Post on 23-Dec-2015
Finite Element Study of Finite Element Study of Structural Structural
DiscontinuitiesDiscontinuities
Presented By: Ike Lee and Nick LinPresented By: Ike Lee and Nick Lin
Project Advisor: Ioannis KorkolisProject Advisor: Ioannis Korkolis
Presentation ObjectivesPresentation Objectives
Discuss background of structural Discuss background of structural discontinuitiesdiscontinuities
Introduce the finite element methodIntroduce the finite element method Explain how to generate a finite Explain how to generate a finite
element modelelement model Review previous workReview previous work Present new workPresent new work Discuss possibilities for future workDiscuss possibilities for future work Answer questionsAnswer questions
What is a Structural What is a Structural Discontinuity?Discontinuity?
A break or gap within a structural A break or gap within a structural component that alters its component that alters its behavior under loadbehavior under load
Examples of Structural Examples of Structural DiscontinuitiesDiscontinuities
Holes:Holes: Often used to lighten an Often used to lighten an aerospace structure or aerospace structure or
to rivet to rivet components togethercomponents together
Cracks:Cracks: Usually a result of material Usually a result of material imperfections or areas imperfections or areas
of high of high stressstress
ConcernsConcerns
Uniform loading of a square plate Uniform loading of a square plate results in a uniform stress distributionresults in a uniform stress distribution
ConcernsConcerns
Holes alter the Holes alter the stress stress distribution and distribution and induce stress induce stress concentrations.concentrations.
Study of Mesh RefinementStudy of Mesh Refinement
EM 360 Fall 2002EM 360 Fall 2002
ConcernsConcerns
Stress concentrations at crack Stress concentrations at crack tipstips
Crack propagationCrack propagation
Possible ConsequencesPossible Consequences
Stress fields around Stress fields around discontinuities can interact with discontinuities can interact with each other and cause failure.each other and cause failure.
Cessna 402C Mishap InvestigationCessna 402C Mishap Investigation, 1999, 1999
Solution MethodSolution Method
Structural discontinuity problems Structural discontinuity problems are often very difficult to solve are often very difficult to solve analytically, sometimes analytically, sometimes impossible.impossible.
Our method is to use ABAQUS, a Our method is to use ABAQUS, a finite element program.finite element program.
The Finite Element The Finite Element Method (FEM)Method (FEM)
General General technique for technique for constructing constructing approximate approximate solutions to solutions to boundary value boundary value problemsproblems
Study of Mesh RefinementStudy of Mesh Refinement
EM 360 Fall 2002EM 360 Fall 2002
How to Generate a Finite How to Generate a Finite Element ModelElement Model
An input file must be written An input file must be written containing the following two parts:containing the following two parts:
Model Data: This portion defines the Model Data: This portion defines the geometry of the model geometry of the model
and and material properties. material properties.
History Data: This portion defines how the History Data: This portion defines how the model will be loaded model will be loaded
and what and what values should be values should be outputted.outputted.
Some Important Factors Some Important Factors to Considerto Consider
Boundary Boundary ConditionsConditions
Load Type and Load Type and DirectionsDirections
Mesh RefinementMesh Refinement
Study of Mesh RefinementStudy of Mesh Refinement
EM 360, Fall 2002EM 360, Fall 2002
Some Important Factors to Some Important Factors to Consider : Mesh RefinementConsider : Mesh Refinement
Peterson’s Stress Concentration Peterson’s Stress Concentration FactorsFactors, 1997, 1997
11 Elements11 Elements
1 Second1 Second
K=4.342K=4.342
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, 2003, 2003
K=K=maxmax________
Some Important Factors to Some Important Factors to Consider : Mesh RefinementConsider : Mesh Refinement
Finite Element Study of Structural Discontinuities, Finite Element Study of Structural Discontinuities, 20032003
67 Elements67 Elements
1 second1 second
K=4.41K=4.41
Some Important Factors to Some Important Factors to Consider : Mesh RefinementConsider : Mesh Refinement
Finite Element Study of Structural Finite Element Study of Structural Discontinuities, 2003Discontinuities, 2003
211 Elements211 Elements
1 second1 second
K=4.47K=4.47
Some Important Factors to Some Important Factors to Consider : Mesh RefinementConsider : Mesh Refinement
