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“DAMAGE TOLERANCE
EVALUATION OF WING BOTTOM
SKIN”
MOHAMMED ABDUL MEHBOOB (3KB06AE002)
ABDUL RAHIMAN GAZZALI (3KB08AE001)
MD. ZUNAID ALAM (3KB08AE018)
SHETTY SHISHIR SITARAM (3KB08AE013)
Aircraft are members and transverse frames to enable it
to resist bending, compressive and vehicles which are
able to fly by being supported by the air, or in general,
the atmosphere of a planet. An aircraft counters the
force of gravity by using either static lift or by using the
dynamic lift of an airfoil, or in a few cases the downward
thrust from jet engines. An aircraft is a complex
structure, but a very efficient man-made flying
machine.
Major Aircraft Components
Fuselage
The main body structure is the fuselage to which all other components are
attached. The fuselage contains the cockpit or flight deck, passenger
compartment and cargo compartment.
Wings
 The wings are airfoils attached to each side of the
fuselage and are the main lifting surfaces that support
the airplane in flight. Wings vary in design depending
upon the aircraft type and its purpose.
The Empennage
 The empennage is most commonly referred to as the tail of
the aircraft. It consists of two primary structures, the
vertical stabilizer and the horizontal stabilizer.
Landing gear
The landing gear is the principle support of the airplane when parked, taxiing,
taking off, or when landing. The most common type of landing gear consists of
wheels, but airplanes can also be equipped with floats for water operations, or
skis for landing on snow.
Control Surfaces
 Following are the various Control Surfaces
 The Flaps on the wings control the drag and lift on the
structure
 The Rudder is used to change pitch (side-to-side) movement.
 The Elevator is used to change pitch (up-down) movement.
 The Aileron is uses to change lift, drag and roll.
 The Slats are used to change lift.
 Following are the various Control Surfaces:
 The Flaps on the wings control the drag and lift on the
structure
 The Rudder is used to change pitch (side-to-side) movement.
 The Elevator is used to change pitch (up-down) movement.
 The Aileron is uses to change lift, drag and roll. The Slats are
used to change life.
Aircraft materials
 Metallic Materials
 Alloys
 Aluminum alloy
 Titanium alloy
 Steel Alloys
 Non Metallic Materials
 Transparent Plastic
 Reinforced Plastic
 Fiber-reinforced composites
Loads
Tension
Compression
Shear.
Torsion
Bending
Damage Tolerance
Damage tolerance is a property of a structure
relating to its ability to sustain defects safely until
repair can be affected. The approach to
engineering design to account for damage
tolerance is based on the assumption that flaws
can exist in any structure and such flaws
propagate with usage.
 Slow Crack Growth Design
 Fail-Safe Design
In service Failures
Recovered parts of
BOAC Flight 781
The fuselage roof fragment
of BOAC Flight
Loads Acting on the panel.
 The all-up weight of the aircraft (30-seater) is 15000 kg

 Weight of the aircraft = 15000 kg.

 Design load factor considered= 3g.

 Total load acting on the aircraft = 15,000×3
 = 45,000 kg

 Factor of safety considered = 1.5

 The design Ultimate load = 45,000×1.5
 = 67,500 kg

 Lift load experienced by both fuselage and wing.

 Lift load on the wing = 80% of total load
 = 0.8×67,500
 = 54,000 kg

 Load acting on each wing = 0.5×54,000
 = 27,000 kg
(Dimensions in the above figure need to be changed
 Total span of the wing = 12000mm

 Bending moment at the section A-A = 27,000×300
 = 81×105 kg-mm

 Depth of the wing at section A-A = 450 mm

 The axial load in the bottom skin= 81×105/450
 = 18,000 kg
Dimensions in the above figure need to be changed
 Axial load acting on the edge of the panel = 18,000×1000/1500
 = 12000 kgs

 This 12000 kg load is converted into uniformly distributed load
(UDL) and applied at the one side of wing bottom skin cutout
panel.

