We participated in the project "Formation of Center for Research and Development of Advanced Deployable Structure Pioneering Innovative Space Science" that is led by Prof. Hiraku Sakamoto of Tokyo Institute of Technology, supported by Coordination Funds for Promoting AeroSpace Utilization, MEXT. Our laboratory was in charge of the micro-gravity experiment of deployable membrane structures by airplane. You can see the detail in the web page "Advanced membrane structure".

We had studied on "combined membrane structure", i.e. membrane with support frame strcuture consisting of inflatable tubes. Combined membrane structure is one of the structures that can deploy and construct a lightweight large surface in short time. In March 2014, we launched the nano-satellite space demonstrator of the combined membrane structure, SPROUT, and conducted the deployment experiment of the combined membrane structure on orbit in June 2015. The hold-relase mechanism and the deployment device worked well, but the tubes did not extend properly, so that the deployment of the membrane failed. We investigated the reason of the failure by conducting the experiments including micro-gravity experiment in an airplane, and determined the reason. Based on the investifation, we considered the checkpoint in the development of combined membrane structure. You can see the detail in the web page "Space demostration of combined membrane structure".

We participated in the FIRST program funded by the Cabinet Office "New paradigm of space development and utilization by nano-satellite" that was led by Prof. Shinichi Nakasuka in the University of Tokyo from the end of FY2009 to the end ofFY2013. Our research topic in this project was "Research and development of deployable structure". This project is called "HODOYOSHI Project", and is the origin of current big wave of nano-satellite development and utilization in Japan. You can see the detail at the other wab page.

When the research group of universities and industries were researching on space inflatable structure, JAXA offered the experiment on the MCE (Multi-mission Consolidated Equipment, right figure) at JEM exposure facility of the International Space Station in public subscription. The group led by Prof. Takahira Aoki of University of Tokyo applied for this experiment, and their application was selected. It was in 2007. The project name is SIMPLE (Space Inflatable Membraine Pioneering Long-term Experiment). The MCE has the dimension about 80cm by 80cm by 180cm, and it carries several experimental systems. On of those systems is SIMPLE. SIMPLE is about 50cm cubed shape (with a dent about 20cm by 20cm by 50cm). The devices were installed within the envelope at launch, and extended/deployed on orbit. Inflatable structure is ultralight structure that consists of thin membrane bag inflated by the injection of gas, has high packaging efficiency, is easy to deploy, and has other excellent properties that are required to space structure. However, it had not been used in space because it was not proven in space.

(c) JAXA http://iss.jaxa.jp/kiboexp/equipment/ef/ mce/images/ef_mce1.jpg

Therefore, we launched the SIMPLE project to show the usefulness of inflatable structure through the long-term operation after its deployment in space, and to accumulate the basic data to apply inflatable structure to future space structure.

The right figure illustrates the appearance of SIMPLE. SIMPLE conducted three experiments: 1) the extension of a mast that was constructed on orbit using an inflatable tube as the extension actuator (IEM), 2) the germination of seeds of plants (IST), 3) material evaluation (IMP). The companies in the team manufactured the hardware of SIMPLE, and the team discussed on the mission. Our laboratory joined the disscussion on IEM.

SIMPLE was launched in July 2012, and conducted the above three experiments in August. The IEM experiment was successful and the mast maintained its configuration without significant degradation. SIMPLE completed the steady-state operation in December 2014.

The experiment on the international space station was an amazing experience for us, and helpful for later research. We were very glad that we worked together with the alumnae and alumni of our laboratory at Tsukuba space center.

The right photo shows (some of) the member of SIMPLE project.

Around FY2007, we were condidering the space verification of inflatable membrane structure for the mission of the nano-saellite SPROUT, and discussing measures against the space debris of post-operative nano-satellites. We determined to develop the device that can make the de-orbit of a 20cm cubed nano-satellite with 8kg in 750km altitude sun-synchronous orbit within 10 years, and conducted this research.

We designed a pyramid-like deployable membrane structure that consists of four inflatable tubes and a membrane. We expected the satellite increases the atmospheric drag by this membrane structure and hence decreases the altitude, which results in the re-entry to the earth atmosphere and the burn-out.

