation time is less than 25% of that of non-parallel calculation. Thus the analysis was completed on time.

This research project finished in March 2010, and IKAROS was launched on 21st May, two month later. It was a great pleasure for us that JAXA used NEDA2.0 for the analysis of IKAROS. During the development of IKAROS, we learnt what is important and what we should consider when we apply the analysis theory and the analysis code to the real development of spacecraft. It was priceless experience for us.

Osamu Mori, Hirotaka Sawada, Fuminori Hanamura, Junichiro Kawaguchi, Yoji Shirasawa, Masayuki Sugita, Yasuyuki Miyazaki, Hiraku Sakamoto, and Ryu Funase, Development of Deployment System for Small Size Solar Sail Mission, Transactions of Japan Society for Aeronautical and Space Sciences, Space Technology Japan, Vol. 7, pp.Pd_87-Pd_94, November 28, 2009, http://dx.doi.org/10.2322/tstj.7.Pd_87

Yasuyuki MIYAZAKI, Dynamic Behavior of Spinning Square Solar Sail, Proceedings of the 18th Workshop on JAXA Astrodynamics and Flight Mechanics, pp. 38-42 , July 28-29, 2008, Sagamihara, Japan.

Through the analysis of IKAROS, we recognized that we should predict the motion of gossamer multi-body system in much shorter time in order to design and develop it and to employ the analysis result for the daily operation after the launch. Especially, they need the code that can conduct the sensitivity analysis and the parametric study quite fast with appropriate accuracy using valid mathematical model. So we thought we should formulate the reduced-order model from necessary minimum number of full model (high fidelity model) and conduct the required analysis such as sensitivity analysis.

TProf. Yamazaki has been researchin on thie model reduction problem since he was a PhD candidate. He tried to obtain apropriate empirical eigenvectors using Karhunen-Loève decomposition so that the eigenvectors describe the feature of the system dynamics well, made a projection of the motion from the state space of the full model to the reduced partial space, calculate the motion in the reduced space, and map the motion to the full space again. The right figure shows an example of this scheme: A circular membrane is connected to a rigid body by tethers. The attitude of the rigid body is forced to change. Then the membrane deforms to follow the attitude change of the rigid body. The red solidline and the broken line represent the result obtained by the full model and that by 1/10 model, respectively. They agrees well with each other.

We thought that this research surely can be applied to other various problems, e.g. to predict the motion more accurately by the fusion of experimental and numerical data, to fill a deficit of the experimental data using numerical analysis result. This idea has evolved into the ext KAKENHI research "Solution structure of gossamer multi-body dynamics".

[reference]

Masahiko Yamazaki and Yasuyuki Miyazaki, Empirical Model Reduction of Spinning Solar Sail, Transactions of Japan Society for Aeronautical and Space Sciences, Space Technology Japan, Vol.8, No.ists27, Pc_35-Pc_40, December 29, 2010, DOI: http://dx.doi.org/10.2322/tastj.8.Pc_35

In addition, we thought it was necessary to evaluate the inplane stiffness of the membrane in compression and the bending stiffness of the crease of the membrane to simulate the motion of the membrane efficiently and accurately. In the conventional analysis, the compressive stiffness was assumed constant. In this research, we formulated a nonlinear approximation model of the compressive stiffness of the membrane that is based on the theoretical solution of the reaction force at the edge of a rectangular membrane subject to uniaxial compression. The result by this model agreed well with the result obtained by shell model. Ms. Inoue won a student award at ISTS symposium [Shoko Inoue, 2009]. She published a paper in 2014 [Shoko Arita, 2014].

Wrinkle in rectangular membrane subject to edge shear

Shoko Inoue, Prediction Methods of Wrinkling in Thin-Membrane, Proceedings of 27th International Symposium on Space Technology and Science, ISTS2009-c-20s, pp.1-7, July 5-12, 2009, EPOCHHALL TSUKUBA, Tsukuba, Japan.

Yasuyuki Miyazaki, and Kosuke Arita, Simplified Model of Membrane for Wrinkle Analysis of Gossamer Structure, AIAA Paper 2008-2134, (CD-ROM Proceeding of 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Schaumburg), pp.1-10, IL, April 9, 2008, DOI:10.2514/6.2008-2134

Kosuke ARITA, Yasuyuki MIYAZAKI and Yoshitaka NAKAMURA, Evaluation of Numerical Analysis Model for Thin Membrane, CD-ROM Proceedings of 26th International Symposium on Space Technology and Science, ISTS2008-c-13, pp.1-6, June 1-8, 2008, Hamamatsu, Japan.

