investigastion of structural analysis themes related to...

Investigation of Structural Analysis Themes related to Inflatable Space Structures, by the use of the Non-Linear,

Multibody Finite Element Code SAMCEF Mecano

February 2 - 3, 2005 Salon de l’Aveyron

PARIS, Bercy FRANCE

G. Augello* ,Marco Nebiolo* E. Carrera**, L. Manfredi**, R. Bodombo**

E. Gabellini***

* Alenia Spazio S.p.A., Torino, Italy ** Aerospace Department, Politecnico di Torino, Italy

***SAMTECH Italia, Milano, Italy

Abstract: In the field of investigation of the Inflatable Space Structures, Alenia Spazio has chosen the SAMCEF Mecano code, as the reference computational tool for the numerical assessment and simulation of the various mechanical problems related to these structures. The suitability of SAMCEF Mecano code in allowing an effective numerical simulation of some of the typical aspects relating the Inflatable Space Structure, has been already verified for the design and the analysis of an Inflatable Re-entry capsule. The use of SAMCEF Mecano for this purpose has been performed in the framework of a joint study named IRT (Inflatable Re-entry Technologies) made for ESA by Alenia and Aero Sekur companies. The work was done in the framework of a scientific collaboration among the Aerospace Department of Politecnico di Torino, Alenia and Samtech Italia. SAMCEF Mecano sofware was, in fact, employed for the inflation process simulation and stress analyses. Obtained results have shown the capability of the employed software along with the suitability of the proposed solutions. Some details of the conducted numerical simulation process will be given later on. However, some of the SAMCEF Mecano simulation capabilities have been assessed, such as: the schematization of membrane composite materials , the treatment of large geometric non-linearities, which are intrinsic to the behaviour of membrane structures under pressure loads, as well as the contact phenomena extended to large areas. The membrane structure inflation phenomena have not been deeply investigated, in the sense that the inflation has been simulated by just applying the related pressure load and not by studying it via the Volume Control Technique.

9th SAMTECH Users Conference 2005 1/52

Further tests have been performed in order to assess the SAMCEF Mecano suitability in simulating some other important aspects related to the Inflatable Space Structures, like manned or unmanned Space Modules. In fact, mainly due to the need for a MMOD (Micro Meteorites & Orbital Debris) protection the shell which constitutes the walls of the Inflatable Module, becomes considerably thicker than the one foreseen for the Re-entry capsule, mentioned above. The overall thickness of the shell can reach 300 mm for long term missions with respect to the about 10 mm of the above mentioned re-entry capsule. Furthermore, in manned Space Modules, the shell is made up of several membrane layers of different materials, each one having to accomplish a dedicated function: air containment, pressure containment, MDPS and thermal insulation. The inflatable structure is a multi-layer shell with a well defined stacking sequence. Then the nonlinearity as well as the extended contact phenomena, makes more and more difficult to set up a simulation approach. The inflation phases starting from a packed position, and considering such a thick shell, is not considered in the present work but it will be taken into account in future activities, since it is a fundamental aspect of the study on Inflatable Structures to predict the on orbit correct deployment. Another problem that has been considered is related to the connection among these packed thin membrane sheets and the mechanical part of the Inflatable module. The interaction between the deployment of a mechanism device, which can guide the membrane shell in reaching the final desired shape, and the inflation phase itself, is foreseen to be investigated during this test study. These aspects related to the numerical simulation of Inflatable Space Modules, have been taken as benchmark for the activities performed in Alenia Spazio in collaboration with the Aerospace Department of Politecnico di Torino, and with the technical support of the Samtech Italia. The results obtained in the study of the Re-entry capsule, as well as the results of the subsequent tests have shown that the SAMCEF Mecano code is well suited to the numerical simulation of the Inflatable Space Structures and it can become a very useful tool for the verification of their design.


1 INTRODUCTION In this paper are presented the activities performed in order to evaluate the suitability of the SAMCEF Mecano code in allowing the numerical simulation of the main physical aspects related to the design and the verification of the Inflatable Space Structures. As will be shown in one paragraph of this article, the SAMCEF Mecano code has been already used for the numerical simulation of the physical behaviour of the Inflatable Structure of a Unmanned Capsule, foreseen for the Re-entry in Earth of experiments and payloads. The activities here presented are focused on some of the main topics which characterize the analysis of Manned Inflatable Space Structures. These physical aspects, related to the inflatable multilayer shell and to the interacting deployment mechanisms, results in constructive solutions which, in some cases, make difficult the numerical simulation for the verification of the adequacy of their design, functionality and strength. The difficulty of this numerical simulation arises from the intrinsic characteristics of the involved phenomena: on one side great geometric non linearity, wide contact areas, possible folding and unfolding of thick membrane shells, connections among flexible and rigid structures, sliding of adjacent layers etc.. and on the other side the necessity of facing problems of different nature like structural problems, kinematical problems, inflation fluid, etc.. often interacting among them. The SAMCEF Mecano code offers in a unique SW package the possibility of simulation of many of these problems, due to its nature of Multi-body code which allows also to account for all the non linear phenomena. This fact results in a very important code characteristic, because the user needs to learn one code only and can easily become familiar with it.


