w. phippen deisgn optmization of cfrp satellite solar panel structures - mech461
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1 Copyright © 2016
MECH461 April 10, 2016, Kingston, Ontario, CA
DESIGN OPTIMIZATION OF CFRP SATELLITE SOLAR PANEL STRUCTURES
William Phippen, 10019055 Queen’s University Department of Mechanical Engineering
Kingston, Ontario, Canada
ABSTRACT
A Carbon Fiber Reinforced Polymer (CFRP) satellite solar
panel structure design was modeled and optimized in Altair’s
HyperWorks. The model was to maximize stiffness while
minimizing cost and maintaining critical stress and deflection
constraints based on the Tsai-Wu Failure Criterion. The
analysis was conducted in four iterative optimization steps for
CFRP: Free Size, Continuous, Discrete, and Shuffle. Two
linear static loading cases were considered, launch at 20G while
the structure is folded and thermal boundaries from -270⁰C to
150⁰C once the structure is fully deployed at geosynchronous
orbit. The model was created in NX10.0 and imported to
Altair’s HyperWorks using PCOMPP shell elements and a
MAT8 orthotropic material property. Hexahedral meshing
criteria and reasonable mesh densities were used to reduce
model error and account for singularities. After simplifying the
model and all optimization iterations, the final design yielded a
feasible solution resulting in a total mass reduction of 71.2%
while satisfying all physical and manufacturing constraints.
Results and accuracy are discussed to reveal the model’s
confidence, and future recommendations are stated to improve
model fidelity.
INTRODUCTION
Composite materials are able to reduce the weight and
increase the customizability while maintaining and in some
cases, increasing the strength and durability of structures. For
this reason the automotive, aerospace and defense industries are
switching to composite materials. However, accurate simulation
and design optimization of anisotropic materials are not as
widely understood.
The satellite structure being considered in this
optimization is the Communication, Ocean and Meteorological
Satellite (COMS-1) [1] which has a seven year life span, launch
mass of 2.5 metric tons, and a solar array that is 10.6m2 [2].
Important design criteria include (but are not limited to)
stiffness, deflection, strength, buckling, delamination, creep,
natural frequency, manufacturing uncertainties and cost.
However, this study will only consider stiffness, deflection,
strength, delamination and manufacturing capability while
optimizing the number of plies, stacking sequence and
composite sizes.
These simulations model the solar panel structure in
two configurations: first in a nested launch position and second
in a full deployed and extended position. Currently both models
use shell elements and a ply based method with 12 CFRP layers
in the initial laminate. These models assume that the ply layers
are only at 0⁰ and 90⁰ from each other and that each layer is a
unidirectional ply. Additionally, the initial ply thickness is 2mm
based on lab created specimens. With these assumptions the
model is considered orthotropic and optimized based on
composite size, layer and sequencing to obtain maximum
stiffness.
NOMENCLATURE
MATERIAL PROPERTIES
Variable Description Unit
F12 Interaction Parameter Mpa-2
Failure Parameters (where i, j =1,.., 6)
E1 Modulus of elasticity in longitudinal
direction
MPa
E2 Modulus of elasticity in lateral direction MPa
Poisson’s ratio
Shear modulus MPa
Transverse shear modulus for shear in 1-Z
plane.
MPa
Transverse shear modulus for shear in 2-Z
plane.
MPa
Allowable stresses in the longitudinal and
lateral directions
MPa
S Allowable for in-plane shear MPa
Thermal expansion coefficient in 1 or 2
direction
Strain/K
Density Ton/mm3
DESIGN VARIABLES
Variable Description Unit
Ply angle Degrees
Number of plies
Stacking sequence
Solar radiation mW/mm²
Heat flux mW/mm²
Thrust force at launch N
Initial deflection mm
Deflection mm
Composite Stress MPa
Ultimate tensile strength MPa
Ultimate compression strength MPa
Delimitation strength MPa
Stress in a principal direction (where i, j,
k = 1, ... , 6)
MPa
Stiffness N/mm
Initial stiffness N/mm
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T Temperature ⁰C
t Ply thickness Mm
Reference temperature ⁰C
Shear stress in the 1-2 plane MPa
B Biaxial Stress Ratio
HYPERWORKS COMMANDS AND TERMS
MAT8 Orthotropic Material Property Card DOF Degrees of Freedom PCOMPP Composite Laminate Property for Ply-Based Composite
FC Failure Criteria
DCOMP Constraints Card DESVAR Design Variable
TMANUF Thickness of Manufacturable Ply
DSIZE Free Size Opt. Design Variable
DSHUFFLE Shuffle Opt. Design Variable
FSTOSZ Free Size Opt. Output
SETOSH Composite Size Opt. Output for Shuffle Opt.
