Presentazione Master's Degree - Space and Astronautical Engineering

1. On the numerical and experimental study of composite
grid structure under compressive load conditions.
Thesis advisor:
Prof. Susanna Laurenzi
Co - advisor:
Ing. Francesco Di Caprio
Candidate:
Antonio Di Felice
ID number:
1823389
Facoltà di Ingegneria Civile e Industriale
Corso di Laurea Magistrale in Ingegneria Spaziale ed Astronautica
Academic year 2019/2020

2. 23/03/21
Objective Page 2/27
Objective
Development of numerical procedure to analyze composite grid structures under
compressive load conditions.
Contents:
• Development of the numerical model at the coupon level (Test Case A)
• Development of methods to determine mechanical properties
• Numerical - experimental analysis and comparison of a more complex test
case (Test Case B)
Test Case A Test Case B
Hoop
Rib

3. Introduction: grid structures
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Grid structure Page 3/27
Advantages:
• Delamination resistance
• High damage tolerance
• Resistance to crack propagation
• Ease of assembly/Reduced
component
Example of grid configurations
View of a grid structure
Disadvantages:
• Little amount of data in the
literature (due to confidentiality)
• Complex and expensive
development process

4. Space applications
Introduction: space applications
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The figures above show Proton – M and Vega – C respectively
Above there some applications
Below the 2/3 interstage of Vega – C is
shown

5. Production process
Production process
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The main phases:
• Preparation and assembly of the
rubber carpet on the mandrel and
general set – up
• Parallel winding of the grid
structure, including black rings
• Winding of the outer skin
(Interstage 2/3)
• Resin infusion at low temperature
under vacuum bag and cure
(autoclave or out – of –
autoclave)
Scheme of the production process
From left to right we can see the model of
the central tube for a satellite and a boom
for a deployable antenna

6. Clepsydra modeling
Clepsydra modeling
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2D model of
Clepsydra
3D model of
Clepsydra
Mesh C3D8
Modeling phases:
• 2D sketch
• Extrusion
• Partitioning
• Section assignment
• Materials
• Mesh
Extraction of single clepsydra
Scheme of numerical
extraction

7. 23/03/21
Mechanical characteristic determination Page 7/27
Mechanical characteristic determination
Number of
tows
Fiber
properties
Matrix
properties
Geometry
(rib, hoop,
node)
Volume fraction
determination
Basic mechanical
properties
Homogenised
mechanical
properties
Number
of layers

8. Investigated parameters
Investigated parameters
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Many cases have been investigated by varying the following parameters:
Geometric data:
• w = 11.2, h = 22 (real
test case)
• w = 8, h = 22
• w = 11.2, h = 17
Integration method:
• Full
• Enhanced reduced
• Incompatible modes
Element type:
• Solid
• Continuum shell
Boundary conditions:
• BC – A
• BC – B
w
w w
h h h
Some examples

9. Boundary conditions
Clepsydra: boundary conditions
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The BC-B condition is composed by:
1) kinematic coupling constraint
2) applied displacement (on RP)
3) lower base fixed
4) symmetry condition in the xy plane
5) symmetry condition in the yz plane
1a)
5b)
4a)
3a)
2a)
The BC-A condition is composed by:
1) kinematic coupling constraint
2) applied displacement (on RP)
3) lower base fixed
4) upper base fixed
1b) 2b) 3b) 4b)
𝑢𝑦 = 𝑑𝑖𝑠𝑝
𝑢𝑥 = 0
𝑢𝑦 = 0
𝑢𝑧 = 0
𝑢𝑥 = 0
𝑢𝑧 = 0
𝐾𝑖𝑛𝑒𝑚𝑎𝑡𝑖𝑐
𝐶𝑜𝑢𝑝𝑙𝑖𝑛𝑔
𝑢𝑦 = 𝑑𝑖𝑠𝑝 𝑢𝑦 = 0 𝑢𝑧 = 0 𝑢𝑥 = 0
𝐾𝑖𝑛𝑒𝑚𝑎𝑡𝑖𝑐
𝐶𝑜𝑢𝑝𝑙𝑖𝑛𝑔

10. Experimental test
Clepsydra: experimental test
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In the experimental
tests, the results are
provided by:
• 2 biaxial strain
gauges
• 2 uniaxial strain
gauges
The numerical results were
compared with the experimental
ones, for example a reference node
corresponding to SG2 is shown

11. Clepsydra: best case
Clepsydra: best case
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Best case parameters:
• Solid element
• Enhanced reduced integration method
• BC – B conditions
• Dimension of the real test case
𝐷𝑖𝑠𝑝 = 0,63
It is possible to notice a
symmetrical deformation

12. Clepsydra: best case
Clepsydra: best case
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Best case parameters:
• Solid homogeneous element
• Enhanced reduced integration method
• BC – B conditions
• Dimension of the real test case
𝐷𝑖𝑠𝑝 = 0,63
The stress graph has been
scaled by a factor of 50 to
make the deformations more
noticeable

13. Clepsydra: best case
Clepsydra: best case
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The numerical results are very close
to the experimental ones, therefore
developed model is able to reproduce
the experimental structural response
with great accuracy.
The load – displacement curve seems
to indicate a small stiffness
overestimation. The difference can be
addressed to experimental data.