2 INFLATABLE SPACE STRUCTURES MAIN CHARACTERISTICS The Inflatable structures can find their application in the following fields : - manned space modules - re-entry vehicle ( like capsules ) - unmanned space structures ( like solar arrays, antennas, etc.. ) In particular, the manned Inflatable Structures can be seen as a convenient answer to the following demands arising from the space activities : - to accomplish long-term manned space missions, like planets explorations - to have the availability of manned modules attached to the ISS - to construct manned Free-Flyer on Low Earth Orbit - to construct permanent bases on other planets An important characteristic of the Inflatable Structures is the possibility to exploit a habitable volume greater than the one offered by traditional metallic space modules. This can assure, among other things, the possibility of increasing the comfort and the number of crew members on board with a consequent benefit for what concern the entire mission result. The necessary volume for a Mars manned mission of 5/6 persons has been estimated to be around 500 m3 . This volume would therefore be sufficient to host the crew for a long term mission as required for interplanetary exploration. If one consider that the traditional metallic modules can offer a volume of about 90 m3 also limited by the launcher fairing or cargo bay capability, it comes out how much appealing are the inflatable manned modules that can exploit the same launch volumes but provide huge on orbit volumes. An example of hypothesis of manned Inflatable Space Module, is given by the NASA TransHab program in which Alenia Spazio was involved from 1998 to 2000 as part of the Italian Space Agency (ASI) team. This was an Inflatable Module with a central structural core which was foreseen as a habitation module to be attached to the ISS Node3 and also to act in a very next future as TRANSFER VEHICLE for a Mars exploration mission. Next Figures 1 and 2 show two pictorial views of the TRANSHAB module structure and its location in the ISS, while the Figure 3 shows some structural solutions foreseen for the Module.


FIG. 1 – Internal view of TRANSHAB Inflatable Space Module


FIG. 2 – TRANSHAB Inflatable Space Module attached to ISSA

MULTI LAYER INFLATABLE SHELL I/F BETWEEN RIGID CORE AND INFLATABLE/FLEXIBLE SHELL STRUCTURAL CENTRAL CORE AND REMOVABLE INTERNAL STRUCTURES MECHANISMS AND MOVABLE FLOORS I/F BETWEEN RIGID CORE AND INFLATABLE/FLEXIBLE SHELL

FIG. 3 – TRANSHAB structural solution Alenia Spazio is currently involved as Prime Contractor in the ESA study “Inflatable Habitat” that is strongly focused on the “habitat” aspects and on the boarded life support systems without however overlooking the inflatable technology issues. During the Inflatable Habitat study several concepts for the inflatable modules are being investigated in relation with different mission scenarios and with different degree of packaging not only for the inflatable part but also for the structural core. In the very next future Alenia Spazio should also be involved in the ASI program FLECS that will be mostly related to the development of the inflatable shell technologies. The FLECS mission will exploit an already scheduled MPLM mission to carry the inflatable module to the ISS. The purpose is to achieve on orbit qualification of the inflatable technology with the temporary permanence of the astronauts on the FLECS inflated volume. Next Figures 4 and 5 show pictorial of the FLECS mission and possible launch configuration.


MPLM FLECS

FIG. 4 – FLECS attached to MPLM in the Shuttle cargo bay

BULKHEAD RIGID FLEXIBLE-RIGID INFLATABLE STRUCTURE I/F STRUCTURE

FIG. 5 – FLECS attached to MPLM cone bulkhead


For long term mission ( 10-15 years ) care must be taken to protect the crew and the integrity of the structure against : - radiation - atomic oxygen - thermal environment - micro-meteoroids and debris impact Due to this protection necessities the shell of the Inflatable Space Module becomes a Multi Layer - Multi Functions Shell. Next Figure 6 and 7 show an hypothesis of shell structure.

FIG. 6 – Inflatable Modules shell structure possible sequence

The bladder function is basically given by air containment, the redundancy against perforations is achieved with at least 3 layers. The structural restraint is the dry composite layer dedicated to sustain the differential pressure with the external environment.


FIG. 7 – NASA TransHab Module shell structure

Another important issue in the construction of Inflatable Space Modules is the connection between the inflatable (flexible) shell and the rigid structures. These connections are for example necessary to realize the interfaces between the inflatable shell and the rigid metallic bulkheads for connection to the ISS or to realize the interfaces between the inflatable shell and rigid frames for windows. The realization of these connections must carefully consider not only the structural strength but also the air tightness of the joint. 3 IMPORTANT ASPECTS OF NUMERICAL SIMULATION OF

