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Structures
Mike McKenzie
Structures
Ansys is being used to do the stress and weight analysis on the HAB.
Ansys is a commercial program that can do linear and non-linear stress analysis.
Other programs that were considered were Catia, ProE, IDEAS, ABAQUS, and
professor Doyle’s program, Stadyn. Ansys was chosen because a few
professors in the AAE department (Professors Doyle and Kim) are familiar with
the program, and it is loaded on all ECN machines and PUCC labs. It can also
do both the modeling and FEA of the s/c.
Our group used a HAB design similar to last semester’s HAB. The HAB is
cylindrical with a hemisphere on top. Counting the top and bottom of the
cylinder, there are 5 floors. There is a hollow pillar in the center of the HAB that
runs the length of the cylinder. The pillar was added to constrain the motion of
the floors in their center to keep the bending stresses from the supplies down.
Frames were added as rings between the floors on the sides of the cylinder to
help keep the hoop stress down. There is a approximately 60,000 kg of supplies
that need to be in the HAB. I distributed the mass evenly onto the 5 floors for
now. I will more accurately model the supplies when I get a more exact mass per
floor from Randy. An internal pressure of 1 atm (101,325 Pa) was applied to the
walls of the shell. The internal pressure was not applied to the floors or pillar of
the HAB.
Sandwich materials were used on all HAB surfaces to keep the
stresses and weight down. The sandwich material being used is 5.2cm thick.
Such a thick sandwich decreases the hoop stress, and increases the flexural
rigidity (EI). A large flexural rigidity keeps the bending stresses down, and
increases the buckling stiffness. The equation for hoop stress is:
H 
Pd
2t
(1)
where P is the internal pressure, d is the diameter, and t is the wall thickness.
The hoop stress is significant for such a large diameter of cylinder. Using a
sandwich structure and having a large t significantly reduces the hoop stress.
The HAB is bigger than last semester’s. See table 1 for a breakdown of
the HAB’s dimensions, and Figure 1 for a schematic of the HAB. Figure 2 shows
a cut-away view to give a better view of the inside of the HAB. Notice the frames
and pillar in Figure 2. The cutting plane for figure 2 is rotated an angle from the
symmetry axis to give a better depth of field. That is why the pillar isn’t shown
running the length of the cylinder, even though it physically does.
Dia [m]
Length [m]
# floors
Mass [kg]
tface plates [mm]
tcore [cm]
Last semester
8.75
13.625
5
8,500
2
3
This semester
13
16.5
5
14,200
2 shell
3 shell
1 other
5 other
Table 1: Values for HAB from last semester and this semester.
Figure 1: Front and side view of HAB modeled in Ansys.
Figure 2: Cut-away view of HAB in Ansys.
A script is used to input the Finite Element Model (FEM) into Ansys. I
included the script file, structure.log, on the zip disk. Using a script file allows
parametric studies to be done on the model. Any aspect of the model can be
changed in the script to see the effect on the results. The script is necessary
since Ansys is not really a parametric modeler like many commercial CAM
packages, and it’s GUI is not as advanced as many CAM programs either. Once
the areas were drawn in Ansys, they had to be ‘glued’ together to simulate them
being fastened together. The supply masses were input into the model as
pressures. Adding the supplies as pressures is not a problem since only the g
loading (more on this later) will be studied, and this is in the (-)z direction. In the
script file, it is possible to define 8 different sandwich thicknesses for the various
surfaces of the s/c. It is also possible to have a different mass of supplies on
each of the five floors.
The sandwich faceplates are made of a Graphite/Epoxy composite. The
core of the sandwich is a honeycomb material. More will be said of the materials
later. The sandwich material was modeled in Ansys using a sandwich shell
element called linear layer 99. This particular element can have a total of 250
different layers, but our sandwich structure only has 3. The thicknesses of the
sandwich components can be seen in table 1. The properties of the sandwich
components are easily specified by entering their material properties into a table.
The only properties necessary to completely describe the materials are:
thickness, density, Young’s modulus, and Poisson ratio.
Graphite/Epoxy was chosen for the faceplates because it is strong and
light. Titanium and Aluminum were the other materials being considered for the
faceplates. See Table 2 for a listing of properties for these 3 different materials.