14. Grid modeling
Panel modeling: grid
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The figures show the full
numerical model and the steps to
obtain the model to be analyzed:
• Cutting of the excess parts
• Resin potting
Mesh details: very regular mesh
(only hexahedral elements have
been adopted).

15. Skin modeling
Panel modeling: skin
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The skin is a shell element and has been portioned
to match the grid. Cuts help to define the potting
regions and the interfacing zones.
Mesh details: quad-dominated method was used for
the mesh, it mainly uses quadrilaterals but allows the
use of triangular elements in the transition regions.

16. Boundary conditions
Panel: boundary conditions
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The applied boundary conditions are:
a) tie constraint
b) kinematic coupling constraint
c) applied displacement (on RP)
d) low region fixed
e) reference point fixed
b) c)
a)
d) e)
𝑢𝑧 = 𝑑𝑖𝑠𝑝 𝐴𝑙𝑙 𝐷𝑜𝑓𝑠 = 0
𝐾𝑖𝑛𝑒𝑚𝑎𝑡𝑖𝑐 𝐶𝑜𝑢𝑝𝑙𝑖𝑛𝑔 𝑢𝑥 = 0
𝑢𝑦 = 0
𝑇𝑖𝑒 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡

17. 23/03/21
Modal analysis Page 17/27
Modal Analysis
The free - free modal analysis allows us to verify that they are not disconnected
parts.
The frequency of the first six modes is very close to zero, as expected.

18. 23/03/21
Modal analysis Page 18/27
Modal Analysis
From the seventh mode onwards the frequency increases.
All parts are perfectly bonded to each other (the model doesn’t have any merged
node).

19. Experimental test
Panel: experimental test
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32 uniaxial strain gauges were used
for the experimental tests
Some examples of the nodes in the
numerical model for comparison with
the experimental data are shown

20. Panel: best case
Panel: best case
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• The best case chosen is the one that uses an enhanced reduced integration
method
• The panel appears to be more deformed at the free ends as expected, due to the
absence of the supporting ribs
𝐷𝑖𝑠𝑝 = 1,97
𝐷𝑖𝑠𝑝 = 0,98

21. 𝐷𝑖𝑠𝑝 = 0,98
Panel: best case
Panel: best case
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The skin is a shell, so it doesn’t read the deformation in the 33 direction

22. Panel: best case
Panel: best case
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The stress graph has been scaled by a factor of 30 to make the deformations more
noticeable
𝐷𝑖𝑠𝑝 = 0,98

23. Panel: best case
Panel: best case
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The average error is very low, so the
curves are very close.
The experimental data are provided by
strain gauges on the inner part of the
skin:
• SG – A, takes the measurement
along the direction of the load
• SG – B, in the transversal direction
Even in the case below, the slope of
the curves is very similar, by
considering the strain gauge SG – C
placed on the rib.
The best results are shown considering
the enhanced reduced integration.

24. Skinless panel analysis
Skinless panel analysis
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The influence of the skin on global structure response has been performed.
The skin has a purely functional role and it helps to stabilize the ribs under
compressive loads.
𝐷𝑖𝑠𝑝 = 0,98

25. Skinless panel analysis
Skinless panel analysis
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The skin shows a small influence on the
global stiffness, as it can be seen in the
numerical comparison between the full
panel and the skinless panel.
𝐷𝑖𝑠𝑝 = 0,98
The stress graph has been scaled by a
factor of 50 to make the deformations
more noticeable.

26. Conclusions
Conclusions
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The Clepysdra allowed us to:
• Calibrate the model to be applied on
the much more complex geometry of
the panel
• Development of a numerical
procedure to find mechanical
properties regardless of size (useful
for small geometric discrepancy)
For the interstage panel is been possible:
• Development of robust numerical
model
• Evaluate the influence of the skin on
the mechanical properties of the panel
The numerical model may have future developments by considering:
• Damage analysis
• Delamination growth study
• Debonding between grid and skin

27. GRAZIE PER
L’ATTENZIONE!
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