INFLATABLE SPACE STRUCTURES From previous paragraphs and the previous shown figures, it can be seen that some aspects of the structural solutions foreseen for the Inflatable Space Modules, become very crucial with respect to the numerical approach to the structure verification. First of all the shell which constitutes the covering wall of the Inflatable Modules, exhibits the following characteristics : - the shell structure is given by a multilayer - each layer has a very thin thickness (except for the MMOD layer ) - the layers are arrayed in such a way that some are superimposed to th others

while heeping the possibility to move with respect to each other


The previous shell characteristics requires that a numerical approach to the analysis of this kind of structures must take into account : - great geometric non-linearities due to large displacements of the layer under

an internal pressure - contact between the shell layer extended to large areas and by taking into

account the friction between them - auto-contact of the layer which can bend into itself during the folding phases An important aspect is due to the possible presence of a deployable mechanism which can act as guide for the shell unfolding phase and which can assure the correct shell inflation, i.e. the reaching of the correct final operative shape. In this case, the interaction between the mechanism deployment and the unfolding shell must be taken into account. Then one must account for : - coupling of a Multi-body Simulation approach to the mechanism study and the

non-linear approach to the shell unfolding study Another important aspect is the fact that, for different purposes ( i.e. design of the inflation device) also the study of the inflation becomes very important. For this purpose one must account for : - the possibility of describing the gas law - the study of the inflation phases by the use of the VOLUME CONTROL

TECHNIQUE algorithm Due to the fact that the inflation duration is not so short, an implicit code, perhaps, can be suitable for analyzing this phenomenon. In any case one must account also for: - the interaction among the non-linear analysis , the multi-body and the

VOLUME CONTROL TECHNIQUE approaches.



4 OVERVIEW OF SAMCEF Mecano NON LINEAR ANALYSIS CAPABILITIES

SAMCEF Mecano is a fully coupled FEA (Finite Element Analysis) and MBS (Multi-Body Simulation) code for non-linear analysis of structures and flexible mechanisms, in transient dynamic, kinematical and/or static conditions. SAMCEF Mecano is well suited for the analysis of inflatable structures because of its rich library of structural elements, such as membranes, cables, etc., and also for some specific elements and boundary conditions dedicated to inflatable structures applications, like a specialized thin shell element and volume control technique. The original formulation of SAMCEF Mecano based on an intrinsic strong coupling between mechanisms and non-linear finite elements, allows the modelling of structural components, SAMCEF Mecano/Structure library of (non-linear) finite elements, that are connected by kinematical joints, SAMCEF Mecano/Motion library of (rigid and flexible) joints, in order to obtain a hybrid inflatable-deployable structure, for example to analyse inflatable structures having an internal deployable skeleton too. The importance of having a direct integration of the structural parts by means of finite elements, instead of modal condensation (super-elements, modal superposition, etc.) can be exploited in several situations:

• geometrical or material non-linear behaviour in the structural parts • problems of contact: the mesh is required in order to apply contact boundary

conditions between the individual bodies that form the flexible mechanism • optimisation of flexible mechanism: the FEM mesh, available in the SAMCEF

Mecano model can be optimised as well as other mechanism parameters • any situation in which a change in the configuration of the structural parts

would require a re-computation of the modal base of the super-elements Nevertheless, SAMCEF Mecano, as every solver for multi-body simulation, allows the use of super-elements and other methods to condensate FEM models when the material behaviour is linear and the deformation remains small. Numerically, SAMCEF Mecano is an implicit solver based on a 2P

ndP order Newmark

predictor/corrector time integration scheme, using a Newton-Raphson procedure and with automatic time-stepping techniques related to different criteria (number of iterations, contact detection, non-linear material laws integration error,...). Several formulations are available for contact conditions, including different types of friction, both in flexible-flexible and flexible-rigid contact cases, such as lagrangian contact, penalty methods, and master-slave surfaces updating the active contact area for CPU time saving. Sparse solver and a parallel version are powerful features to approach large size problems. Moreover, SAMTECH is collaborating with ESA in order to enhance the state-of-the-art of computational tools and to make it possible to perform reliable numerical simulations of large space structures with reasonable computational time. SAMTECH is currently carrying out two important development projects in SAMCEF, funded by

ESA contracts, and one of them, named PASTISS (Professional Analysis Software Tool for Inflatable Space Structures), is about inflatable structures. The main purpose of the PASTISS project is to develop supplementary functionalities in SAMCEF, in order to introduce new algorithms and components explicitly dedicated to inflatable structures applications. Alenia will be the end- user for the industrial validation of these new functionalties introduced by PASTISS 5 DEFINITION OF ANALYTICAL TEST CASES For the purpose of analyzing the Infatable Structures and mainly for the numerical investigation of the structural themes put in evidence in the previous paragraph, some test cases have been set up, in order to evaluate the capabilities of the SAMCEF Mecano code. Firstly some test cases regarding the non-linear and the contact aspects have been analyzed. In this article the results of the investigation of these test cases are reported. 6 TEST CASES INVESTIGATION The test cases foreseen for the investigation of the SAMCEF Mecano capabilities in the field of the great geometric non linear static analysis have been set up, by taking into account of a progressive character of difficulty and finalizing the tests to the schematization of a shell similar to that shown in the previous paragraph 2.