 UDL = 12000/width of bottom skin
 = 12000/1000

 UDL= 12 kg/mm

Material specification
 The testing done on the materials are the linear elastic
ones. In material specification the kin d has to be specified.
The material may be hollow or a non hollow cross sectional
kind. In the thickness along with the aspect ratio has to be
specified.
 Young’s Modulus = Modulus of elasticity = Stress /
Strain

 For ALUMINIUM,
 Young’s Modulus = 7000 kg/ mm².
 The unit can be expressed as ‘ kg/ mm² ’.

 Poisson’s Ratio = Lateral Strain/ Longitudinal Strain.

 Poisson’s Ratio is dimensionless.


 Poisson’s Ratio = 0.3 .
FINITE ELEMENT ANALYSIS
Steps involved in FEA
 1. Discretization of the geometry into nodes and
elements.
2. Stiffness matrix is calculated for each element.
 3. Assembly of stiffness matrix
 4. For the equation F=K Q applying the boundary
conditions.
 5. Solving the set of simultaneous equations using
different mathematical techniques.
 6. Displacements are calculated first
 7. Using displacements strains and stresses are
calculated
Finite Element Analysis software programs
Calculate element stresses and reaction forces from the displacement results.
Solve the matrix equation {F} = [K].{u} for displacements.
Apply loads to the model (Forces, moments, pressure, etc.)
Apply boundary conditions to constrain model.
Assemble all element stiffness matrices into a global stiffness matrix.
Formulate element stiffness matrices from element properties, geometry, and material properties .
Represent a continuous structure as a collection of grid points connected by discrete elements.
NASTRAN Solution Flow Chart
Validation through MVCCI Method
Validation of FEA
Theoretical method
Validation of FEA
Tetra elements
2a A Kt v1 v2 ∆v f1 f2 f G Kfea Ki/Ko Kt new %Error
100 50 23.49368 0.14321 0.13274 0.01047 1.65E+01 1.60E+01 3.24E+01 0.084937 24.3836 1.03389 24.28988 3.64951
90 45 22.28806 1.42E-01 1.32E-01
0.009857
8 1.55E+01 1.50E+01 3.06E+01 0.075321 22.9618 1.02688 22.88715 2.9341
80 40 21.01339 1.41E-01 1.31E-01
0.009225
9 1.45E+01 1.41E+01 2.86E+01 0.066043 21.5011 1.02081 21.45067 2.268533
70 35 19.65623 1.39E-01 1.31E-01
0.008571
9 1.35E+01 1.31E+01 2.66E+01 0.057089 19.9906 1.01562 19.96328 1.672438
60 30 18.19813 1.38E-01 1.30E-01
0.007886
4 1.25E+01 1.21E+01 2.46E+01 0.04841 18.4084 1.01126 18.40303 1.142192
50 25 16.61254 1.37E-01 1.30E-01
0.007155
7 1.13E+01 1.10E+01 2.23E+01 0.039957 16.7241 1.00768 16.74005 0.667109
40 20 14.85871 1.37E-01 1.30E-01
0.006360
3 1.01E+01 9.81E+00 1.99E+01 0.031688 14.8935 1.00482 14.93039 0.233714
30 15 12.86802 1.36E-01 1.30E-01
0.005467
1 8.76E+00 8.48E+00 1.72E+01 0.023563 12.8429 1.00267 12.90233
-
0.195251
20 10 10.50669 1.35E-01 1.31E-01
0.004411
4 7.16E+00 6.94E+00 1.41E+01 0.015541 10.4302 1.00117 10.51894
-
0.733278
10 5 7.429355 1.34E-01 1.31E-01
0.003020