PLYPCT Ply Thickness Constraint
MAXSUCC Maximum Number of Successive Plies
COMPOSITE FAILURE CRITERIA There are numerous failure theories being used for
CFRP based on maximum strain energy, maximum stress, Tsai-
Wu, Tsai-Hill, and more. Each failure theory is based on a
different set of criterion. In these simulations the Tensor
Polynomial Criterion set by Tsai and Wu [3] is used. This
failure method is not associated with the failure modes and uses
determined parameters (where i, j, k = 1, ... , 6)
which are related to the lamina strengths in the principal
direction [4]. In general for an anisotropic material the Tsai-Wu
Failure Criteria is given by [4]:
This can be simplified when working with an orthotropic
material as the terms =0. Giving the expression
[4]:
Reducing this to a plane stress the composite failure parameters
can be expressed as terms of all uni-axial based tests and a
single biaxial test. Knowing that this simplified form of Tsai-Wu Failure Criteria is shown by [5][6]:
Where 1 coincides with the longitudinal direction of the
composite, 2 coincides with the transverse direction of the
composite and 6 is the shear component in the 1-2 plane [6].
Each parameter is defined by the following set of equations.
Coefficients based on Uniaxial Tensile Test [4][5]:
Coefficient Based on Bi-Axial Test [4]:
The parameter is known as the interaction parameter and is
sometimes difficult to accurately find, as performing a biaxial
test can prove to be difficult. The following range is considered
an acceptable approximation [5]:
The interaction parameter is an important factor in the Tsai-Wu
Failure Theory as is determines the rotation, position relative to
origin and length of the semi-axis for the failure stress space [6]
[7]. This can be seen visually in Figure 1 to Figure 4 with a
normalized as given [6][8]:
Figure 1: The Rotation of the Failure Surface Axes as a Function of
F12*[6]
Figure 2: The Position of Origin (Xo,Yo) of the Failure Surface as a
Function of F12*[6]
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Figure 3: The Length of the Semi-axes of the Failure Surface as a
Function of F12*[6]
Figure 4: Failure Surfaces in Stress Space for Various Values of
F12*[6]
Wu found the resolution of is minimum for
close to zero. For >0, transverse compression and
longitudinal biaxial experiments with biaxial ratio -6 < B < -14
provide good resolution. Whereas, for <0 biaxial
compression test with biaxial ratio 6< B < 14 provides good
resolution [9]. Where B is simply the principal stress ratio as
shown:
Wu also indicated that there is an optimum stress ratio
for determining with the greatest accuracy for every
system. Wu found that the variation in depends not only on
the magnitude of the biaxial stress ratio but also on the
magnitude of itself [6][9]. Table 1 summarizes known
values and approximations for F12.
PROBLEM DEFINTION
The satellite is made from CFRP using a dry fiber lay
up at room temperature with fibres at 0° and 90° and a volume
fraction of 60%. The material properties for CFRP based on
these manufacturing techniques is shown in , and used for this
set of optimizations.The interaction parameter F12= -4.29133E-
06 Mpa-2
is used for determining the failure criteria index,
based on the Tsai-Han/Tsai-Wu approximation [8].
Table 2: Material Properties of CFRP[10]
E1 70,000 MPa
E2 70,000 MPa
0.1
5000 MPa
5000 MPa
5000 MPa
600 MPa
570 MPa
S 90 MPa
2.10E-06 Stain/K
1.60E-9 ton/mm3
These simulations model the solar panel structure in
two configurations: first in a nested launch position and second
in a full deployed and extended position. The initial super ply
thickness is 2mm based on lab created specimens. the model is
considered orthotropic and optimized based on composite size,
layer, and sequencing to obtain maximum stiffness and
minimum cost. Minimum cost is cosidered to be obtained if all
manufacturing constraints can be met.