6.1 CASE 1 : SINGLE FLAT SQUARE MEMBRANE This test case has been used in order to compare an analytical solution with the SAMCEF Mecano numerical solution. The analytical solution is based on the approximate solution for the deflection of a square membrane obtained by the means of an energy method and reported in Ref [2] pag. 419. This test case is based on a square membrane having the following characteristics : - membrane half side length a = 500 mm - membrane thickness t = 0.26 mm - membrane uniform pressure load q = 0.01 Mpa - Young Modulus E = 4200 Mpa - Poisson ratio ν = 0.36 - constraints : the four sides are fixed Based on these assumptions, the analytical results are the following : - displacement in the middle of the membrane w0 = 65.628 mm - stress in the middle of the membrane σ = 48.245 Mpa The same characteristics have been used for the numerical analysis of a square membrane by using the SAMCEF Mecano code. The geometry of this square memebrane is shown in the next Figure 8.

FIG. 8 – Square membrane geometry The mathematical model of this square plate has been created by using the Triangular Elements with the hypotesis of “MEMBrane FLEXion “.

The SAMCEF Mecano command written via the Epilogue option, is the following : .HYP GROUP "ipotesi" MEMB FLEX These Triangular Elements are triangular shell element with no rotational dof. If the structure becomes very thin, the stiffness matrix will be identical to the one of a membrane element, but it will not be ill-conditioned as for classical shell element with rotational dof. The element is a triangle defined by 3 nodes. The unknowns are the three displacements (u, v and w). It is a superposition of a membrane element and a Kirchhoff plate element. For the membrane behavior, there are two options. The first one is very classical: the displacement is linear over the area of the element and the membrane strains are constant. In the second option, the membrane strains are computed from a patch of elements and the behavior is similar to a 6 node triangular element. For the plate behavior, we consider an element with transverse displacements at nodes and rotations of the edges; the rotations of the edge are computed as a function of the displacements of a patch of elements. In the following Figure 9, the rotation around side 13 is computed as function of the displacements of nodes 1, 3, 2 and 5. In case of no neighboring, the edge is considered either clamped or free. 6 1 5

B

A 2 3

Figure 9: Triangular Element with MEMBrane FLEXion hypothesis The mathematical model of the membrane is shown in the next Figure 10.

Figure 10 : Finite Element Model of the square membrane


The pressure is applied with the SAMCEF Mecano commands listed below. .FCT CREE FONCTION I 1 CREE VALEUR Y U ANALYTIQUE " 10*$U" ! Pressure on Elements .CLM ADD ELEMENT 328 PRES V -1 NF 1 TIME ELEMENT …… Based on these commands the pressure load is applied with the time histroy shown in next Figure 11.

FIG. 11 – Square membrane pressure load time history


The Non-Linear Static analysis performed with SAMCEF Mecano, with an analysis duration from 0 to 1 and with an archive time of 0.05. The results, in terms of displacements field , are shown in the Figure 12 , while the Figure 13 shows the stress field.

FIG. 12 – Square membrane displacements

FIG. 13 – Square membrane stress


The displacement of the square membrane center point versus the time of load application is shown in the Figure 14.

FIG. 14 – Square memebrane center point displacement

The maximum values of the displacement and the stress , given by SAMCEF Mecano, at the center of the square membrane is : - Max-Disp = 58.66 mm - Max-Stress = 52.011 MPa These values are a bit different to those given with the assumption of Ref [ 2 ]. This discrepancy is due to the fact that the analytical solution is approximate as it is said in the Ref [ 2 ]. Anyway the values given by SAMCEF Mecano are in a satisfactory agreement with the analytical values and they are coincident with those computed with many other codes. SAMCEF Mecano then shows a good capability in treating such kind of problems which involves structures which exhibit very large geometric non linearity. The Triangular Element with the MEMBrane FLEXion hypothesis, shows to be very suitable in treating membrane very large deflection, even without accounting for structure prestressing. In fact a comparison has been made with the standard SAMCEF Mecano membrane Element. This element has been used for the creation of the square membrane FEM.


All other parameters are left the same. The only difference in the analysis has been the application of a temperature field which gives an initial structure prestressing, which is remoced in the course of the analysis. Without this prestress field, the analysis cannot be accomplished. Next Figure 15 shows the application of this temperature field to the square membrane, in superimposition to the pressure load shown in Figure 11.

FIG. 15 – Temperature field applied for prestressing purpose The results obtained in this case are shown in Figures 16, 17 e 18.

FIG. 16 – Displacements in classic membrane FEM


FIG. 17 – Stress in classic memebrane FEM

FIG. 18 – Classic membrane center point displacement

The agreement between the MEMB-FLEX Triangular element and the classic membrane element is very good.