3 5.10E+00 4.94E+00 1.00E+01 0.007582 7.28516 1.00029 7.431483
-
1.979298
-3
-2
-1
0
1
2
3
4
1 2 3 4 5 6 7 8 9 10
Series1
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1 2 3 4 5 6 7 8 9 10
Series1
Error(THEORITICAL)
variation
Error(FEA) variation
LOADS AND BOUNDARY CONDITIONS.
The load applied= 5000 kgs.
The span= 1000 mm.
Load/unit length = 5000/1000= 5 kg/mm
In this case while applying boundary conditions.
Stress (linear) = F/A.
= ( kg *9.81)/(mm^2).
STRESS ANALYSIS
The main steps employed in this are as follows in detail:
 Geometry
 Element Size
 Material Specifications
 Material Properties
 Analysis
Displacement and Stress results
Stress Concentration Factor
ELEMENT SIZE 16-2
ELEMENT SIZE 16-2
ELEMENT SIZE 16-2
ELEMENT SIZE 32-4
ELEMENT SIZE 64-8
ELEMENT SIZE 128-16
MODIFIED VIRTUAL CRACK CLOSURE INTEGRAL
 In this paper, attention is focussed on a new predictor-
corrector method that results in an incremental
curved approximation of the crack path on the basis of
quantities which the straight forward MODIFIED
VIRTUAL CRACK CLOSURE INTEGRAL Method can
provide. In order to show significance of the proposed
simulation technique computational results are
compared with the findings from experimental
investigation with the aid of specially designed
specimens under proportional loading conditions, in
particular under combined proportional bending and
shear loading.
Tetra elements
CRACK INITIATION AND PROPAGATION ATTACHMENTS
CRACK INITIATION AND PROPAGATION ATTACHMENTS
CRACK INITIATION AND PROPAGATION ATTACHMENTS
2a A Kt v1 v2 ∆v f1 f2 F G Kfea
154.5 77.25 29.20218 1.49E+00 1.46E+00 0.03 7.54E+01 8.32E+01 1.59E+02 2.379 129.0465
149 74.5 28.67769 1.49E+00 1.46E+00 0.03 7.79E+01 9.14E+01 1.69E+02 2.5395 133.3285
144.5 72.25 28.24132 1.49E+00 1.45E+00 0.035286 5.10E+01 5.76E+01 1.09E+02 1.915231 115.7869
130.5 65.25 26.83838 1.48E+00 1.44E+00 0.03803 5.77E+01 6.47E+01 1.22E+02 2.329171 127.6879
116 58 25.30347 1.47E+00 1.44E+00 0.034036 5.65E+01 6.44E+01 1.21E+02 2.058363 120.0356
101.5 50.75 23.66923 1.47E+00 1.43E+00 0.032157 5.60E+01 6.12E+01 1.17E+02 1.885251 114.8771
87 43.5 21.91345 1.46E+00 1.43E+00 0.029881 5.32E+01 5.71E+01 1.10E+02 1.64857 107.4244
72.5 36.25 20.00415 1.46E+00 1.43E+00 0.028496 5.04E+01 5.42E+01 1.05E+02 1.490643 102.1494
58 29 17.89226 1.46E+00 1.43E+00 0.026844 4.75E+01 5.03E+01 9.79E+01 1.313488 95.88752
43.5 21.75 15.49515 1.46E+00 1.44E+00 0.02498 4.36E+01 4.70E+01 9.05E+01 1.130912 88.97407
29 14.5 12.65174 1.47E+00 1.44E+00 0.028843 4.12E+01 4.29E+01 8.42E+01 1.213714 92.17373
0 0 0 1.47E+00 1.45E+00 0.022211 5.52E+01 5.59E+01 1.11E+02 0.822004 75.85529
0
50
100
150
200
250
300
1 2 3 4 5 6 7 8 9 10 11 12
Chart Title
Kfea
2a
K(FEA) variation with Crack Length
CONCLUDING REMARKS
 Damage tolerance design philosophy is generally used in the
aircraft structural design to reduce the weight of the structure.