 [kg/m3]
Specific Modulus
(E/) [Pa/]
Specific max
(max/)
Tmax [°K]
[Pa/]
Graphite/Epoxy
1600
40.9e6
159.4e3
450
Aluminum
2600
26.9e6
173.1e3
933
Titanium
4500
22.2e6
177.8e3
1940
Table 2: Properties of 3 materials considered for the faceplates.
Material properties for the metal are taken from reference 1, material
properties for the composite can be found in reference 2. From the table above,
it can be seen that Titanium had the highest specific strength, but the composite
material had the highest Specific Modulus. A high specific modulus adds to the
flexural rigidity of the structure (EI). The composite material had the lowest Tmax.
Using more TPS to keep the temperature of the composite low uses less mass
than using Ti with less TPS. This will be verified later with the trade studies. The
thickness of the faceplates should not be less than 1mm to avoid local buckling
of the material. Using 1mm of the Graphite/Epoxy meets the stress and buckling
requirements. Less than 1mm of Titanium would be needed to meet the stress
requirements, but since the thickness should not be less than 1mm, 1mm of Ti
would have to be used anyway. Therefore, using Ti would raise the structural
mass considerably because its density is so much greater than that of
Graphite/Epoxy. An important difference between the composite being used and
structural metals is that the composite doesn’t have a yield strength like the
metals. The composite only has an ultimate strength. This is why a safety factor
(SF) is being used when designing the structure.
The composite is from the [0/±45/90]s family of composites. The s means
the composite is symmetric. Therefore, each layer of the composite is made
from 8 bonded plies in the 0°, ±45° and 90° directions. This means 25% of the
plies are in the 0° direction, 50% of the plies in the ±45° directions, and 25% in
the 90° direction. Using this arrangement lets the composite be modeled as a
Quasi-Isotropic material. This means material direction doesn’t need to be taken
into account when specifying material properties. A carpet plot is used to find
material properties based on the % of 0°, and ±45° plies. The carpet plot used to
find the Young’s Modulus (E) for the Graphite/Epoxy is shown in Figure 3 below.
For 25% 0° plies, and 50% ±45° plies, E is found to be ~9.5 Msi, or 65.5 Gpa.
Other properties are found in the same manner using similar carpet plots, see
reference 3.
Figure 3: Carpet plot used to find E for the Graphite/Epoxy composite.
As can be seen from the figure, E is dependent on the # and % of
directions of the plies. If the plies could be placed on the structure in the
direction of the loading (which is currently possible in industry), then a higher
stiffness could be attained. Because this wasn’t taken into account when
designing the HAB, the values found in this structural report are conservative.
A honeycomb material made by the Hexcel Corporation was chosen for
the sandwich core material. The particular honeycomb material is HRH-327
vented Glass Reinforced Polyimide Honeycomb. HRH-327 was chosen because
of it’s high tmax and because it is an insulator. An insulator needs to be used
between the face sheets to keep the heat out of the s/c. A vented honeycomb
needs to be used so that the core isn’t pressurized in space. Properties of the
honeycomb are listed in table 3 below. The material properties listed were taken
from reference 4 page 6. Note that E is in units of Mpa (E for the face sheets is
~66 Gpa). Also note how light the core material is compared to the face sheets.
HRH-327
Tmax [°K]
E [Mpa]
 [kg/m3]
max [Mpa]
773.15
870
128
6.9
Table 3: Material properties of the core material.
The flexural rigidity of the sandwich material is
Etot=E1I1 + E2I2
(2)
Where material 1 is the composite and 2 is the honeycomb,
I1=8*t*d2
I2=1/12*h3
(3)
(4)
Where d is the distance between the face sheets, t is the thickness of the face
sheets, and h is the thickness of the core. The width of the sandwich is taken to
be unity in the above equations. This is not the case, but allows for comparison
of equations 3 and 4. During my trade studies, I am going to use equation 2 to
find the optimum thickness for the face sheets and the core to get the maximum
Etot while keeping the weight to a minimum. Equations 1, 2, and 3 are taken from
reference 1, p397-9.