Firstly, we conducted the numerical simulation of the orbit and the attitude of the satellite considering the perturbation of the gravity due to the J2 term, aerodynamic drag, and solar radiation pressure, and showed that 1.2m square membrane (the area is 1.44 square meter) is enough, the inclination angle of the tube should be less than 20degree, and 0 degree is the best, i.e. the flat membrane rather than the pyramid is most efficient for the orbit descent.

After that, we make a prototype of the de-orbit device, and conducted the vacuum experiment, deployment experiment, and showed the device can be installed in 20cm cubical satellite. This research led to the development of the inflatable structure system, especially gas-supply subsystem of SPROUT, and evolved to the proposal of PRIMROSE at the Satellite Design Contest. [reference] Yasuyuki Miyazaki, Nobuaki Kinoshita, Yuta Araki, and Takafumi Masuda, A Deployable Membrane Structure for De-Orbiting a Nano Satellite, IAC-07-B.4.5.08, CD-ROM Proceedings of 58th International Astronautical Congress (IAC), pp.1-8, September 26th 2007, Hyderabad, India.

There has been lots of research on the free-fall motion of the parachute with payload since long time ago, and it seems that almost nothing was remained to be researched in 1980's. In the middle of 2000's, the research was actively conducted on the numerical simulation f the flow around the parachute or parafoil (ram-airparachute) based on numerical fluid dynamics.

It was researched in that time to apply the come back system of the parafoil system with payload to the transport of the relief good or the recovery system of rocket. Our laboratory conducted the experiment to fly the CanSat to the target point in ARLISS for several years, so that we thought we could conduct the basic research on those systems on the basis of our experience.

Many people may imagine the problem of minimization of damage to the driver and occupants at car crash from the word "impact analysys". In fact, the industries analyze the car crash problem using the commertial software such as PAM-CRASH, and desgin the structure of the chassis of the car. In case of space engineering, people may imagine the damage estimation at the collision of space debris with spacecrafts. This research is much more basic one, i.e. to formulate the numerical method of estimation of the deformation and the impact pressure distribution at the collision of two elastic bodies.

Prof. K.C. Park in University of Colorado at Boulder and his colleague had been researcing on "contact/impact analysis using localized Lagrange mutiplyer". The concept of localized Lagrange multiplyer formulation is such that the system is divided into subdomains, the connectivity relation between the subdomains is described in terms of Lagrange multiplyers, and the system is regarded as the set of constrained subdomains. This concept can be applied to various fields. For example, structural analysis of large-scale structure is condcted by dividing the structure into lots of substructures. Control is carried out by distributing the sensors and actuators. The interaction analysis between structural deformation and external field such as the fulid dynamics or electro-magnetic field can be conducted by modeling the structure and the external field separately and describe the interaction by using "localized" Lagrange mutiplyers. Off course the physical meanings of the Lagrange multiplyer in each cahse is different from each other. This concept is suitable in case of changing the finite element mesh pattern of each subdomain in the structure, and using the different mesh between structure and fluid in the interaction analysis.

The contact/impact analysis is one of the best example to show the above concept efficient. In the contact/impact analysis, the virtual surface called "contact frame" is located between the mutually contacting two bodies as in the right figure, and each body is assumed to contact with the contact frame. Only if we introduce the contact frame, we can easily avoid the problems such as the over-constraint associated with the contact problem, and obtain more accurate solution of the distribution of the contact pressure in the contact surface. In case of conventional contact/impact analysis, it is not easy to set up the appropriate constraint condition after the contact search (e.g. the set-up of the master element and the slave node). It is combersome to carry out this set-up procedure without any inconsitencies if the contacting bodies have complicated shape. Such a problem is resolved if we introduce the contact frame.

Conversely, the placement of the contact frame is the point of this method. Fortunately, there has been derived mathematically strict condition for location of the finite element nodes constituting the contact surface. Thus we just consider the location of the nodes to make the mathematical model of the system.