 Stiffened panel is a generic structural element of the fuselage
structure. Therefore it is considered for the current study.

 A FEM approach is followed for the stress analysis of the
stiffened panel.

 The internal pressure is one of the main loads that the fuselage
needs to hold.

 Stress analysis is carried out to identify the maximum tensile
stress location in the stiffened panel.
REFERENCES
 T. Swift “Damage tolerance capability”, international journal of
fatigue, Volume 16, Issue 1, January 1994, Pages 75-94.

 F. Erdogan and M. Ratwani, International journal of fracture
mechanics, Vol. 6,
 No.4, December 1970.

 H. Vlieger, 1973, “The residual strength characteristics of
stiffened panels containing fatigue crakes”, engineering
fracture mechanics, Vol. 5pp447-477, Pergamon press.

 H. Vlieger, 1979, “Application of fracture mechanics of built up
structures”, NLR MP79044U.

Thank you

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Damage Tolerance Evaluation of Wing Bottom Skin Panel by Analytical Approach

  • 1. “DAMAGE TOLERANCE EVALUATION OF WING BOTTOM SKIN” MOHAMMED ABDUL MEHBOOB (3KB06AE002) ABDUL RAHIMAN GAZZALI (3KB08AE001) MD. ZUNAID ALAM (3KB08AE018) SHETTY SHISHIR SITARAM (3KB08AE013)
  • 2. Aircraft are members and transverse frames to enable it to resist bending, compressive and vehicles which are able to fly by being supported by the air, or in general, the atmosphere of a planet. An aircraft counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines. An aircraft is a complex structure, but a very efficient man-made flying machine.
  • 4. Fuselage The main body structure is the fuselage to which all other components are attached. The fuselage contains the cockpit or flight deck, passenger compartment and cargo compartment.
  • 5. Wings  The wings are airfoils attached to each side of the fuselage and are the main lifting surfaces that support the airplane in flight. Wings vary in design depending upon the aircraft type and its purpose.
  • 6. The Empennage  The empennage is most commonly referred to as the tail of the aircraft. It consists of two primary structures, the vertical stabilizer and the horizontal stabilizer.
  • 7. Landing gear The landing gear is the principle support of the airplane when parked, taxiing, taking off, or when landing. The most common type of landing gear consists of wheels, but airplanes can also be equipped with floats for water operations, or skis for landing on snow.
  • 8. Control Surfaces  Following are the various Control Surfaces  The Flaps on the wings control the drag and lift on the structure  The Rudder is used to change pitch (side-to-side) movement.  The Elevator is used to change pitch (up-down) movement.  The Aileron is uses to change lift, drag and roll.  The Slats are used to change lift.  Following are the various Control Surfaces:  The Flaps on the wings control the drag and lift on the structure  The Rudder is used to change pitch (side-to-side) movement.  The Elevator is used to change pitch (up-down) movement.  The Aileron is uses to change lift, drag and roll. The Slats are used to change life.
  • 9. Aircraft materials  Metallic Materials  Alloys  Aluminum alloy  Titanium alloy  Steel Alloys  Non Metallic Materials  Transparent Plastic  Reinforced Plastic  Fiber-reinforced composites
  • 15. Damage Tolerance Damage tolerance is a property of a structure relating to its ability to sustain defects safely until repair can be affected. The approach to engineering design to account for damage tolerance is based on the assumption that flaws can exist in any structure and such flaws propagate with usage.  Slow Crack Growth Design  Fail-Safe Design
  • 17. Recovered parts of BOAC Flight 781 The fuselage roof fragment of BOAC Flight
