Post on 24-Mar-2018
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CHAPTER 6
STRUCTURAL STRESS AND BUCKLING ANALYSES OF
MICRO-SATELLITE
6.1 LINEAR STATIC ANALYSIS
Linear static analysis represents the most basic type of analysis.
The term "linear" means that the computed displacement or stress is linearly
related to the applied force. The term “static” means that the forces do not
vary with time or, that the time variation is insignificant and can therefore be
safely ignored. The static analysis equation is:
[K]{u} = {f}
Where ‘K’ is the system stiffness matrix, ‘f’ is the applied force vector, and
‘u’ is the displacement vector. Once the displacements are computed, the
solver uses these to compute element forces, stresses, reaction forces, and
strains. The applied forces may be used independently or combined with each
other. The loads can also be applied in multiple loading subcases, in which
each subcase represents a particular loading or boundary condition. Multiple
loading subcases provide a means of solution efficiency, whereby the solution
time for subsequent subcases is a small fraction of the solution time for the
first.
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6.2 OBJECTIVE
The reliability of satellite structural components is greatly
increased, and their cost and weight reduced by the systematic and rigorous
application of stress analysis principles as an integral part of the design
process. The structural stress analysis performed guides the design of the
satellite and sizing of the components and provide a high degree of
confidence before launch. Structural stress analysis is performed in order to
ensure that a structure will fulfill its intended function in a given loads
environment. It is important to anticipate all the possible failure modes and
design it against them. For a space structure, the common failures to be
considered are as follows:
Ultimate failure, rupture and collapse due to the stresses
exceeding the ultimate strength of the material.
Detrimental yielding that undermines structural integrity or
performance due to stresses exceeding the yield strength of the
material.
Instability (buckling) under a combination of loads,
deformation and part geometry such that the structure faces
collapse before buckling strength of the material is reached.
“Excessive” elastic static or dynamic deformations causing
loss of function, preload or alignment, interference, and
undesirable vibration noise.
6.3 FAILURE MODES OF SANDWICH PANELS
The micro-satellite structures like bottom deck, middle deck, top
deck, cross webs, vertical webs and solar panels are constructed of
honeycomb sandwich panels where the skin is made of aluminium alloy and
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the core is made of aluminium honeycomb. The following are the common
failure modes seen in the sandwich panels.
6.3.1 Strength
The skin and core materials should be able to withstand the tensile,
compressive and shear stresses induced by the design load. The skin to core
adhesive must be capable of transferring the shear stresses between skin and
core. The Figure 6.1 shows the skin compressive failure.
Figure 6.1 Skin compressive failures
6.3.2 Stiffness
The sandwich panel should have sufficient bending and shear
stiffness to prevent excessive deflection. The Figure 6.2 shows the excessive
deflection.
Figure 6.2 Excessive deflection
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6.3.3 Panel buckling
The core thickness and shear modulus must be adequate to prevent
the panel from buckling under end compression loads. The Figure 6.3 shows
the panel buckling mode of failure.
Figure 6.3 Panel buckling
6.3.4 Shear crimping
The core thickness and shear modulus must be adequate to prevent
the core from prematurely failing in shear under end compression loads. The
Figure 6.4 shows the shear crimping in sandwich panel.
Figure 6.4 Shear crimping
6.3.5 Skin wrinkling
The compressive modulus of the facing skin and the core
compression strength must both be high enough to prevent a skin wrinkling
failure. The Figure 6.5 shows the failure due to skin wrinkling.
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Figure 6.5 Skin wrinkling
6.3.6 Intra cell buckling
For a given skin material, the core cell size must be small enough to
prevent intra cell buckling. The Figure 6.6 shows the intra cell buckling
happening in sandwich panel.
Figure 6.6 Intra cell buckling
6.3.7 Local compression
The core compressive strength must be adequate to resist local
loads on the panel surface. The Figure 6.7 shows the failure by local
compression.
