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1.1 Description of TWF 1 INTRODUCTION SUMMARY OF THE WORK

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SUMMARY OF THE WORK

1

INTRODUCTION

The work introduced in this report is focused on the finite element modeling of Triaxial Woven Fabrics (TWF). Different finite element models to predict the mechanical and thermo-elastic behaviour of TWF are developed and compared. Techniques to reduce the detailed unit cell models are discussed. TWF are considered in the design of antenna reflector structures in order to achieve the several requirements for areal weight. They are used in solid and sandwich construction. TWF is a particular weaving developed on one plane; its preform is made up of three sets of yarns, which intersect and interlace with each other at 60 deg angles. Thanks to the presence of the three yarns along these directions, TWFs have an almost quasi-isotropic behavior in the plane of the fabric. Thanks to this they are attractive to designers of spacecraft antennas and the next generation of low cost deployable structures.

1.1

Description of TWF

TWFs are obtained building a starting dry preform. Because of the particular geometry it is not easy to manufacture the weaving. The yarns are woven into the basic weave pattern, which results in hexagonal open hole unit cell. The final product is manufactured by the resin film infusion (RFI) process in which triaxial dry fabric is laid up interleaved with layers of semi-solid resin film supplied on a release paper; the following picture shows the process.

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The lay-up is then heated to allow the resin first to melt and then to flow into the fabric. The lay-up is then put in a refrigerator for an allotted amount of time, after which the released paper is removed; then, the entire structure is cured in an autoclave. The geometry of the single unit cell is triangular and depending on the manufacturing used it can have some differences. Figure 2 shows a fragment of TWF specimen in which it is possible to see the single repeated unit cell (RUC).

Figure 2: microscopic photo of a fragment of TWF fabric[ 3]

The geometry is then modeled defining the main geometrical parameters: Figure 3 shows a plan of the RUC.

Figure 3: geometrical parameters of the RUC.[1]

Moreover, the single yarn has a lenticular section; Figure 4 shows a micrograph of the single yarn. It is possible to see that the yarn has a lenticular section which changes through the interlacing with the other yarns and it is clear that it will be not easy to model a geometry like this; in particular a rectangular section will be considered according to the same equivalent area.

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Figure 4 : microsopic photoes of a sectioned RUC [2]

Because of the strong influence of the geometrical parameters and the particular geometry of the single repeated cell, the behavior of the TWF under either thermal and mechanical loads is complex and therefore difficult to analyze and to reproduce. In fact TWF can exhibit significant out-of-plane deformation under both mechanical and thermal loads. As a consequence, complex analytical or FEM models are needed to simulate correctly all these effects; in particular detailed FEM models need to adequately represent the behavior of the RUC. But because of this, there is a limit in the field in which detailed FEM models can be used; in fact a too detailed FEM model cannot be applied to a full reflector structure so some simplified models have to be derived.

1.2

TWF in Space applications.

TWF offers an alternative to sandwich composite structures for the manufacture of antenna reflectors. The launch phase is critical for the structural integrity of the antenna reflectors. During this phase, large accelerations and acoustic loads generated by the vibrations in the launcher attack the reflector. This acoustic pressure impacts against the reflector structure and could cause permanent deformation or in the worst case destruction.

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Figure 5: Launch system [ 5]

Structural instability influences the correct behavior of the antenna, which could work differently from what was designed. In fact this structure is used for downloading and uploading signals. Every deformation disturbs the correct way of transmission and it means that there will be a bad exchange of information between satellite and receiving ground station. For these reasons, sandwich materials are chosen over alluminium alloy because they offer bigger stiffness and a reduction of weight still comparing to the alloys. Problems are the big thickness and the large surface exposed to the acoustic pressure loads. TWFs are widely used for building Antenna reflectors.

Characteristics of TWF are:

• High lightness (1kg./m2) Low density

• High in-plane stiffness

• Almost isotropic in-plane behavior • Low manufacturing cost

• Good response to acoustic loads

Another advantage of TWF is to have holes through the thickness. This is really useful because the difference of pressure between the two main surfaces of the skin of the plate is null; therefore no pressure loads act on the plate so it reduces the risk of distortion.