Important design criteria include (but are not limited
to) stiffness, deflection, strength, buckling, delamination, creep,
natural frequency, manufacturing uncertainties, and cost.
However this study will only consider stiffness, deflection,
strength, delamination and manufacturing capaibility while
optimizing the number of plies, stacking sequence and
composite sizes.
With these assumptions and properties the mathematical
Table 1: Comparison of Known Values of F12 Approximations
Theory Approximation Justification F12 (ksi^-2
) F12 (Mpa^-2
) Source
Narayanswami-
Adelman F12= 0 Modified Hill 0 0 [13]
Tsai-Hahn F12=
Generalized von Mises -2.04E-04 -4.29133E-06 [8]
Wu-Stachurski F12= -1/(XX’+YY’) Geometric -4.20E-05 -8.8351E-07 [14]
Wilczynski F12= -1/(XY+X’Y’) Stability -1.07E-04 -2.25085E-06 [15]
Measured Value N/A Measured -1.62E-04 -3.40782E-06 [13]
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problem statement for this optimization can be seen below:
OBJECTIVE FUNCTION:
SUBJECT TO:
In order to optimize the two configurations subject to the
above constraints, design variables were adjusted to alter the
lamina of the structures. More specifically, the numbers of
plies, the ply thickness, ply placement and sequence stacking of
each ply were varied. A true image of COMS-1 can be seen in
Figure 5.
Figure 5: Solar Panel Array [1]
PRELIMINARY MODEL
Before analyzing the designs and conducting design
optimization, the solar panel structure was simplified for each
loading case. The structure is modeled as a single component
with hinges only at the connection point to the satellite bus, and
does not include the mass of additional components. Figure 6
and Figure 7 show this simplified model created using NX10.0.
Annex A provides more detailed drawings as well as the model
simplification progression.
Figure 6: Nested Model for Launch Simulation
Figure 7: Fully Deployed Model for Thermal Boundaries Simulation
FE MODEL DEVELOPMENT
The geometry of the solar panel structure was
imported to Altair’s HyperWorks for FE development. Using
the mid-plane of the geometry the plane was sectioned in order
to use 2D auto meshing. The panel was meshed with
hexahedral shell elements, totaling 39904 for the nested model
and 29568 for the deployed model. All elements have been
restricted to an aspect ratio of 5 and no element exceeds 2.86,
additionally all element angles fall between 45⁰ and 135⁰. PCOMPP shell elements were used for ply based
modeling of the structure. Using MAT8 for the material
properties, each ply layer was created. Six 2mm thick plies
were created based on the 2D mesh on the mid-plane. Three
plies had an orientation of 0⁰ with respect to the global
coordinate system and the remaining three had an angle of 90⁰. Using symmetric stacking a laminate was built to include 12
plies. Before applying the model loads and boundary
conditions, each ply layer of the laminate was verified for
orientation with respect to the global coordinate system.
Both models were constricted to zero DOF at the
connecting hinges to the satellites bus. The launch model was
also restricted to zero DOF on 4 corner sections of each panel.
Each node in a 100mmx40mm area was restricted to simulate
the locking mechanisms used to constrain the structure while
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launching. Figure 8 and Figure 9 show the initial models
created using this methodology.
Figure 8: Deployed Model
Figure 9: Launch Model
INITIAL FE ANALYSIS
Once the model was completed a finite element
analysis was conducted to determine the initial model’s
composite stress, strain, displacement and shear based on the
Tsai-Wu Failure Theory. The results for the launch model are
graphically shown in Figure 10 to Figure 13 and summarized in
Table 3. The initial results for the deployed model can be found
in Annes B.
Figure 10: CSTRESS [MPa]
Figure 11: CSTRAIN
Figure 12: Displacement [mm]
Figure 13: Shear Stress [MPa]
Table 3: Launch Model Initial Results Summary
Model Force
(N) Strain Stiffness
Mass
(kg)
Displacement
(mm)
Stress
(Mpa)
Shear
(Mpa)
Initial 27939 2.51E-04 7.25E+03 142.4 3.854 13.24 2.061
To ensure the results of the analysis area reasonable
representation of the physical model, the sources of error were
taken into account. Discretization error, caused by poor mesh
quality, was reduced by using a reasonable mesh density,
accounting for areas of interest such as the hinges, fold points
and arms.