Figure 6.7 Local compression
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6.4 SUMMARY OF SATELLITE LOADS
The most common loads encountered on a satellite in the space
applications are given in Table 6.1.
Table 6.1 Loads acting on the satellite
Loading (Event) Significance
Inertia loads (Launch and landing) Loads that drive the design ofprimary structure
Vibration (Flight and Orbitoperations)
Structurally transmitted, Causingfatigue/fracture
Vibro-acoustic (Launch) Acoustically transmitted,especially for low mass/area parts
Thermally induced (Flight and orbitoperations)
Dictates allowable temperaturesand gradients, compatibility ofmaterials
Pressurization and flow induced(flight and orbit operations)
For pressure vessels, pipe lines,housings
Mechanical/Thermal(Fabrication/Assembly))
Material Residual stresses,Fastener/seal preloads,misalignment
Mechanical/Thermal(Verificationtesting)
May limit useful life of material
Mechanical/Inertial(Ground handlingand Transportation)
Important for the design ofmechanical ground supportequipment (MGSE) and spacecraftinterface with MGSE, may limituseful life of material.
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Structural loads are specified at maximum expected level and
referred to as the design or limit loads. Usually, two or more of these loads act
simultaneously and their combined effect needs to be considered. It was noted
that the loads environment applied to the structure during the verification
testing may be more significant than the loads experienced during flight.
Many structural failures have occurred during the action of the combined
loads on the satellite structures. Therefore, these loads must be considered
very carefully in the strength and fatigue calculations. The impact of the
satellite with the orbital debris was not included in the possible loads a
structure may encounter. The micro satellite considered is subjected to both
static and dynamic loads and are given below.
Longitudinal acceleration (Static+ Dynamic): 7g compression/2.5g tension
Lateral acceleration (Static + Dynamic) : 6g
Load factor : 1.25
The load cases derived for the analysis are given in Table 6.2.
Table 6.2 Load cases for stress analysis
Load case number
(LC)
Lateral X Lateral Y Longitudinal Z
LC 1 7.25g 0 -8.25g
LC 2 0 7.25g -8.25g
LC 3 7.25g 0 3.75g
LC 4 0 7.25g 3.75g
LC 5 5.75g 5.75g -8.25g
LC 6 5.75g 5.75g 3.75g
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A finite element model of the micro-satellite structure with all the
subsystems was developed in MSC PATRAN and analysis was done using
MSC NASTRAN inorder to predict deformations, internal forces and stresses.
It was based on an idealization of the actual structure using simplified
assumptions on geometry, loads and boundary conditions. Structural stress
analysis should define and address all the loads acting on the primary and
secondary structures. The following results were noted from the analysis.
Deformation of the micro-satellite structure
Von Mises stress distribution
Forces acting on the Multi Point Constraint
6.5 FAILURE CHECK MODES OF MICRO-SATELLITE
STRUCTURE
Adequacy of the structure to withstand the calculated forces and
stresses is checked by calculating the margin of safety (MS) values which is
defined as
Failure is predicted for MS < 0 where SF is the safety factor.
Failure stress or force is determined by means of failure theories. Some of the
most commonly used ones are summarized below
(a) Maximum Normal Stress theory is used to predict ultimate failure with
MS = Ftu/(SF x max) - 1. Here Ftu is the ultimate tensile stress of the material
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and max is the maximum normal stress due to the external loading. In general,
this theory is more applicable to brittle materials.
(b) Maximum Shear Stress theory is used to conservatively predict ultimate
failure for ductile materials. MS = Fsu/(SF x max) - 1, where Fsu is the
ultimate shear stress of the material and max is the predicted maximum shear
stress. This theory can also be used to predict the onset of yield by replacing
Fsu by Fsy, the shear yield strength of the material.