Based on such idea, we had researched on numerically stable and highly accurate analysis method of impact problem by combining the localized Lagrange multiplyer method with contact frame and the energy momentum method.

The right figure illustrates an example of the calculated result of the pressure distribution at the contact surface when two hyperelastic brick with same dimension and material were subject to uniformly distributed load and pushed each other. In this example, the solution should be same as that for the case where the brick is pushed to a rigid wall like figure (a). However, if the finite element mesh of each brick is different from the other like figure (b), there are small difference between the solution of (a) and that by the localized Lagrange mutiplyer method (blue line), that by conventional maste-slave method (green). It is obvious that the localized Lagrane mutiplyer method gives good solution compared with the master-slave method (The solution by the master-slave method can be improved more by considering the algorithm and the processing of the obtained result).

The right figure and movie show the collision of a flexible ring and a rigid wall. Theer are slight difference between frictional contact and non-frictional one. It is an important research topic to solve the frictional contact/impact precisely. [reference] Miyazaki Y., Park K.C., A Formulation of Conserving Impact System Based on Localized Lagrange Multipliers, International Journal for Numerical Methods in Engineering, Vol.68, No.1 pp.98-124, 2006.

We started the energy-conserving method for structural dynamics since 1993, and developed the analysis code NEDA that is based on so-called Energy-Momentum method (EMM) (In that time, we did not know about EMM and that our method is essentially identical with EMM). We analyzed the development of membrane using NEDA. This research aimed for formulating more general theory that is avialable for the multi-body system with rotational degree of freedom such as rigid body, shell, and beam, and for the constraint system. In the resutl, the research was something like a summary and a re-construction of the theory od EMM, but we achieved to apply the EMM to the dynamics of membrane and to formulate the generalized method to implement the constraint condition, which was developed to the later research on gossamer multi-body dynamics and to the deployment analysis of IKAROS. [reference] Yasuyuki Miyazaki and Tsuyoshi Kodama, Formulation and interpretation of the equation of motion on the basis of the energy-momentum method, Journal of Multi-body Dynamics, Vol.218, No.1, pp.1-7, March 2004, doi: 10.1243/146441904322926832.

The prediction technique of the deployment motion is necessary to realize the practical use of inflatable strucrure, but there had been few data of deployment motion by ether numerical analysis nor experiment. Though inflatable structure adopts simple deployment sequence that it deploys just by the gas pressure, and it was said that inflatable structure is reliable and its repeatability of the motion is high, there had not been conducted sufficiently the numerical analysis and the experiment on the evaluation of the effect of the gas pressure and the cerase of the folded membrane on the deployment motion of the membrane. So we developed a numerical analysis code that can simulate the deployment motion of an inflatable thin membrane tube, which was a modification of NEDA, and analyzed the deployment motion of an zig-zag folded inflatable tube in zero-gravity. We showed that pendulum motion can occur by the interaction of elastic deformation of the tueb and change of the pressure of inflation gas, and analyzed the feature of this motion. Next, we carried out an deployment experiment of an inflatable tube under micro-gravity environment to verify the numerical analysis results. The experimment was conducted at JAMIC in Kamisunagawa, Hokkaido (Unfortunately, JAMIC was closed in middle of 2000's). We compared the experimental results with the numerical results and proved that our numerical analysis code can simulate the deployment motion of inflatable tube in micro-gravity environment. The following two points are the main point of this research: 1) we proved that the effect of the stiffness of the fold line of the tuben on the whole motion of the tube is predictable by numerical analysis, 2) we showed the mechanism of the interaction of inflation gas and deformation of the tube. Furthermore, we showed that our code can simulate the moving hinge effect of the fold line of the tube during the deployment by considering the self-contact of the membrane. This research was followed (developed) by the KAKENHI research "Dynamics of inflatable space structure".

[reference] 磯部洋，水野妙子，宮崎康行，「微小重力下でのインフレータブルチューブの展開挙動（第2報）」，第43回構造強度に関する講演会講演集，pp.125-128，2001年8月． 水野妙子，宮崎康行，中村義隆，「微小重力下でのインフレータブルチューブの展開挙動」，第44回宇宙科学技術連合講演会，1E-1，2000年10月． Taeko Mizuno, Yasuyuki Miyazaki, and Yoshitaka Nakamura, Deployment Analysis of Inflatable Tube, Proceedings of 22nd International Symposium on Space Technology and Science (ISTS), pp.525-530, Morioka, Japan, June 2000.