P1 P2 P1 P2

A B

A B

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The case A displayed in Figure 6 represents a reflector with holes inside while case B is without holes. If we go to calculate the pressure variation for the case A it will be equal to 0, and for the B it will be higher. This difference of pressure causes the larger acoustic loads on a sandwich reflector compared to TWF reflectors. Another aspect to consider is the environment in which the antenna operates; this influences the life and the good working of the structure. In the space, the structures are subjected to very high temperature gradients that stress the material. The temperature varies from –100 C0 to 180 C0 and passes

through the entire range in few minutes. The resulting thermal deformations have to remain within a determined tolerance. The engineer has to guarantee and keep in consideration the functional requirements. During the natural life cycle, every component of the space system must behaves following two simple rules:

1. The structure must not fail under static and dynamic load 2. Interface forces are acceptable to the system

As written above, TWF offers advantages compared to common antenna sandwich structures. However also some disadvantages are present for designing with this material: the complex geometry of interlacing of the yarns is difficult to take in consideration and to model with structural programs; the mechanical behavior of the material is really difficult to understand and to reproduce due to the particular geometry of the fibers; the mechanical response of the fabric varies significantly depending on the kind of specimen used.

1.3

TWF modelling

One of the most important research activities currently under development is to model TWF in order to have a good prediction of its thermo-elastic and mechanical behavior. Due to its complex geometry and due to its complex behavior under deformation, it is necessary a very detailed model. Many streets were followed for this; in particular, three preliminary mathematical models were published in the literature. The first concerns an application of the classical lamination theory with the schematization of the TWF with a laminate composed of three layers disposed at 00 –600 +600 degrees. The second

concerns the variational potential method from which upper and lower limits can be obtained for the elastic properties; however this model does not show the deformation out of the plane that

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characterizes this material. The third model is based on the building of two Superelement models that are composed of 2D and 3D elements; despite the approach on the model is really valid due to the good representation of the real behavior, it is not possible to implement this procedure on a commercial code calculation. For the details of each of these numerical models it is suggested to read the previous work of Giuseppe Palermo “Finite Element Modeling of Triaxial Woven Fabric for Aerospace Structures [1]”. In the present work improvements will be introduced on the finite element model available from the previous work which will be considered as the starting point of this study. The starting finite element model is a very detailed one; it considers all the geometrical parameters necessary to describe the single TWF yarn. The single yarn is interpreted as made by straight parts, no curves are used to model the free parts of it and the cross section is modeled as rectangular. Moreover, three different groups of properties were defined according to the three yarn directions 0, + 60 and – 60 deg angles; at the same time, each group has properties referred to Coordinate Systems of fixed orientations. Since very detailed FEM models cannot be practically used for the analysis of large surfaces such as an antenna reflector, techniques of model reduction were considered and evaluated both in the present and the previous work. In particular, the previous work tried to model the TWF defining an equivalent plate; the advantage of this technique is an easier and lighter model to implement for large surfaces. For more detail it is recommended to refer to the previous work. Since the results obtained were not satisfactory, another approach was considered in the present work; MSC/NASTRAN Superelement technique. It has to be interpreted as a sub-structural organization of a starting model; this technique allows the definition of Superelements which have to be considered as independent entities linked to what is named residual structure (the final structure that will be solved). The gain is that it is possible to define a Superelment as copy of another one. In this way the TWF specimen can be seen as made up of a main Superelement, made up of a single RUC, and many copies of it. It will be shown that mechanical tests applied on TWF specimens defined in this way give very good results but with some precaution.

1.4

Target of the study

The modeling of the TWF fabric is the main subject of the present work. The starting point will be to improve and to optimize the finite element model available from the previous work carried out by

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1) Improvement of the available finite element model:

• More accurate representation of the geometry of a representative unit cell of the TWF.