(c) Distortion Energy theory is used for predicting the initiation of yield in a
structure for the micro-satellite considered and gives more accurate results
than the maximum shear stress theory. The margin of safety is given by
MS = Fty/(SF x VM) - 1, where Fty is the tensile yield stress, and VM is the
Von Mises stress. A similar criterion used for the prediction of failure in
laminated composite materials by the Tsai-Hill Theory. A typical SF value
used for the ultimate failure of the spacecraft structures is 1.25. In addition a
yield SF typically equal to 1.25 is selected to prevent structural damage or
detrimental yielding during structural testing or flight. The tensile yield
strength of the materials is listed in the Table 6.3. Figures 6.8 to 6.13 show the
Von mises stress distribution in the satellite structures. The Table 6.4 shows
the margin of safety values calculated by using Distortion theory for the
maximum Von mises stress values identified in the micro-satellite structures
for the derived load cases.
Table 6.3 Tensile yield strength of the materials
Material Tensile strength in MPa
Aluminium Face sheet 280
Aluminum Honey comb 0.816
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Figure 6.8 Von mises Stress distribution in bottom deck for LC2
Figure 6.9 Von mises Stress distribution in middle deck for LC2
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Figure 6.10 Von mises Stress distribution in top deck for LC6
Figure 6.11 Von mises Stress distribution in cross webs for LC2
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Figure 6.12 Von mises Stress distribution in vertical webs for LC2
Figure 6.13 Von mises Stress distribution in solar panels for LC5
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Table 6.4 Margin of safety of the satellite structures
Structure Load case Von mises stress(MPa)
Margin ofSafety
Bottom deckLayer 1 LC 2 71.6 2.13Layer 2 LC 5 0.571 0.14Layer 3 LC 2 71.5 2.13
Middle deckLayer 1 LC 2 41.3 4.42Layer 2 LC 2 0.630 0.03Layer 3 LC 2 41.2 4.42
Top deckLayer 1 LC 6 36.7 5.10Layer 2 LC 5 0.341 0.909Layer 3 LC 6 36.6 5.10
Cross webs ( Between Bottom deck and Middle deck)Layer 1 LC 2 138 0.623Layer 2 LC 6 0.0958 5.79Layer 3 LC 2 138 0.623
Vertical webs ( Between Middle deck and Top deck)Layer 1 LC 2 24.8 8.03Layer 2 LC 2 0.0903 6.00Layer 3 LC 2 24.6 8.03
Solar panelsLayer 1 LC 5 21.8 9.27Layer 2 LC 2 0.0457 13.24Layer 3 LC 5 21.8 9.27
Interface ringLayer 1 LC 2 34.4 5.51Layer 2 LC 2 35.2 5.36
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6.6 MULTI POINT CONSTRAINT FORCE ON THE JOINTS
Multi Point Constraints (MPC) establishes geometric relationships
that have to be met by the displacements of certain nodes of the structure.
This is useful for modelling very stiff elements, without numerical difficulties
that would imply to model them as truly flexible bodies of high stiffness.
MSC NASTRAN has included rigid elements namely RBAR, RBE, etc that
generate internally these relationships from the geometric data provided by
the user. These forces are often essential for the correct dimensioning of the
structure. This concept is used in the case of screwed joints, very stiff
elements, etc. The M6 inserts were used to integrate the bottom deck of the
satellite with the interface ring at 12 points. All the structural inserts except
the edge inserts and the interface ring are M4 inserts and all subsystem
integration with primary structure are M4 inserts. The M6 inserts can
withstand a load of 600 N and M4 inserts can withstand the load of 400 N.
The Table 6.5 shows the maximum MPC force taken from MSC PATRAN/
MSC NASTRAN for the 6 different load cases shown in Table 6.2.
Table 6.5 MPC forces of the joints
StructuralComponent
Insert type Load CaseMaximum
MPC Force (N)
Bottom deck M4 LC 2 345
Middle deck M4 LC 2 320
Top deck M4 LC 1 85.6
Cross webs M4 LC 2 384
Vertical webs M4 LC 2 153
Solar panels M4 LC 5 242
Interface ring M6 LC 5 292
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The stress values of the micro-satellite structures obtained from the
Von Mises stress distribution and the MPC forces obtained at the joint
locations are well within the safe limits. The static analysis results show that a
high value of margin of safety has been obtained for certain structures, but it
was proved that for small satellite, dynamic design consideration is the main
criteria on the structure capability under applied load. Since the thickness of
the aluminum face sheet is already small the reduction of the thickness of the
aluminum face sheet has only negligible effect on the weight reduction of the
satellite. So the analytical results may be used for the design.