As for the crease of membrane, we analyzed the elasto-plastic deformation in the folding process, and used the analysis result to formulate a simplified model of the stiffness at the crease. We assumed the folding process as the sheet hemming in the elasto-plastic analysis.

[reference]

Ryo Hayase, Yasuyuki Miyazaki, Hiroyuki Kamemura, and Shoko Inoue, A Study on Mechanical Model of Crease of Membrane, The 28th International Symposium on Space Technology and Science, 2011-c-31, pp.1-5, Okinawa Convention center, Okinawa, June 5-12, 2011.

As for inflatable structure, we studied on the folding method of an inflatable tube that has high repeatability in the extension motion using the knowledge of quality engineering, and verified our design method by experiments. We proposed a nano-satellite for the space verification of an inflatable membrane structure as a piggy-back launch with GCOM satellite. Our proposal was not selected, but we applied our proposal again to the piggy-back launch with ALOS-2 satellite, which was selected and the satellite was launched in 2014. That's SPROUT.

The above research, i.e. formulation of compressive stiffness of membrane, mechanical model of crease, evaluation of dynamics of inflatable tube, was conducted to increase the application of the structure preserving method by NEDA that can be verified through the comparison with the calculated results and experiments. Other than these examples, we applied EMM to the long-term (several ten years) orbit prediction of a satellite with the attitude prediction that has a short period compared with the orbit period, and we confirmed that EMM is numerically more stable than other method. We think the structure preserving method, especially EMM in enegineering field, can provide more reliable numerical results, so that we would popularize the structure preserving method.

This research project follows the previous KAKENHI research and studied on the evaluation method of the fold/deployment method of membrane. We compared several foild/deployment method that were proposed at the solar sail working group in JAXA. We studied on the effect of the compressiive stiffness on the distribution of the wrinkle on the membrane, and showed the mathematical model of compressive stiffness that simulates the motion of membrane more accurately. We compared the result by NEDA and that by ABAQUS®, and showed the 有効性 of NEDA.

We studied on the similarity rule of the motion of membrane concerned with spin-type solar sail spacecraft, and derived the similarity parameter theoretically, and showed the validity of our similarity rule using the result of the deployment experiment on the ground (1G) with 1 atom pressure, low pressure, vaccum). However, this research showed that it is not easy to predict the motion of the membrane in space from the experimental result on the grounnd, and it is difficult to formulate the similarity rule with theoretical validity that can predict the motion in space unless we conduct the experiment under micro-gravity, e.g. by using an airplane or a drop tower (This result is one of the motivation of the later KAKENHI research "Establishment of prediction method of dynamics of large gossamer muti-body space structures and understandings of their dynamics".

Prof. Natori in ISAS proposed the concept of "combined membrane structure", and we conducted numerical simulation of the deployment of a combined membrane structure with a graduate student in Natori laboratory.

[Difference of deployment by folding pattern]

Left: with compressive stiffness right: with no compressive stiffness

[Spin deployment of spirally folded membrane]

[Spin deployment of membrane in vaccum chamber]

[Combine membrane structure]

[Deployment simulation of combined membrane structure]

[reference]

Hiraku Sakamoto, Yasuyuki Miyazaki, and K.C. Park, Finite Element Modeling of Sail Deformation Under Solar Radiation Pressure, Journal of Spacecraft and Rockets, Vol.44, No.3, pp.514-521, May-June 2007.

Kosuke Arita, Sotaro Hashiguchi, and Yasuyuki Miyazaki, Evaluation of deployment method of Spin-Deployable Membrane, ISAS 17th Workshop on Astrodynamics and Flight Mechanics, pp.251-254, July 23-24, 2007, Sagamihara.

Masashi Hashimoto, Naoko Kishimoto, Yasuyuki Miyazaki, and Michihiro C. Natori, Deployment Analysis on Membrane Structures Combined with Inflatable Tubes, CD-ROM Proceedings of 25th International Symposium on Space Technology and Science, ISTS06-c-13, pp.1-5, Kanazawa, Japan, June 2006.

Yasuyuki Miyazaki, Wrinkle/Slack Model and Finite Element Dynamics of Membrane, International Journal for Numerical Methods in Engineering, Vol.66, No.7, pp.1179-1209, May, 2006, DOI: 10.1002/nme.1588

Prof. Miyazaki has been participating in the solar sail working group of JAXA since the end of FY2002. So we planned to develop an analysis code available for the development of solar sail spacecraft and investigate the dynamics behavior of spin-deploying membrane.