The calculation error was also considered and
regarded as negligible due to high computational accuracy
provided by Altair’s Opistruct Software. However, rounding
numbers could propagate throughout the calculations to result
in minor discrepancies.
Idealization error was the most significant contributor
to model error, skewing results due to oversimplification.
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Assumptions such as the constant loading and fixed surface
boundary conditions (zero DOF) were necessary to build the
model, however they vary from the true physical
representation. Instead of a constant gravity force or constant
thermal boundary, there would be varying thrust forces in
launch and varying heat fluxes once the satellite was deployed.
Additionally once deployed the satellite would be a risk of
impact from space debris. These simulations also ignore hinge
joints and core materials that would be used, and completely
neglect the deployment of the satellite and solar array.
Lastly, singularities were considered in the initial
FEA, the most significant occurring at the hinge boundary
condition restricting all DOF. This perfect joint caused a stress
concentration along its edges specifically where the arm and
hinge meet as there is a perfect 90⁰ joint, noted in Figure 14.
Additional singularities can be seen where connection points
are modeled as a perfect 90 transition, which induces stress
concentrations. In reality, there would be a fillet in these
transitional locations. These stress concentrations were the
cause of the model’s maximum stress in both the launch and
deployed models but, when reviewing the other criteria such as
strain, shear, displacement and Tsai-Wu Failure Theory the
effect of these areas can be minimized.
Figure 14: FE model singularities
COMPOSITE OPTIMIZATION
With a well-defined initial model and an
understanding of its limitations, composite optimization
analysis was conducted from Free Size Optimization using
Altair’s Opistruct Package. This Free Size Optimization allows
the thickness of each ply to vary and the total laminate
thickness can change ‘continuously’ throughout the structure,
while at the same time, the optimal composition of the
composite laminate at every point (element) is achieved
simultaneously [11]. This optimization is set up using a DSIZE
input card, and three optimization responses: weight
compliance (conceptually the inverse of stiffness), mass, and
stress. Additionally, composite constraints are set to a minimum
ply thickness of 0.2mm and maximum of 30mm.
Setting the objective function to minimize compliance,
effectively the goal of maximizing stiffness is set. Using the
mass and stress constraints, along with the chosen failure
theory the optimization was run with an output card FSTOSIZ
to provide a model that can be used in Composite Size
Optimization. Figure 15 and Figure 16 show the output
determined by Free Size Optimization which is clear to be
nonmanufacturable. The models were manually cleaned up to
give a reasonable starting point for Composite Size
Optimization as shown in Figure 17 and Figure 18.
Figure 15: Free Size Opt. Output Deployed Model
Figure 16: Free Size Opt. Output Launch Model
Figure 17: Free Size Output Cleaned Up for Deployed Model
Figure 18: Free Size Output Cleaned Up for Launch Model
Composite Size Optimization has two successive
stages: Continuous and Discrete. Continuous size optimization
uses varying thicknesses that may not be in the manufactures
capabilities, nevertheless will produce a model that is better set
up to run discrete optimization. Since the output control
FSTOSZ was used with Free Size Optimization the input file
for Composite Size Continuous Optimization all design
variables and responses are carried over. Using the output
model from continuous optimization Composite Discrete
Optimization was run and manufacturing constraints added.
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Using TMANUF the minimal manufacturing thickness of each
ply can be set and using the output card SETOSH the
optimization provides an input model for Shuffle Optimization.
Using the Shuffle Optimization the maximum number of
successive plies of same orientation can be set and the optimal
stacking sequence is determined. The stacking sequences for
both models were two layers of 90⁰ followed by two layers of
45⁰ ply until all 30 layers of laminate were completed. The
results of each optimization for stiffness and mass can be seen
in Figure 19 and Figure 20. All results for both models are
given in Table 4 and Table 5.