6.2 CASE 2 : THREE FLAT RECTANGULAR MEMBRANES A second test case has been set up in order to verify the numerical aproach of SAMCEF Mecano to the treatment of the contact among three rectangular flat memebrane structures. The contact is a flexible/flexible contact which is simulated with the SAMCEF Mecano commands listed below. .MCT GROUP "membrane_sup" GTAR "Membrane_middle_ele" nlim -4 opt 2 .MCT GROUP "Membrane_node_middle" GTAR "Membrane_ele_inf" nlim -4 opt 2 It is a nodes and facets contact. The contact in this case, is extended to a large area of the membrane structures. The characteristics of this second test case are the following : - membranes long side length a = 1000 mm - membranes short side length b = 500 mm - membrane thickness t = 0.26 mm - membrane uniform pressure load q = 0.014 Mpa - Young Modulus E = 4200 Mpa - Poisson ratio ν = 0.36 - constraints : fixation of the membranes short sides - analysis duratio from 0 to 1 s. The geometry of these memebranes is shown in the next Figure 19. The distance between the upper and the middle membrane is 30 mm, while the distance between the middle and the bottom membrane is 20 mm.

FIG. 19 – Three rectangular memebranes geometry

The mathematical model of these three membranes has been created by using the Triangular Elements with the hypotesis of “MEMBrane FLEXion “. The mathematical model of the membranes is shown in the next Figure 20.

Figure 20 : Finite Element Model of three rectangular membranes

The pressure load is applied, downward, to only the upper membrane, which will displace and will go in contact with the middle memebrane as soon as the displacement reaches the value of 30 mm. After this, the middle membrane will be displaced by the upper one, while the contact area increases. As soon as the displacement of the upper membrane reaches the value of 50 mm, and that of the middle one the value of 20 mm, the middle membrane goes in contact with the bottom one. Then also the bottom membrane will be displaced while the contact area between the middle and the bottom membrane increases. The pressure load time history applied to the upper membrane, is the same as that of Figure 11. The Figures 21, 22 and 23 show the displacement phases of the upper, middle and bottom membranes. The Figure 24 shows the stress field arising progressively in the three membranes. The Figure 25 shows the contact pressure arising during the membranes displacements.


Finally the Figure 26 shows the comparison among the displacements of the three membrane center points.

Figure 21 : Three membranes mode : upper membrane displacement

Figure 22 : Three membranes mode : upper and middle membranes displacement


Figure 23 : Three membranes model : Overall displacement

Figure 24 : Three membranes model : Overall stress field


Figure 25 : Three membranes model : contact pressures

Figure 26 : Displacement of membranes center points



The previous results show that the physical behaviour related to this test case is well followed by the SAMCEF MECANO code. In fact the contact fenomena as well as the simultaneous non linear membrane very large deflection, are very well numerically described by the code, which then exhibits its suitability for treating these kind of problems. 6.3 CASE 3 : PACKAGE OF FIVE FLAT RECTANGULAR MEMBRANES An extension of the previous test case has been made in order to achieve a membranes configuration similar to that foreseen for the Inflatable Structures and shown in the previous paragraph 2. The purpose of this test case is then to extend the numerical simulation of a very large non linear behaviour of membranes, as well as the Flexible/Flexible contact among membranes structures, from three well spaced memebranes to five almost geometrically coicident membranes. All the five membranes can go in contact with eachother and the load will be transmitted, as in the previous case, from the upper pressurized membrane to the other lying below it. The characteristics of this third test case are the following : - membranes long side length a = 1000 mm - membranes short side length b = 500 mm - membrane thickness t = 0.26 mm - membrane uniform pressure load q = 0.01 Mpa - Young Modulus E = 4200 Mpa - Poisson ratio ν = 0.36 - constraints : fixation of the membranes short sides - analysis duration from 0 to 1 s. The geometry of the five membranes is shown in the next Figure 27. The distance among the all five membranes is 0.5 mm, so they appear to be superimposed in the Figure 27. The mathematical model of these membranes has been created by using theTriangular Elements with the hypotesis of “MEMBrane FLEXion “. The mathematical model of the five membranes is shown in the next Figure 28.

FIG. 27 – Five rectangular membranes geometry

Figure 28 : Finite Element Model of five rectangular membranes


The pressure load is applied, downward, to only the upper membrane, which will displace and will go in contact with the second memebrane as soon as the displacement reaches the value of 0.5 mm. After this, the second membrane will be displaced by the upper one, while the contact area increases. As soon as the displacement of the upper membrane reaches the value of 1 mm, and that of the middle one the value of 0.5 mm, the second membrane goes in contact with the third one. Then also the third membrane will be displaced while the contact area between the upper and the second membrane as well as between the second and the third membrane, increases. This process will continue until the fourth membrane will go in coontact with the fifth and all the membrane will displace. The pressure load time history applied to the upper membrane, is the same of that of Figure 11. The Figures 29 shows the displacement field of the overall model, while the Figure 30 shows stress field of the overall model. Finally the Figures 31 and 32 show the displacements of the five membrane center points and the displacements of the upper and lowest membranes center points.

FIG. 29 – Displacements in five membranes FEM


FIG. 30 – Overall stress field in five memebranes FEM

Figure 31 : Displacement of five membranes center points


Figure 31 : Displacement of upper and lower membranes center points Also in this test case of almost geometrically coincident five membranes the SAMCEF Mecano code exhibits its suitability for treating these kind of problems.