We updated NEDA so that it can take into account various effects such as the self-contact of membrane. We proposed several evaluation criteria of the deployment motion of spin-deploying membrane, i.e. deployment ratio, 累積 strain energy density, maximum strain energy 頻度, and compared and evaluated several folding/deploying method using these criteria. When many design are proposed, it is quite important in the design and development of the spacecraft to 設定する the criteria to compare them quantitatively. We looked over such a situation in near future of the solar sail project, and researched on the evaluation criteria.

Y. Iwai and Y. Miyazaki, "Dynamics of Membrane Deployed by Centrifugal Force", CD-ROM Proceedings of 24th International Symposium on Space Technology and Science, ISTS04-c-12, pp.1-6, June 2004, Miyazaki.

Prof. Miyazaki developed a Matlab-based code for the analysis of membrane structure when he stayed in University of Colorado at Boulder (UC Boulder) from 2001 to 2002. Mr. Hiraku Sakamoto, a PhD candidate of UC Boulder, used this code and we proceeded the research on the de-wrinkle design method of large membrane structure with Mr. Skamoto and Prof. K.C. Park in UC Boulder.

Perspecting the development status of solar sail in and out of Japan, it seems that the tension and flatness of the membrane can not be managed presicely because the membrane is so large. Howeve, if a structure that is not subject to severe limitation of the weight as solar sail will be developed, modular structure can be applied and the tension and the flatness of the membrane in each module can be maneged. In such a case, this research can be empolyed.

[reference]

H. Sakamoto, Y. Miyazaki, and K.C. Park, Evaluation of Cable Suspended Membrane Structures for Wrinkle-Free Design, AIAA Paper 2003-1905, pp.1-10, April 2003. (Proceedings of 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (SDM)), DOI:10.2514/6.2003-1905

JAXA analyzed the membrane using so-called multi particle method that approximates the membrane by mass-spring network. Their approximation was available only for right triangle membrane. We thought it does not have general versatility. Therefore we proposed an approximated method that is available for arbitrary non-structural finite element mesh division. We compared the simulation result by this approximation with that by membrane element, and showed the validity of this approximation (Off course, this approximation is less accurate in case that the influence of the wrinkle is large because this approximation limits the direction of the wrinkle).

Yasuyuki Miyazaki and Yuka Iwai, Dynamics Model of Solar Sail Membrane, 2004 ISAS 14th Workshop on Astrodynamics and Flight Mechanics, pp.32-37, July 2004, Sagamihara.

Y. Iwai and Y. Miyazaki, Dynamics of Membrane Deployed by Centrifugal Force, CD-ROM Proceedings of 24th International Symposium on Space Technology and Science, ISTS04-c-12, pp.1-6, June 2004, Miyazaki.

We continued the research on inflatable structure. We clarified the characteristics of rolled-up inflatable tube by the numerical analysis using LS-DYNA and the experiment.

[reference]

Yohei Hamamoto, Yasuyuki Miyazaki and Yoshitaka Nakamura, Deployment Dynamics of a Rolled-up Inflatable Tube, Collected Papers of 24th International Symposium on Space Technology and Science, ISTS04-c-13, pp.297-302, Miyazaki, Japan, October 2004.

Yohei Hamamoto and Yasuyuki Miyazaki, Stable Deployment of Rolled-up Inflatable Tube by Control of Gas Flow, IAC-03-I.2.07, CD-ROM Proceedings of 54th International Astronautical Congress (IAC), pp.1-6, Bremen, Germany, September 2003.

The most important result is that we developed NEDA.

Inftable structure had been expectid strongly as next generation large space structure. We tried to apply our energy-preserving method to inflatable structure, and achieved the simulation of the deployment as in the right figure before 1999.
We planned to improve the code for more accurate analysis and to enable the code to simulate the deployment of various inflatable structure, so Prof. Miyazaki applied his proposal to KAKENHI.

The proposal was adopted and we sthought to modify the theory and code in FY2000. We also conducted "Deployment experiment of inflatable tube unde micro-gravity with the support of Research Grant of Nihon University College of Science and Technology. So we started the research from the simulation of this micro-gravity experiment.

The result is shown in the below figure and movie. We think we realized a good research style that we obtain better result supported by KAKENHI onthe basis of the research supported by the grant in our university.

As the result of the modification of the theory and code, we developed NEDA. We have been researching on EMM deeply since then, and developed a flexible multi-body dynamics analysis code "lag" to verify our theory. Reflecting the knowledge obtained by the development of "lag" to NEDA, we improved NEDA to more and more poweful tool. In addition, Mr. Hiraku Sakamoto, a master course student of Natori laboratory in ISAS, used NEDA for the analysis of multi-cell inflatable tube, and we improved NEDA more by considering his research result.

