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

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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

Materials," Journal of Composite Materials, vol. 12, pp. 63-75, 1978.

[14] R.-Y. a. S. Z. Wu, "Evaluation of the Normal Stress Interaction Parameter in the Tensor

Polynomial Strength Theory for Anisotropic Materials," Journal of Composite Materials,

vol. 18, p. 456, 1984.

[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