Finite Element Study of Structural Finite Element Study of Structural Discontinuities, 2003Discontinuities, 2003
823 Elements823 Elements
2 seconds2 seconds
K=4.512K=4.512
Some Important Factors to Some Important Factors to Consider : Mesh RefinementConsider : Mesh Refinement
Finite Element Study of Structural Discontinuities, 2003Finite Element Study of Structural Discontinuities, 2003
Approx. 3000 ElementsApprox. 3000 Elements
4 seconds4 seconds
K=4.517K=4.517
Some Important Factors to Some Important Factors to Consider : Mesh RefinementConsider : Mesh Refinement
Finite Element Study of Structural Discontinuities, Finite Element Study of Structural Discontinuities, 20032003
Approx. 19000 ElementsApprox. 19000 Elements
21 seconds21 seconds
K=4.520K=4.520
Mesh Convergence CurveMesh Convergence Curve
Mesh Convergence
4.32
4.34
4.36
4.38
4.4
4.42
4.44
4.46
4.48
4.5
4.52
4.54
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
Number of Elements
Ktg
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, , 20032003
Computation TimeComputation Time
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, , 20032003
Effect of Number of Elements on Compuation Time
0
5
10
15
20
25
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
Number of Elements
Co
mp
uta
tio
n T
ime
(s
ec
)
Mesh ConvergenceMesh Convergence
Refining a coarse finite element Refining a coarse finite element mesh will result in a more mesh will result in a more accurate solution at the cost of accurate solution at the cost of computation time.computation time.
Caveat and ApproachCaveat and Approach
Just because a solution is obtained Just because a solution is obtained does not necessarily mean it is correct. does not necessarily mean it is correct. Therefore, it is important to study the Therefore, it is important to study the results and compare your solution with results and compare your solution with a known, correct solution.a known, correct solution.
Previous WorkPrevious Work
Model 1Model 1
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, 2003, 2003
Peterson’s Stress Concentration FactorsPeterson’s Stress Concentration Factors, 1997, 1997
Previous WorkPrevious Work
Model 1 (continued)Model 1 (continued)
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, 2003, 2003
Stress Concentration Factor (Model 1)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 0.1 0.2 0.3 0.4 0.5 0.6
d/H
Ktg
ABAQUS
Peterson
Ktg = max/
Previous WorkPrevious Work
Model 2Model 2
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, 2003, 2003
Peterson’s Stress Concentration FactorsPeterson’s Stress Concentration Factors, 1997, 1997
Previous WorkPrevious Work
Model 2 (continued)Model 2 (continued)
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, 2003, 2003
Stress Concentration Factor (Model 3)
0
0.5
1
1.5
2
2.5
3
3.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
d/l
Ktg
ABAQUS
Peterson
Ktg = max/1
New WorkNew Work
Reduction of stress concentrations Reduction of stress concentrations from edges of holesfrom edges of holes
Finite element modeling of cracksFinite element modeling of cracks
Reduction of crack stress intensity Reduction of crack stress intensity factorfactor
Reducing Stress Reducing Stress Concentrations from Concentrations from
HolesHoles Method:Method:
Add another hole to alleviate the stress Add another hole to alleviate the stress concentration.concentration.
Constant:Constant: Radius of original hole = 2 inRadius of original hole = 2 in
Tensile Load = 1 psi in horizontal Tensile Load = 1 psi in horizontal direction direction
Variables:Variables: R = radius of added holeR = radius of added hole
L = distance between L = distance between centers of holes centers of holes
Reducing Stress Reducing Stress Concentrations from Concentrations from
HolesHoles
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, 2003, 2003
Reducing Stress Reducing Stress Concentrations from Concentrations from
HolesHoles
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, 2003, 2003
Reducing Stress Reducing Stress Concentrations from Concentrations from
HolesHoles
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, 2003, 2003
Reducing Stress Reducing Stress Concentrations from Concentrations from
HolesHoles
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, 2003, 2003
Reducing Stress Reducing Stress Concentrations from Concentrations from
HolesHoles Conclusion:Conclusion:
Adding holes in a plane Adding holes in a plane perpendicular to the loading perpendicular to the loading direction does not reduce the direction does not reduce the stress concentration factor.stress concentration factor.