  • 18. Loads Acting on the panel.  The all-up weight of the aircraft (30-seater) is 15000 kg   Weight of the aircraft = 15000 kg.   Design load factor considered= 3g.   Total load acting on the aircraft = 15,000×3  = 45,000 kg   Factor of safety considered = 1.5   The design Ultimate load = 45,000×1.5  = 67,500 kg   Lift load experienced by both fuselage and wing.   Lift load on the wing = 80% of total load  = 0.8×67,500  = 54,000 kg   Load acting on each wing = 0.5×54,000  = 27,000 kg
  • 19. (Dimensions in the above figure need to be changed
  • 20.  Total span of the wing = 12000mm   Bending moment at the section A-A = 27,000×300  = 81×105 kg-mm   Depth of the wing at section A-A = 450 mm   The axial load in the bottom skin= 81×105/450  = 18,000 kg
  • 21. Dimensions in the above figure need to be changed
  • 22.  Axial load acting on the edge of the panel = 18,000×1000/1500  = 12000 kgs   This 12000 kg load is converted into uniformly distributed load (UDL) and applied at the one side of wing bottom skin cutout panel.   UDL = 12000/width of bottom skin  = 12000/1000   UDL= 12 kg/mm 
  • 23. Material specification  The testing done on the materials are the linear elastic ones. In material specification the kin d has to be specified. The material may be hollow or a non hollow cross sectional kind. In the thickness along with the aspect ratio has to be specified.
  • 24.  Young’s Modulus = Modulus of elasticity = Stress / Strain   For ALUMINIUM,  Young’s Modulus = 7000 kg/ mm².  The unit can be expressed as ‘ kg/ mm² ’.   Poisson’s Ratio = Lateral Strain/ Longitudinal Strain.   Poisson’s Ratio is dimensionless.    Poisson’s Ratio = 0.3 .
  • 26. Steps involved in FEA  1. Discretization of the geometry into nodes and elements. 2. Stiffness matrix is calculated for each element.  3. Assembly of stiffness matrix  4. For the equation F=K Q applying the boundary conditions.  5. Solving the set of simultaneous equations using different mathematical techniques.  6. Displacements are calculated first  7. Using displacements strains and stresses are calculated
  • 27. Finite Element Analysis software programs Calculate element stresses and reaction forces from the displacement results. Solve the matrix equation {F} = [K].{u} for displacements. Apply loads to the model (Forces, moments, pressure, etc.) Apply boundary conditions to constrain model. Assemble all element stiffness matrices into a global stiffness matrix. Formulate element stiffness matrices from element properties, geometry, and material properties . Represent a continuous structure as a collection of grid points connected by discrete elements. NASTRAN Solution Flow Chart
  • 28. Validation through MVCCI Method Validation of FEA
  • 31. 2a A Kt v1 v2 ∆v f1 f2 f G Kfea Ki/Ko Kt new %Error 100 50 23.49368 0.14321 0.13274 0.01047 1.65E+01 1.60E+01 3.24E+01 0.084937 24.3836 1.03389 24.28988 3.64951 90 45 22.28806 1.42E-01 1.32E-01 0.009857 8 1.55E+01 1.50E+01 3.06E+01 0.075321 22.9618 1.02688 22.88715 2.9341 80 40 21.01339 1.41E-01 1.31E-01 0.009225 9 1.45E+01 1.41E+01 2.86E+01 0.066043 21.5011 1.02081 21.45067 2.268533 70 35 19.65623 1.39E-01 1.31E-01 0.008571 9 1.35E+01 1.31E+01 2.66E+01 0.057089 19.9906 1.01562 19.96328 1.672438 60 30 18.19813 1.38E-01 1.30E-01 0.007886 4 1.25E+01 1.21E+01 2.46E+01 0.04841 18.4084 1.01126 18.40303 1.142192 50 25 16.61254 1.37E-01 1.30E-01 0.007155 7 1.13E+01 1.10E+01 2.23E+01 0.039957 16.7241 1.00768 16.74005 0.667109 40 20 14.85871 1.37E-01 1.30E-01 0.006360 3 1.01E+01 9.81E+00 1.99E+01 0.031688 14.8935 1.00482 14.93039 0.233714 30 15 12.86802 1.36E-01 1.30E-01 0.005467 1 8.76E+00 8.48E+00 1.72E+01 0.023563 12.8429 1.00267 12.90233 - 0.195251 20 10 10.50669 1.35E-01 1.31E-01 0.004411 4 7.16E+00 6.94E+00 1.41E+01 0.015541 10.4302 1.00117 10.51894 - 0.733278 10 5 7.429355 1.34E-01 1.31E-01 0.003020 3 5.10E+00 4.94E+00 1.00E+01 0.007582 7.28516 1.00029 7.431483 - 1.979298