After completing these initial iterations, the final
HyperWorks optimization produced a feasible design with a
mass reduction of 65-70%, maximum stress of 48MPa and
maximum displacements of 3.5mm after deployment and 3mm
during launch. All manufacturing constraints were met with a
minimum ply thickness of 0.2mm and no more than two
Figure 19: Launch Model Results
Figure 20: Deployed Model Results
Table 5: Results from Deployed Model
Model Force (N) Strain Stiffness Mass (kg)
Iterations Displacement
(mm) Stress (Mpa)
Shear (Mpa)
Initial 1.90E-03 931543 1.07E-06 142 N/A 3.496 48.18 16.26
Free Size 1.67E-03 950086 1.05E-06 51.03 2 3.539 48.18 14.2
Free Size - Cleaned Up
1.90E-03 952886 1.09E-06 51.18 N/A 3.496 48.18 16.19
Size
Continuous 1.90E-03 929535 1.08E-06 51.18 6 3.496 48.18 16.23
Size Discrete 1.90E-03 916450 1.09E-06 49.29 3 3.496 48.18 16.19
Shuffle 1.90E-03 916450 1.09E-06 49.29 3 3.496 48.18 16.26
Table 4: Results from Launch Model
Model Force (N) Strain Stiffness Mass
(kg) Iterations
Displacement
(mm)
Stress
(Mpa)
Shear
(Mpa)
Initial 27938.88 2.51E-04 7.25E+03 142.4 N/A 3.854 13.24 2.061
Free Size 8564.13 3.45E-05 1.54E+04 30.8 13 0.555 2.651 2.854
Free Size -
Cleaned Up 9788.418 5.85E-05 2.37E+04 43.65 N/A 0.4135 2.797 0.627
Size
Continuous 9788.418 8.50E-05 9.01E+03 49.89 7 1.086 8.4 0.627
Size Discrete 8022.618 1.32E-04 3.21E+03 40.89 4 2.497 16.6 0.9979
Shuffle 8022.618 1.51E-04 2.81E+03 40.89 3 2.85 10.66 1.142
8 Copyright © 2016
consecutive plies with the same orientation, thus it is assumed
manufacturing cost has been minimized. Lastly, looking at
Figure 21, it can be seen that the Tsai-Wu Failure Criterion is
met at the failure index is much less than one, 1.062E-3.
Figure 21: Tsai-Wu Failure Index Contour Plot
The solar panel structure design evolution can be seen
in Figure 22. Here, it is clear that the optimization techniques
were effective for the launch model. However, the deployed
model reduced in thickness and number of plies but, the plies
were all uniform in dimension. It is suspected that this
optimization occurred based on the thermal boundary
conditions being uniform over the structure.
Figure 22: Design Evolution CFRP Solar Panel Structure
DISCUSSION AND SUMMARY
Composite failure theories and various concepts of
design optimization were applied, tested, and adapted, from
problem formulation and simplification, to Altair’s HyperWorks
modeling and analysis.
By examining the final structure geometry and
Optistruct results, it is not believed that an alternative or
equivalent optimum design could be obtained with the current
degree of accuracy and detail, without using the computer aided
analysis and design.
The approach used to optimize the composite
structures required a significant number of interdependent
calculations which were used to model the behaviour of the
structure under the two loading conditions. Solving these sets
of equations for the optimization techniques used is not
possible with methods other than computational design
optimization due to the number and complexity of the
calculations being made. To complete this optimization without
computational aid would be extremely time consuming.
Additional simplifying assumptions would have to be made to
address the time constraint which reduces the accuracy of the
model and the validity of the design that would be found.
In order to further improve the FE model components
attached to the structure masses, core material and secondary
hinge points should be considered. The specific hinge type and
accurate modelling of the joint itself should also be included.
The FE model itself could also be improved using a mesh
convergence test to know the optimal mesh density. The last
model improvement would be to test multiple load cases
including vibration in launch, multiple thrust loads in launch
and the heat flux due to solar radiation once deployed. Even
more complex models should be completed if the true structure
is to be represented by including simulation of deployment and
impact of space debris once deployed.
ACKNOWLEDGMENTS I would like to thank Brad Taylor for assistance with the
use of Altair’s HyperWorks, and for his comments and insight
that greatly improved this research. I would also like to show
my gratitude to Dr. Il Yong Kim for sharing his wisdom and
knowledge of FEA and material properties with me during the
course of this research.