6.7 SANDWICH INSTABILITY
The margins of safety for the Sandwich Instabilities of the micro-
satellite structures are calculated as shown below.
6.7.1 Face wrinkling of Bottom deck
For 0.25 mm face skin and 40 mm core sandwich
Density of the core dcore = 32 kg/m3
Density of the face skin dface = 2700 kg/m3
Elastic modulus of face skin Ef = 70 GPa
Elastic modulus of core Ec E fd face
d core
Elastic modulus of core Ec = 829.6 MPa
Thickness of face skin tf = 0.25 mm
Thickness of core tc = 40 mm
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Stress acting in core c = E ft cE f
t fEc2/1
33.0
= 195 MPa
Maximum stress acting in face skin a = 71.6 MPa
(From FE analysis)
Margin of Safety MS = 1ac
Margin of Safety MS = 1.72
6.7.2 Face wrinkling of Middle deck
For 0.25 mm face skin and 20 mm core sandwich
Density of the core dcore = 32 kg/m3
Density of the face skin dface = 2700 kg/m3
Elastic modulus of face skin Ef = 70 GPa
Elastic modulus of core Ec E fd face
d core
Elastic modulus of core Ec = 829.6 MPa
Thickness of face skin tf = 0.25 mm
Thickness of core tc = 20 mm
Stress acting in core c = E ft cE f
t fEc2/1
33.0
= 275.7 MPa
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Maximum stress acting in face skin a = 41.3 MPa
(From FE analysis)
Margin of Safety MS = 1ac
Margin of Safety MS = 5.67
6.7.3 Face wrinkling of Cross webs
For 0.20 mm face skin and 15 mm core sandwich
Density of the core dcore = 32 kg/m3
Density of the face skin dface = 2700 kg/m3
Elastic modulus of face skin Ef = 70 GPa
Elastic modulus of core Ec E fd face
d core
Elastic modulus of core Ec = 829.6 MPa
Thickness of face skin tf = 0.20 mm
Thickness of core tc = 15 mm
Stress acting in the core c = E ft cE f
t fEc2/1
33.0
= 284 MPa
Maximum stress acting in the face skin a= 138 MPa
(From FE analysis)
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Margin of Safety MS = 1ac
Margin of Safety MS = 1.06
6.7.4 Intracellular buckling / dimpling of Bottom and Middle deck
For core with 0.25 mm face skin
Elastic modulus of face skin Ef = 70 GPa
Thickness of face skin tf = 0.25 mm
Poisson’s ratio = 0.3
Cell size of honeycomb core S = 4.76 mm
Stress acting in the core c =2
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St fE f
= 416 MPa
Maximum stress acting in the face skin
of bottom deck and middle deck a = 71.6 MPa
(from FE analysis)
Margin of Safety MS = 1ac
Margin of Safety MS = 4.81
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6.7.5 Intracellular buckling / dimpling of Cross webs, Vertical webs,
Top deck and solar panels for core with 0.20 mm face skin
Elastic modulus of face skin Ef = 70 GPa
Thickness of face skin tf = 0.20 mm
Poisson’s ratio = 0.3
Cell size of honeycomb core S = 4.76 mm
Stress acting in the core c =2
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St fE f
= 266 MPa
Maximum stress acting in the face skin
of bottom deck and middle deck a = 138 MPa
(from FE analysis)
Margin of Safety MS = 1a
c
Margin of Safety MS = 0.91
The margin of safety values obtained for the instabilities like face
wrinkling, intra cellular buckling/dimpling of micro-satellite sandwich
structures like bottom deck, middle deck, top deck, cross webs, vertical webs
and solar panels are positive, and it is clear that there is no possible modes of
failure of sandwich panels for the loads considered.