There has been proposed various methods on topology optimization, e.g. homogenization method and level-set method, and also on shape optimization that optimize the boundary of the body, e.g. force method. Prof. Nakamura had researched on topology optimization based on homogenization, and proposed "Imaginary Boundary Element Method" that is a kind of boundary shape optimization method. Followinf this method, Prof. Nakamura researched on efficient numerical scheme to calculate the compliance when the boundary is modified.

We had thought that Nihon University Department of Aerospace Engineering is famous on human powered aircraft, but we should do something about space engineering science. The students had applied to the Satellite Design Contest in 1996 and 1997 as a project of a class in graduate school. A venture company had offered out department to develop 50kg piggy-back satellite. On such background, our laboratory started the planning of a piggy-back sateppite with other faculties in our department in FY1997.

Then, it happened around January 1998 that JAXA advatised for a piggy-back satellite at the launch of ADEOS-II. Our department applied two proposal. The one is a re-entry mission of small satellite, and the other one is space demonstration of spin deployment of membrane because our laboratory research on deployable membrane structure. The photos and movie below shows the deployment of a full scale membrane model. Our proposal was not chosen for the piggy-back satellite. In the process of preparing the application form, we tried but could not obtain the numerical simulation result of the deployment of the membrane, which resulted in the accelaration of the KAKENHI research"Behavior of Deployable Cable/Membrane structure under slack" that started in April 1997.

By the way, the folding method of this membrane is same as that of IKAROS as it happened. The difference is only the shape, i.e. this membrane is hexagon, and the membrane of IKAROS is square. As shown in Research by KAKENHI, this folding pattern corresponds to the folding pattern of a hexagonal membrane that is compressed at six corners toward the center of the membrane, which means that this folding method is quite natural.

Highly flexible elastic bodies such as slender beam and thin shell often presents unstable behavior. We focused on such unstable behavior and derived analytical solution and numerical solution, which includes various interesting mathematical topics such as the bifurcation, snap through, catastrophy. We think it is interesting to analyze such a problem by finite element method.

Foe example, various bifurcation and snap through phenomena occur when a slender rod is twisted and compressed axially. We derived the analytical solution of three dimensional deformation of an extensible and shear flexible slender rod. That analytical solution involves the self-contact of the rod with kinking.

The right figure illustrates an example of snap through of a twisted rod. When a twisted rod is compressed axially, kinking occurs. There is a histeresis between the compessin process and the extension process.

The below left figure illustrated the shape of the rod under axial compression. As in the figure, the secondary buckling occurs when the amoount of the axial compression reaches a critical value. For the further axial compression, the rod presents the self-contact. We obtained the analytical solution of the secondary buckling point, too. The right figure shows the snap through behavior of the rod twisted under a constant axial compression.

Including the above examples, we obtained the solution surface of the kinking problem and clarified the solution structure. This problem is a good example of stability problem of nonlinear system.

We analyzed the dynamics of kinking by geometrically nonlinear finite element method, too. The right figure illustrates the shape of the rod during the kinking motion. Generally speaking, we should take great care of the numerical time integration scheme in case of evaluate the elastic stability by numerical simulation of the motion of the elastic bodies. If we employ inappropriate scheme, unnecessary energy is supplied to the elastic body and it is difficult to evaluate the stability. We had developed a numerical time integration code that can evaluate the dynamic stability of nonlenar system based on Energy-Momentum method, a kind of nonlinear dynamic analysis method. We applied this code to the analysis of kinking problem.

Furthermore, we showed these phenomena experimentally, and validated the theory and the numerical method by the comparison of the experimental results with the theoretical and numerical results. We think the analysis of nonlinear system should be approached by three way, i.e. experiment, theory, and computation. If one of them is lacked, it is difficult to solve the nonlinear problem.