Reducing Stress Reducing Stress Concentrations from Concentrations from
HolesHoles
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, 2003, 2003
Reducing Stress Reducing Stress Concentrations from Concentrations from
HolesHoles
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, 2003, 2003
Reducing Stress Reducing Stress Concentrations from Concentrations from
HolesHoles
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, 2003, 2003
Reducing Stress Reducing Stress Concentrations from Concentrations from
HolesHoles
Variation of Stress Concentration Factor with Second Hole Radius(L = 4 in)
1.5
1.7
1.9
2.1
2.3
2.5
2.7
2.9
3.1
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
R (in)
SC
F
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, 2003, 2003
Reducing Stress Reducing Stress Concentrations from Concentrations from
HolesHoles
Variation of Stress Concentration Factor with Second Hole Radius(L = 5 in)
2
2.2
2.4
2.6
2.8
3
3.2
0 0.5 1 1.5 2 2.5
R (in)
SC
F
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, 2003, 2003
Reducing Stress Reducing Stress Concentrations from Concentrations from
HolesHoles
Variation of Stress Concentration Factor with Second Hole Radius(L = 7.50 in)
1.5
1.7
1.9
2.1
2.3
2.5
2.7
2.9
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
R (in)
SF
C
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, 2003, 2003
Reducing Stress Reducing Stress Concentrations from Concentrations from
HolesHoles
Effect of Hole Spacing on Stress Concentration Factor
2.35
2.4
2.45
2.5
2.55
2.6
0 1 2 3 4 5 6 7 8
L (in)
Op
tim
al S
FC
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, 2003, 2003
Reducing Stress Reducing Stress Concentrations from Concentrations from
HolesHoles Conclusion:Conclusion:
Adding holes in a plane parallel to Adding holes in a plane parallel to the loading direction does reduce the loading direction does reduce the stress concentration factor.the stress concentration factor.
Finite Element Analysis Finite Element Analysis of Cracksof Cracks
Crack configuration models:Crack configuration models:
Tada Tada The Stress Analysis ofThe Stress Analysis of
Cracks HandbookCracks Handbook
Model 1Model 1 Model 2Model 2 Model 3Model 3
Finite Element Analysis Finite Element Analysis of Cracksof Cracks
Crack Model 1 (Center Cracked Plate)Crack Model 1 (Center Cracked Plate)
Finite Element Analysis Finite Element Analysis of Cracksof Cracks
Crack Model 2 (Edge Cracked Plate)Crack Model 2 (Edge Cracked Plate)
Finite Element Analysis Finite Element Analysis of Cracksof Cracks
Crack Model 3Crack Model 3
Tada, Tada, The Stress Analysis of Cracks HandbookThe Stress Analysis of Cracks Handbook
Finite Element Analysis Finite Element Analysis of Crack Repairof Crack Repair
Crack repair models:Crack repair models:
Finite Element Study of Structural DiscontinuitiesFinite Element Study of Structural Discontinuities, 2003, 2003
Finite Element Analysis Finite Element Analysis of Cracksof Cracks
Center Cracked Plate with Stop HolesCenter Cracked Plate with Stop Holes
Finite Element Analysis Finite Element Analysis of Cracksof Cracks
Center Cracked Plate with an Array of Holes Near the Crack TipCenter Cracked Plate with an Array of Holes Near the Crack Tip
Finite Element Analysis Finite Element Analysis of Cracksof Cracks
Patch Repair of Center Cracked PlatePatch Repair of Center Cracked Plate
Finite Element Analysis Finite Element Analysis of Cracksof Cracks
Arrester Repair of Center Cracked PlateArrester Repair of Center Cracked Plate
Finite Element Analysis Finite Element Analysis of Cracksof Cracks
Variation in Stress Intensity Factor with Arrester Strip DistanceVariation in Stress Intensity Factor with Arrester Strip Distance
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
0 1 2 3 4 5 6 7
L (in)
K (
ps
i-in
0.5)
Summary of Work Summary of Work Completed This SemesterCompleted This Semester
Used the FEM to determine how Used the FEM to determine how holes and cracks affect stress holes and cracks affect stress distributions.distributions.
Devised a method to alleviate Devised a method to alleviate stress concentrations around holes.stress concentrations around holes.
Investigated crack repair methods.Investigated crack repair methods.
Possibilities for Future Possibilities for Future WorkWork
Finite element modeling of structural Finite element modeling of structural discontinuities under cyclic loadingdiscontinuities under cyclic loading
Finite element modeling of structural Finite element modeling of structural discontinuities in more complex discontinuities in more complex structuresstructures
Adaptation of scripting feature in Adaptation of scripting feature in ABAQUSABAQUS