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6.8 SUBSYSTEM LOADS ON INSERT
The margins of safety for the subsystem loads on the insert are
calculated as shown below.
6.8.1 Calculation for largest subsystem Bus Electronics loads on M4
insert
Out of plane acceleration acting on the subsystem (LongG) = 30g
In plane acceleration acting on the subsystem (LatG) = 20g
Center of Gravity of the subsystem bus Electronics C.G = 0.06524 m
Mass of the subsystem = 3. 068 kg
Pitch Diameter of inserts PCdia = 0.209 m
Lateral force acting on the subsystem LatF = Lat G*Mass
= 601.94 N
Longitudinal force acting on the subsystem LongF = LongG*Mass
= 902.91 N
Moment = Lat F*C.G
= 39.27 Nm
Number of inserts resisting Lateral load N = 4
Longitudinal non-uniformity factor (Longnuf) = 1
Load per insert in Longitudinal load (LongL) =4
LongF Longnuf
= 225.72 N
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Load per insert in Lateral load (LatL) =NPC
Momentdia *
= 46.97 N
Total pull out load on insert Lsi = LongL+ LatL
= 272.69 N
Inplane load on insert Lso =N
LatF
= 150.48 N
Maximum inplane load of M4 insert Pci = 2000 N
Maximum outplane load of M4 insert Pco = 1200 N
Margin of Safety MS =22
1
PL
PL
co
so
ci
si
- 1
Margin of Safety MS = 3.099
6.8.2 Calculation for subsystem Power Electronics loads on M4
insert
Out of plane acceleration acting on the subsystem (LongG) = 30g
In plane acceleration acting on the subsystem (LatG) = 20g
Center of Gravity of the subsystem Power Electronics C.G = 0.0548 m
Mass of the subsystem = 2.084 kg
Pitch Diameter of inserts PCdia = 0.183 m
Lateral force acting on the subsystem (LatF) = Lat G*Mass
= 408.88 N
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Longitudinal force acting on the subsystem (LongF) = LongG*Mass
= 613.32 N
Moment = Lat F*C.G
= 22.40 Nm
Number of inserts resisting Lateral load N = 4
Longitudinal non-uniformity factor (Longnuf) = 1
Load per insert in Longitudinal load (LongL) =4
LongF Longnuf
= 153.33 N
Load per insert in Lateral load LatL =NPC
Momentdia *
= 30.60 N
Total pull out load on insert Lsi = LongL+ LatL
= 183.93 N
Inplane load on insert Lso =N
LatF
= 102.22 N
Maximum inplane load of M4 insert Pci = 2000 N
Maximum outplane load of M4 insert Pco = 1200 N
Margin of Safety MS =22
1
PL
PL
co
so
ci
si
- 1
Margin of Safety MS = 7.00
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6.8.3 Calculation for subsystem Power Distribution loads on M4
insert
Out of plane acceleration acting on the subsystem (LongG) = 30g
In plane acceleration acting on the subsystem (LatG) = 20g
Center of Gravity of the subsystem Power Distribution C.G = 0.03225 m
Mass of the subsystem = 1.178 kg
Pitch Diameter of inserts PCdia = 0.205 m
Lateral force acting on the subsystem (LatF) = Lat G*Mass
= 231.12 N
Longitudinal force acting on the subsystem (LongF) = LongG*Mass
= 348.68 N
Moment = Lat F*C.G
= 7.45 Nm
Number of inserts resisting Lateral load N = 4
Longitudinal non-uniformity factor (Longnuf) = 1
Load per insert in Longitudinal load (LongL) =4
LongF Longnuf
= 86.67 N
Load per insert in Lateral load (LatL) =NPC
Momentdia *
= 9.09 N
Total pull out load on insert Lsi = LongL+ LatL
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= 95.75 N
Inplane load on insert Lso =N
LatF
= 57.78 N
Maximum inplane load of M4 insert Pci = 2000 N
Maximum outplane load of M4 insert Pco = 1200 N
Margin of Safety MS =22
1
PL
PL
co
so
ci
si
- 1
Margin of Safety MS = 13.5
The margins of safety calculations of subsystem loads of bus
Electronics, Power Electronics and Power Distribution which have mass
values greater than 1 kg on M4 inserts show positive values and it is evident
that the inserts used can withstand the loads of the subsystem packages
accommodated in the micro-satellite structure. Similar calculations are made
for all the subsystems which are comparatively small and have less mass than
the subsystems for which the calculations are shown, the margins of safety
values obtained are still higher.