6.4 CASE 4 : PACKAGE OF CURVED MEMBRANES SIMULATING A REALISTIC CASE This test case, related to the numerical analysis of curved membranes, is performed in order to simulate a realistic case of Inflatabele Structure Module. All the topics analyzed in the previous test cases are maintained in this analysis, i.e. the very large membrane deflection and the wide contact areas. The novelties of this test case consist in the shape of the membranes which is related to a possible configuration of an Inflatable Module. The model exploits the simmetry of the simulated Inflatable Module, then only 1/8 of the model has been shematized. All the membranes can go in contact with eachother and the load will be transmitted, in the present case, from the lowest pressurized membrane to the other lying above it. Then the inner membrane is upward pressurized, so simulating tha real physical case. The schematization of the shell has been made on the basis of the shell characteristics shown in the previous Figure 6. A semplification has been made in this study, by adopting the following layers: - a first layer which simulates the MLI ( Multi Layer Isulation or thermal

blanket ) - a second layer simulating the MMOD without the filling material foam ( i.e.

only the Nextel layers of the MMDO have been schematized and not the foam which does not have a strength function )

- a third layer which incorporates all the other layers. This layer results in a layup pf two external kevlar leyers and three internal layers of polymide 6.

The MLI is considered as a composite shell with the following two layers :

• Beta Cloth

Thickness layer: 0.5 mm Mass density: 1500 Kg/mP

3P

Young moduls: 6550 MPa Poisson ratio: 0.34

• Kapton

Number of layers: 1 Thickness layer: 1.5 mm Mass density: 1420 Kg/mP

3P

Young moduls: 2800 MPa Poisson ratio: 0.34


The MMDO is considered as a composite shell with the following four layers :

• Nextel

Numbers of layers: 4 Thickness layer: 1.375 mm

Mass density: 2700 Kg/mP

3P

Poisson ratio: 0.36 Young moduls: 150 Gpa The last composite shell consists of five layers set up as follows :

• Kevlar

Number of layer: 1 Thickness layer: 3 mm Mass density: 1400 Kg/mP

3

Poisson ratio: 0.36 Young moduls: 4300 MPa

• Polyamide 6

Number layer: 3 Thickness layer: 0.15 mm Mass density: 1080 Kg/mP

3

Poisson ratio: 0.3 Young moduls: 1720 MPa • Nomex

Number of layer: 1 Thickness layer: 2 mm Mass density: 1450 Kg/mP

3

Poisson ratio: 0.36 Young moduls: 4400 MPa All the layers are considered isotropic. The geometrical characterisitcs of the model are the following : - inner module radius R Bi B = 1600 mm - outer module radius R BeB = 1609.225 mm - module overall length L = 7640 mm - opening radius r = 500 mm - MLI thickness t BMLI B = 2 mm - MMOD thickness t BMMOD B= 5.5 mm - INNER layer thickness t BIL = B5.45 mm

- total shell thickness ttotal = 12.95 mm In the model, each layer is placed in the middle of each shell composite. The analysis duration is 1 s. The constraints applied as well as the geometry of the analyzied model, are shown in the next Figure 33.

Figure 33 : Geometry and constraint of the Inflatable Module test case


The mathematical model of these membranes has been created by using theTriangular Elements with the hypotesis of “MEMBrane FLEXion “. The mathematical model of the model under study is shown on the next Figure 34.

Figure 34 : Finite Element Model of the Inflatable Module test case

The time history of the pressure applied to the inner shell of the Inflatable Module used in this test case is shon in the next Figure 35.

Figure 35 : Applied pressure time history


The results of the analysis in terms of overall model displacements and shell contact pressure are shown in the next Figures 36 and 37 while the Figure 38 shows the comparative displacements of three correspondent points of the three shells.

Figure 36: Test case Inflatable Module overall displacements

Figure 37: Test case Inflatable Module shell contact pressure


Figure 38: Three correspondent points displacements comparison

The analysis of this example of Inflatable Module, which has just an hypothesis of a configuration usefull for this study test case, has put in evidence the suitability of the SAMCEF Mecano code also for the numerical simulation of this kind of structures. Some special topics have been found in this test case analysis. One of these is that the mesh of the curved ( in this example, spherical ) shells must be create with carefulness, in order to avoid problems for the contacts detection.