• More accurate property assignment to the yarns.

• Compare improved models to available literature data.

2) Develop an approach to reduce the model size using the Superelement technique available in MSC/NASTRAN.

• Explore how MSC/NASTRAN Superelement technique can be applied to TWF models

• Verify Superelement models by comparing responses to full detailed model responses.

• Show the gain of Superelement technique.

3) Develop tools using the MSC/PATRAN command language to automatically generate geometry of RUC of TWF and FEM of the RUC and models representing flat test specimens.

In order to achieve the objectives listed above, specific software will be used; in particular, MSC/PATRAN will be used to create all the different finite element models and all the PCL functions necessary to automatically create the TWF specimen and the single unit cell. MSC/NASTRAN will be used for the resolution of mechanical tests and later for the application of the superelement philosophy to the TWF itself; moreover Matlab will also be used to define the text files that will be used in the

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MSC/NASTRAN routine to automatically define and organize the superelement organization in a TWF specimen of general given size.

1.5

OVERVIEW OF THE THESIS

The present work is organized in five Sections. Section 1 will start with the description of the finite element model created by Giuseppe Palermo, which will be considered as reference.

It will be described in detail the way used to build the starting FEM, pictures of it will be shown and simulation of mechanical tests will be performed on it. Since this starting model is characterized by a geometry based on straight segments both in the cross region and the free parts of the yarn and since the material property definition is not able to follow the shape of the single yarn, being linked to Coordinate Systems of fixed orientations, improvements to the FEM will be introduced in Section 2. In Section 2 all the improvements revealed analyzing the starting FEM model will be introduced and new FEMs will be defined; the geometry will be described as close to reality as possible, considering either straight parts in the cross region of the yarn and either sine curve functions in the free parts of it. A local Coordinate System will be defined and the material properties will be referred to it, so they will be able to follow the yarn shape (see appendix A). Simulations of mechanical tests will be performed on the models introduced, comparison and comments will be added to. Unexpected results will suggest additional tests that will be introduced in Section 3, referring to University of Cambridge data base which worked on TWF developing its own TWF-FEM; a detailed analysis will be performed working on single yarn with different shapes and comments will be added; according to these a new FEM, based on a new geometrical assumption, will be introduced, mechanical simulation test will be performed on it and the comparison with Cambridge FEM will show very good results.

Section 4 will introduce the MSC/NASTRAN Superelement technique about the reduction of the size of a FEM. This approach will be applied to a TWF flat test specimen. Mechanical simulation tests will be performed on both Superelement TWF model and full detailed TWF models. Results and comments will be added; in particular the results will show that this technique gives very good values if it is applied when mechanical loads are defined; otherwise, if thermal load are defined the results show an error of more or less 15% from the real values in the out of plane displacement. Because of this, additional analysis will be introduced trying to discover the reason of this error, performing the same tests on easier geometry FEMs; the results will show that if easy geometry are used, Superelement technique is

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absolutely perfect and the quality of the results is the same of the full detailed FEM; otherwise, when a too complicated geometry like RUC of TWF is introduced, there are some unavoidable errors in the results. So the conclusion will be that MSC/NASTRAN Superelment technique is a good approach, but some precautions have to be considered. In Section 5 a summary of the work carried out in the present study will be added; moreover suggestions for future works will be added. In particular the attention should be focused to the TWF modeling of the geometrical assumptions introduced in this report using Solid elements; CATIA is recommended for this, because of the too complicated new geometry yarn set. In Appendix A the attention will be focused on the difference that we have if material properties are linked to a Coordinate System defined with a fixed orientation and Local Coordinate Systems; moreover, the MSC/NASTRAN definition of the elements used to mesh the yarn geometry will be introduced. In particular Hex, Shell and Beam elements will be shown focusing the attention on how the element coordinate system is defined.

Figura

Figure 2: microscopic photo of a fragment of TWF fabric[ 3]
Figure 4 : microsopic photoes of a sectioned RUC [2]

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