6.9 BUCKLING ANALYSIS
In linear static analysis, a structure is normally considered to be in a
state of stable equilibrium. As the applied load is removed, the structure is
assumed to return to its original position. However, under certain
combinations of loadings, the structure may become unstable. When this
loading is reached, the structure continues to deflect without an increase in the
magnitude of the loading. In this case, the structure has actually buckled or
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has become unstable; hence, the term “instability” is often used
interchangeably with the term “buckling”.
The principal sources of external load tending to buckle the satellite
are the direct pressure of photons from the sun (solar pressure) and the
pressure exerted by impact with the molecules of the very thin atmosphere
through which the satellite must orbit (dynamic pressure).The loads for
buckling analysis are as same as that of the static analysis. The Table 6.6
shows the derived load cases for the buckling analysis.
Table 6.6 Load cases for buckling analysis
Load case number
(LC)Lateral X Lateral Y Longitudinal Z
LC 1 7.25g 0 -8.25g
LC 2 0 7.25g -8.25g
LC 3 7.25g 0 3.75g
LC 4 0 7.25g 3.75g
LC 5 5.75g 5.75g -8.25g
LC 6 5.75g 5.75g 3.75g
6.9.1 Buckling load factor (BLF)
The Buckling Load Factor (BLF) is an indicator of the factor of
safety against buckling or the ratio of the buckling loads to the currently
applied loads. The BLF values are directly calculated from MSC
PATRAN/MSC NASTRAN. A knock down factor of 0.6 is used for
incorporating the material non-homogeneity, material imperfections, etc.The
Table 6.7 shows the buckling status for the BLF values calculated.
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Table 6.7 Interpretation of the Buckling Load Factor (BLF)
BLF value Buckling status Remarks
0<BLF<1 Buckling predicted The applied loads exceed the estimatedcritical loads. Buckling will occur.
BLF=1 Buckling predicted The applied loads are exactly equal tothe critical loads. Buckling is expected.
-1<BLF<1 Buckling possible Buckling is predicted if the loaddirections are reversed.
BLF=-1 Buckling possible Buckling is predicted if the loaddirections are reversed.
BLF>1 Buckling notpredicted
The applied loads are less than theestimated critical loads.
BLF<-1 Buckling notpredicted
The applied loads are less than theestimated critical loads even if theloading directions are reversed.
6.9.2 Verification for Global stability of micro-satellite
The buckling analysis is carried out for all the derived load cases
and the Table 6.8 shows the minimum buckling load factors obtained for all
the load cases. The Figure 6.14 shows the buckling plot obtained for mode 11
of LC 1 and Figure 6.15 shows the buckling plot obtained for mode 9 of LC 2.
Table 6.8 Buckling Load Factor values (BLF)
Load case number Minimum Buckling Load Factor
LC 1 -1.86
LC 2 5.16
LC 3 1.90
LC 4 -5.22
LC 5 -2.36
LC 6 2.41
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The minimum buckling load factor values obtained for the micro-
satellite for all the derived load cases are BLF>1 and BLF<-1.From Table 6.8
it is seen that the structure would not undergo any buckling instability as BLF
values are either less than -1 or greater than +1.
Figure 6.14 Buckling plot obtained for mode 11 of LC 1
Figure 6.15 Buckling plot obtained for mode 9 of LC 2