6.5 CASE 5 : FLAT MEMBRANE SUBSIDING INTO TUBULAR STRUCTURES The last test case presented in this article, is related to study of the interaction between a flat membrane structure and a tubular membrane structure. This kind of physiscal problem can occur whereas the design of an Inflatable Structure foresees the simultaneous presence of tubular sturtcures as well as flat or curved membrane shells. This design solution will appear in the example of a numerical simulation of an Inflatable Structure, shown in the next paragraph. In this case, problems can arise from the definition of the contact zones between the tubular and the flat or curved membrane shells. In fact for the numerical point of view the contact areas must be as little as possible, because of computational time and contact detction difficulties. But in this case the contact areas depends on the pressure load acting on the flat or curved membrane shell, then it is difficult to define the contact zone in advance. Furthermore in this case the pressurizazion of the structures happen in different times, ( for example in the example of the next paragraph, the tubular stucture must be inflate before the dynamic pressure acts on the curved shell ). The test case is based on the following geometric characteristics. Tubular Stucture : - tube radius = 200 mm - tube Length = 1000 mm - tube wall thickness = 0.26mm Membrane Shell Structure : - radius of shell curved parts = 201 mm - angle extension of the shell curved part = 270 deg - shell width = 1000mm - shell length = 2000mm The shell has been schematized as composite layered shell, in the same way used for the schematization of the TPS ( Thermal Protection System ) of the IRDT Inflatable Structure of the next paragraph. The material characteristics for the composite shell are the following : ply_1 - Material: Elastic – Isotropic - Young Modulus: E= 4300Mpa - Poisson ratio: ν= 0.36 - Mass density: ρ= 1400kg/m3 - Thickness: 0.26mm ply_2


- Material: Elastic – Isotropic - Young Modulus: E= 1.72 Mpa - Poisson ratio: ν= 0.3 - Mass density: ρ= 1470 kg/mP

3P

- Thickness: 6mm ply_3 - Material: Elastic – Isotropic - Young Modulus: E= 5050 Mpa - Poisson ratio: ν= 0.4 - Mass density: ρ= 750 kg/mP

3P

- Thickness: 0.26mm ply_4 - Material: Elastic – Isotropic - Young Modulus: E= 0.1 Mpa - Poisson ratio: ν= 0.4 - Mass density: ρ= 110 kg/mP

3P

- Thickness: 5mm The tubular structure has the foolowing material characteristics : - Material: Elastic – Isotropic - Young Modulus: E= 4300 Mpa - Poisson ratio: ν= 0.36 - Mass density: ρ= 1400 kg/mP

3P

Next Figure 39 shows a schematic representation of this composite layers.

FIG. 39 – Geometry of the shell The analysis duration is of 2 s. The Boundary conditions applied to the structures are the following : - the boundary of the model is restraint along transversal movement - restraints along the tangential direction on the points placed on the tube ends The shell is glued to the tubes on its short edges at the end of the circular arc. The next Figure 40 shows the geometry of the shell, while the Figure 41 shows the geometry of the tubes.


FIG. 40 – Geometry of the shell

FIG. 41 – Geometry of the tubes


The pressure loads are applied following the subsequent steps : - from 0 to 1 s the tubes are pressurized until 125 Kpa according to the pressure

time history of next Figure 42 - from 1 to 2 s the shell is pressurized until 10 Kpa according to the pressure time history of next Figure 43

FIG. 42 – Tubes pressure time history

FIG. 43– Shell pressure time history


The mathematical model related to this test case is shown in the nex Figure 44.

FIG. 44 – Shell and tubes FEM model

According to these pressure application time histories the results have been obtained in terms of displacements, stress and contact pressure. Some of these results are shown in the next Figures. These results are shown as contact pressure arising in the tubes , in next figure 45. The Figure 46, shows the displacement of a point situated in the center of the shell placed between two tubes, and the displacement of a point situated in the middle of the left tube.


FIG. 45 – Contact pressure on the tubes

FIG. 46 – Comparison between a shell and a tube point displacements As a conclusion of this test case one can say that also in this kind of problems, SAMCEF Mecano shows its suitability for the numerical simulation of this pfysical behaviour.


7 FUTURE INVESTIGATION The test cases presented in this article have been used in order to investigate the suitability of the SAMCEF Mecano of well describing the large displacements of membrane structures. This corresponds to the first of the three important aspects which seem to be important in the verification of the Inflatable Structures. Further investigation are foreseen for what concern the study of the interaction between the non-linear and contact phenomena and the Multi-body simulation of deployable mechanism. Finally, investigations are also foreseen for the interaction of the Volume Control Technique with the previous two themes. 8 USE OF SAMCEF Mecano FOR IRDT TECHNOLOGICAL STUDY The SAMCEF Mecano code has also been used for the verification of the design of a re-entry capsule, in the frame of an ESA Technological Study named IRT ( Inflatable Re-entry and Descent Technology ). The re-entry capsules are foreseen for applications such as International Space Station sample return and the return to Earth of launcher upper stages. These entry capsules can also be foreseen for the delivery of networks of small stations to the Martian surface. Next Figures 47 shows a pictorial view of the IRDT mission scenario.

FIG. 47 – IRDT capsule mission scenario


The SAMCEF Mecano code has been used in order to perform a non-linear static analysis for the assessing of the suitability of the inflatable re-entry capsule to withstand the loads arising from the re-entry and descent environment as well as the structure pressurization. The CAD model of the structure foreseen for the capsule is shown in the next Figures 48.