  • 32. -3 -2 -1 0 1 2 3 4 1 2 3 4 5 6 7 8 9 10 Series1 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1 2 3 4 5 6 7 8 9 10 Series1 Error(THEORITICAL) variation Error(FEA) variation
  • 33. LOADS AND BOUNDARY CONDITIONS. The load applied= 5000 kgs. The span= 1000 mm. Load/unit length = 5000/1000= 5 kg/mm In this case while applying boundary conditions. Stress (linear) = F/A. = ( kg *9.81)/(mm^2).
  • 34. STRESS ANALYSIS The main steps employed in this are as follows in detail:  Geometry  Element Size  Material Specifications  Material Properties  Analysis
  • 35. Displacement and Stress results Stress Concentration Factor
  • 42. MODIFIED VIRTUAL CRACK CLOSURE INTEGRAL  In this paper, attention is focussed on a new predictor- corrector method that results in an incremental curved approximation of the crack path on the basis of quantities which the straight forward MODIFIED VIRTUAL CRACK CLOSURE INTEGRAL Method can provide. In order to show significance of the proposed simulation technique computational results are compared with the findings from experimental investigation with the aid of specially designed specimens under proportional loading conditions, in particular under combined proportional bending and shear loading.
  • 44. CRACK INITIATION AND PROPAGATION ATTACHMENTS
  • 45. CRACK INITIATION AND PROPAGATION ATTACHMENTS
  • 46. CRACK INITIATION AND PROPAGATION ATTACHMENTS
  • 47. 2a A Kt v1 v2 ∆v f1 f2 F G Kfea 154.5 77.25 29.20218 1.49E+00 1.46E+00 0.03 7.54E+01 8.32E+01 1.59E+02 2.379 129.0465 149 74.5 28.67769 1.49E+00 1.46E+00 0.03 7.79E+01 9.14E+01 1.69E+02 2.5395 133.3285 144.5 72.25 28.24132 1.49E+00 1.45E+00 0.035286 5.10E+01 5.76E+01 1.09E+02 1.915231 115.7869 130.5 65.25 26.83838 1.48E+00 1.44E+00 0.03803 5.77E+01 6.47E+01 1.22E+02 2.329171 127.6879 116 58 25.30347 1.47E+00 1.44E+00 0.034036 5.65E+01 6.44E+01 1.21E+02 2.058363 120.0356 101.5 50.75 23.66923 1.47E+00 1.43E+00 0.032157 5.60E+01 6.12E+01 1.17E+02 1.885251 114.8771 87 43.5 21.91345 1.46E+00 1.43E+00 0.029881 5.32E+01 5.71E+01 1.10E+02 1.64857 107.4244 72.5 36.25 20.00415 1.46E+00 1.43E+00 0.028496 5.04E+01 5.42E+01 1.05E+02 1.490643 102.1494 58 29 17.89226 1.46E+00 1.43E+00 0.026844 4.75E+01 5.03E+01 9.79E+01 1.313488 95.88752 43.5 21.75 15.49515 1.46E+00 1.44E+00 0.02498 4.36E+01 4.70E+01 9.05E+01 1.130912 88.97407 29 14.5 12.65174 1.47E+00 1.44E+00 0.028843 4.12E+01 4.29E+01 8.42E+01 1.213714 92.17373 0 0 0 1.47E+00 1.45E+00 0.022211 5.52E+01 5.59E+01 1.11E+02 0.822004 75.85529
  • 48. 0 50 100 150 200 250 300 1 2 3 4 5 6 7 8 9 10 11 12 Chart Title Kfea 2a K(FEA) variation with Crack Length
  • 49. CONCLUDING REMARKS  Damage tolerance design philosophy is generally used in the aircraft structural design to reduce the weight of the structure.   Stiffened panel is a generic structural element of the fuselage structure. Therefore it is considered for the current study.   A FEM approach is followed for the stress analysis of the stiffened panel.   The internal pressure is one of the main loads that the fuselage needs to hold.   Stress analysis is carried out to identify the maximum tensile stress location in the stiffened panel.
  • 50. REFERENCES  T. Swift “Damage tolerance capability”, international journal of fatigue, Volume 16, Issue 1, January 1994, Pages 75-94.   F. Erdogan and M. Ratwani, International journal of fracture mechanics, Vol. 6,  No.4, December 1970.   H. Vlieger, 1973, “The residual strength characteristics of stiffened panels containing fatigue crakes”, engineering fracture mechanics, Vol. 5pp447-477, Pergamon press.   H. Vlieger, 1979, “Application of fracture mechanics of built up structures”, NLR MP79044U. 