The only loads that will be modeled are the launch loads. An eigen-value
buckling analysis will also be done on the s/c for the launch loads. Jon gave a gload at launch of ~4g’s. I input a gravity field of 4g’s in Ansys to simulate the
launch loads, along with the supply masses on the floors and the internal
pressure. The combination of these three aspects of loading gives a good
representation of the loads incurred by the s/c during launch. If a metal had been
used for the s/c, a Von Mises max stress criterion could be used. But, since
composites are used this can’t be done. To make sure the composite doesn’t
fail, each axial and shear stress must be checked to make sure it is not over the
limit of the material. Figure 4 below is one example of this. In this figure the
maximum stress in the z-dir (perpendicular to the axis of symmetry) is graphed.
Figure 4: Max stress in the z direction.
From the figure it can be seen that the max stress of 255 Mpa has not
been exceeded. For this sample case, the stress in the z direction is the largest
of the stresses. Therefore, the structure can withstand the g loading with a SF of
about 1.6. The ability of Ansys to cut away a part of the s/c makes it possible to
see the stresses in the floors as you can see in Figure 4.
The launch loads are the greatest loads the s/c will encounter during its
mission. If there was more time, I would’ve also modeled the pressure on the s/c
during aero braking and the loads during the parachute deployment. But, since
the s/c holds up so well to the launch loads, it will not fail during the other
loading.
An Eigen buckling analysis was also done on the s/c during launch. It was
found from Ansys that the Eigen value is 81. This means that the applied loads
during the launch are only
1
of the loading required to make the s/c buckle.
81
The value is so high because of the rigidity of the s/c from the thick walls of the
sandwich structure. Eigen-value buckling was chosen because it takes much
less computer time than doing a non-linear buckling analysis. When doing a
non-linear buckling analysis, the shape history of the structure is found after the
buckling has occurred to see if it is stable buckling. This is not necessary for a
preliminary analysis of the s/c.
Several analytical calculations were carried out to test the accuracy of the
Ansys program. The hand calculations were: stress in the x direction (x) for the
s/c, an eigen value buckling analysis of a simple beam, hoop stress (H) of the
s/c, and the mass of the s/c. The buckling problem was taken from section 7.6 in
the Ansys help files. The results of these hand calculations are listed in Table 4.
x (from weight of s/c only) [MPa]
Mass of s/c only [kg]
H [MPa]
By hand
In Ansys
1.7
1.7
51,000
51,000
14.90074
15.3 w/ floors
14.9 w/o floors
Eigen-value Buckling
Numbers agreed to 99.999%
Table 4: Comparison of analytical and Ansys calculations.
A convergence test needs to be done during the trade studies to be sure
the data Ansys gives is accurate. During a convergence test the mesh is refined.
As the mesh is refined, stresses and the Eigen value should approach some
number (a different number for each individual stress and buckling value). If this
is not the case than the model must be meshed differently to make it more
accurate. The buckling analysis is the most sensitive to mesh quality.
Other people in the group depend on data from me: Damon needs the
thickness and materials of the shell for his heating code, Randy needs the cg of
the structure to combine with his cg of the supplies to give to Giles, and Tami
needs the mass of the structure to enter into her trajectory code. For this sample
case I told Tami the mass was 14,500kg. But, I found an error in my script file
and the mass is actually 14,200kg.
I depend on other people in the group for certain numbers. They are:
Randy for the distribution of the supply masses in the s/c, and Jon for the launch
loads.
When a student does the structural analysis next time, more can be
analyzed. It took a great amount of time learning the ropes with Ansys, so there
was less time for analysis. Next time the following should be considered in the
analysis: a vibration analysis (this is a must next time), a more accurate model of
the s/c (having reinforced joints and adding a bulkhead are two examples),
analyzing more of the loading conditions, and analyzing other parts of the s/c
(like the landing gear). Using the manual that will be written from Shin and I’s
experience with Ansys, the next student should have a much easier time
modeling the vehicle.
References:
1. Gere, and Timoshenko, Mechanics of Materials, Fouth Edition 1997.
2. http:www.structures.ucsd.edu/casl/data_analysis/carpet_plots.htm
3. I got the carpet plots from Professor Kim. He is trying to find out what book
he got them out of, He said Prof Sun would know, but he is on sabbatical.
4. Hexcel Corporation, The basics on bonded sandwich construction
TSB124, 1987.
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