FIG. 48 – IRDT capsule CAD model – exploded view By exploiting the structural symmetry properties (geometric, material, loads and constraints are symmetric) only a portion of 1/8 of the whole CAD model has been imported into CAE environment and used for the Finite Element schematization. The figures 49 shows 1/8 CAD model of the capsule, used for the FEM creation, while the figures 50 and 51 show the FEM models of the tubular part and of the TPS ( Thermal Protection System ) respectively.

FIG. 49 – IRDT capsule 1/8 of the CAD model – exploded view


FIG. 50 – IRDT capsule pneumatic structure FEM model

FIG. 51 – IRDT capsule TPS structure FEM model


For the tubular, i.e. pneumatic part, hypothesized by prevailing membrane stiffness, the linear quadrangular and triangular membrane elements, of the SAMCEF Mecano elements library, have been used. The thickness of the membranes which constitute the tubular structure is 0.26 mm. The Thermal Protection System, hypothesized by prevailing membrane stiffness too, has been modelled by special linear triangular shell elements, which do not have stiffness associated to the rotational dof. However, roughly, a bending stiffness computed on the basis of the displacements of the neighbour nodes, is associated to these elements. Then, the elements act as membrane stiffness element, but it exhibits a great robustness than the standard membrane elements. So the use of this special triangular membrane element allows to solve the big problems of convergence arising from the use of the standard, membrane elements. The material of the tubes, which are the pneumatic structure of the capsule, is foreseen to kevlar. It is considered as a single, thin membrane isotropic layer. For this material, the Young Modulus, as well as the Ultimate Strength, is considered varying with respect to the temperature change. Figure 52 and Figure 53 show these behaviour, respectively. The Young Modulus at 00

C is equal to 4300 Mpa, while the Ultimate Strength at 00 C is 150 MPa.

FIG. 52 – Young Modulus relative variation w.r.t. Temperature change


FIG. 53 – UltimateStrength relative variation w.r.t. Temperature change The TPS is considered to be composite shell, composed by four different isotropic layers. The following Figure 54 shows a pictorial view of such a kind of schematization. The total TPS thickness is of 11.52 mm.

FIG. 54 – TPS composite shell structure


The constraints to the structures have been applied as shown in the next Figures 55 and 56. FIG. 55 – External constraints FIG. 56 – Symmetry constraints The Flexible/Flexible contacts have been defined among the surfaces shown in the next Figures 57 and 58. FIG. 57 – Tube contact surface FIG. 58 – TPS contact surface


The loads applied to the structure are the following : - internal differential pressure applied to the tube of the pneumatic structure of

120 Kpa - dynamic pressure applied to the TPS of 7 Kpa - temperatute distribution, varying a long the thickness, applied to the TPS shell - constant temperature applied to the tubes of the pneumatic structure The presures as well as the temperature application sequence are those shown in the next Figures 59, 60 and 61, 62 ,63. FIG. 59 – Tubes pressure application FIG. 60 – TPS pressure application

FIG. 61 – Tubes temperature application


FIG. 62 – Mean T applied to the TPS FIG. 63 – Delta T applied to the TPS The results in term of displacements and stress fileds are shown in the next Figures 64 and 65.

FIG. 64 – Overall structure displacements filed

FIG. 65 – Pneumartic structure stress filed


From the displacement point of view a requirement of the design is that the relative displacement between the TPL and the tubes mus be of about 11 mm. By considering two points, one on the middle of the TPS shell and one on the TPS, the relative displacements is shown in the next Figures 66 and 67. From the analysis

FIG. 66– TPS pint displacement FIG. 67 – tube point displacement From the previos Figures one can see that the relative displacement is in a good agreement with the requirement. From the stress point of view one can see that the overall stress field is of about 60 Mpa, with the exception of some very localized parts, placed in the connections of the tube, and easily removable by design activities. The overall stress field is lower than the structure strength. The Mecano code has proven, in this analysis, its capabilty in managing problems with large displacements and large flexible/flexible contact areas. No friction has been taken into account in this analysis. The description of all other analysis aspects ( mechanical properties varying with the temperature, schematization of a composite shell, temperature linearly varyiing along the shell thickeness, etc.. ) results very easily and user friendly.


9 CONCLUSIONS From the activities presented in this article one can see that the SAMCEF Mecano code shows a good suitability in describing the behaviour of thin membranes structures subjected to pressure loads. The code shows an excellent capability in executing the non-linear static analysis of these thin membranes, even if no prestressing are foreseen for the structures. The special triangular element shows a good numerical stability expecially at the beginning of the analysis, where some other codes fail without accounting for a prestress of the transversally pressurized membranes. The contact phenomena which interest a very large amount of the membranes area in addition to the non-linear approach to the analysis, are very weel treated by the code which exhibits a good convergence even in this numerical field which is not so easy to treat. ACKNOWLEDGEMENTS The authors acknowledge the Samtech Italia support group for its competent and always patient help, given during the performances of all analysis activities. REFERENCES 1) SAMCEF Mecano 2) THEORY OF PLATES AND SHELLS – Second edition

Stephen P. Timoshenko – S. Woinowsky - Krieger


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