Finally I would like to pay credit to Markus Kriesch and
André Wehr for their tutorial on Composite Optimization with
Optistruct 11.0 on the example of a Formula-Student-
Monocoque.
REFERENCES
[1] National Meteorological Satellite center, "Introduction of COMS," National Meteorological
Satellite center, 2010. [Online]. Available:
http://nmsc.kma.go.kr/html/homepage/en/chollian/choll_info.do. [Accessed January 2016].
[2] H. J. Kramer, "eoPortal Directory," Sharing Earth Observation Resources, 2002. [Online].
Available: https://directory.eoportal.org/web/eoportal/satellite-missions/c-missions/coms-1.
[Accessed January 2016].
[3] S. W. a. W. Tsai, "General Theory of Strength for Anisotropic Materials," Journal of
Composite Materials, pp. 58-80, 1971.
[4] P. P. Camanho, "FAILURE CRITERIA FOR FIBRE-REINFORCED POLYMER
COMPOSITES," Departamento de Engenharia Mecânica e Gestão Industrial, Secção de
Mecânica Aplicada, 2002.
[5] P. Mallick, Fiber-Reinforced Composites: Materials, Manufacturing, and Design, Third
Edition, Florida: CRC Press, 2007.
[6] W. C. Hansen, "The Significance and Measurement of the Tsai-Wu Normal Interaction
Parameter F12," Oregon State University, 1992.
[7] B. a. C. R. Collins, "A Graphical Representation of the Failure Surface of a Composite,"
Journal of Composite Materials, vol. 5, p. 408, 1971.
[8] S. a. H. H. Tsai, Introduction to Composite Materials Lancaster, PA: Technomic Publishing
Co., Inc., 1980.
[9] Wu, "Optimal Experimental Measurements of Anisotropic Failure Tensors," Journal of
Composite Materials, vol. 6, p. 472, 1972.
[10] Performance Composites, "Mechanical Properties of Carbon Fibre Composite Materials,
Fibre / Epoxy resin (120°C Cure)," Performance Composites, [Online]. Available:
http://www.performance-composites.com/carbonfibre/mechanicalproperties_2.asp.
[Accessed 08 02 2016].
[11] Altair, "Optimization of Composite Structures," Altair User's Guide, vol. 13.0, 2016.
[12] V. G. Baghdasarian, "Hybrid solar panel array". US Patent US 5785280 A, 28 July 1995.
[13] R. T. M. Nanyaro, "Evaluation of the Tensor Polynomial Failure Criterion for Composite
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[14] R.-Y. a. S. Z. Wu, "Evaluation of the Normal Stress Interaction Parameter in the Tensor
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[15] A. Wilczynski, "Some Relationships and Limitation of Tensor Polynomial Strength
Theories," Composite Science and Technology,, vol. 44, p. 209, 1992.
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ANNEX A
MODEL SIMPLIFICATION AND DETAILS
The base model is assumed to use a Hybrid solar panel
array closing and deployment hinge, see Figure 24 and Figure
25 .
Figure 24: Hybrid Solar Panel Deployment [12]
Figure 25: Hinge Design [12]
Using this hinge style and the dimension of COMS-1 Figure 23
was created.
In order to remove the complexity of accurate hinge
modelling the hinges between panel 1 and panel 2 seen above
were removed. This allowed the structure to be modelled as a
single component but, also introduces a second model. One
model for nested launch position and one for deployed
geosynchronous orbit.
Figure 23: Dimensions [mm] with thickness of 25.4[mm]
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ANNES B
INITIAL RESULTS DEPLOYED MODEL
CONTOUR PLOTS
The composite stress, strain, deflection and shear
stress are seen in for -270⁰C thermal boundary case as this is
the most drastic temperature difference given =25⁰C
.
Figure 26: CSTRESS [MPa]
Figure 27: CSTRAIN
Figure 28: Displacement [mm]
Figure 29: Shear Stress [MPa]
Table 6: Deployed Model Initial Results -270⁰C
Model Strain Stiffness Mass
(kg)
Displacement
(mm)
Stress
(Mpa)
Shear
(Mpa)
Initial 1.90E-03 1.07E-06 142 3.496 48.18 16.26