Hiraku Sakamoto, Michihiro C. Natori, and Yasuyuki Miyazaki, Deflection of Multicellular Inflatable Tubes for Redundant Space Structures, Journal of Spacecraft and Rockets, Vol.39, No.5, pp.695-700, September 2002.

Yasuyuki Miyazaki and Tsuyoshi Kodama, A Conservation Scheme of Energy and Momentum for Flexible Multibody Dynamics, Proceedings of The First Asian Conference on Multibody Dynamics 2002, T-3-1-4, pp.1-6, August 2002, Iwaki (CD-ROM).

Yasuyuki Miyazaki and Michiharu Uchiki, Deployment dynamics of Inflatable Tube, AIAA Paper 2002-1254, pp.1-10, April 2002. (CD-ROM Proceedings of 43rd AIAA/ASME/ASCE/ AHS/ASC Structures, Structural Dynamics, and Materials Conference ), doi: 10.2514/6.2002-1254.

Cable-membrane structure is excellent in the points of deployment, packaging, and light weight, so that it had been expected as a structural 様式 of space structure. In fact, cable-network strucrure was adopted as the radio astronomy satellite MUSES-B (HALCA) and used in space. However, it was recognized that it was difficut to analyze the behavior of the structure when the cables are slacked or the membranes are wrinkled, and that the behavior is not predicable at all.

Cable and membrane buckle easily with low compressive load and then their stiffness decreases drastically, so that the equations of motion are highly stiff differential equations. Therefore, the numerical time integration of the differential equations gets instability.
We were interested in the dynamic analysis of kinking phenomena of flexibl beam (cable) and the motion analysis of the structure that has different stiffness in betwwn tensile state and compression state. We thought the time integration scheme that preserves the energy strictly is neccesary to obtain appropriate solution.
Based on this motivation, we had been studying on the solution method that preserves the energy since 1993, which was the same idea as the structure-preserving method such as the energy-momentum method, 可積分法, simplectic integral, Stäckel method, discrete variational principle).

Prof. Miyazaki applied his proposal to KAKENHI and the proposal was adopted in 1998. After that, our laboratory have been mainly researching on so-called gossamer structure such as cable and membrane. In this sense, this research project was very important for our laboratory.

In fact, we developed an analysis code that is the basis of the later Nonlinear Elasto-Dynamic Analysis code NEDA.

This code has two "sales points": it consider the compressive stiffness of the membrane appropriately, and it is based on the energ-momentum method (EMM). We did not know that the research on EMM had been in progress at CalTech. Our code also preserved the energy, linear momentum, and angular momentum, and we found later that out code is essentially identical with EMM.

As we implemented the energy and momentum preservation procedure, the code became to be able to simulate the deployment and packagin of hexagonal membrane under gravity and zero-gravity. Based on the numerical analysis result, we proposed a "natural" folding pattern of membrane that is shown in the right figure. If we apply this folding pattern to a square membrane, it is identical with that of IKAROS.

We proved that it is necessary to consider the compressive stiffness of the membrane by comparing the experimental result with the numerical result. The below figure illustrates an example, in which a square membrane is supported at its two corners of a side and the mid-pint of the opposite side under the gravity, and the membrane is going to be wrinkled/slacked when the mid-point is getting closer to the opposite side. As in the center figure, the numerical result gets closer to the experimental result by considering the wrinkle of the membrane.

[reference]

Masaki Namaizawa, Yoshitaka Nakamura, and Yasuyuki Miyazaki, Dynamic Analysis of Membrane Structures with Wrinkling Members, Proceedings of Asia-Pacific Vibration Conference, Vol.2, pp.782-787, December 1999.

Yasuyuki Miyazaki and Yoshitaka Nakamura, A Geometrically nonlinear finite element of flexible structures that conserves total energy, Modeling and Simulations based Engineering (Proceedings of ICES'98), Vol.1, pp.349-358, October 1998.

Yasuyuki Miyazaki and Yoshitaka Nakamura, Dynamic Analysis of Deployable Cable-Membrane Structures with Slackening Members, Proceedings of 21st International Symposium on Space Technology and Science, ISTS98-b-13, pp.1-6, May 1998.

Miyazaki and Yamazaki Laboratory
College of Science and Technology, Nihon University
7-24-1 Narashinodai, Funabashi, Chiba 274-8501, Japan
e-mail: asel (at) forth.aero.cst.nihon-u.ac.jp