finite element study of structural discontinuities presented by: ike lee and nick lin project...

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


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


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________


Finite Element Study of Structural Discontinuities, Finite Element Study of Structural Discontinuities, 20032003


1 second1 second

K=4.41K=4.41


Finite Element Study of Structural Finite Element Study of Structural Discontinuities, 2003Discontinuities, 2003


1 second1 second

K=4.47K=4.47


Finite Element Study of Structural Finite Element Study of Structural Discontinuities, 2003Discontinuities, 2003


2 seconds2 seconds

K=4.512K=4.512


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


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


Peterson’s Stress Concentration FactorsPeterson’s Stress Concentration Factors, 1997, 1997


Model 1 (continued)Model 1 (continued)


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/


Model 2Model 2


Peterson’s Stress Concentration FactorsPeterson’s Stress Concentration Factors, 1997, 1997


Model 2 (continued)Model 2 (continued)


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


HolesHoles



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.


HolesHoles



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



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



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



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



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


Crack Model 1 (Center Cracked Plate)Crack Model 1 (Center Cracked Plate)


Crack Model 2 (Edge Cracked Plate)Crack Model 2 (Edge Cracked Plate)


Crack Model 3Crack Model 3


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:



Center Cracked Plate with Stop HolesCenter Cracked Plate with Stop Holes


Center Cracked Plate with an Array of Holes Near the Crack TipCenter Cracked Plate with an Array of Holes Near the Crack Tip


Patch Repair of Center Cracked PlatePatch Repair of Center Cracked Plate


Arrester Repair of Center Cracked PlateArrester Repair of Center Cracked Plate


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

Questions?Questions?

finite element study of structural discontinuities presented by: ike lee and nick lin project...

Documents

load slide

areas of high stress

finite element program

concerns stress concentrations

model data

structural component

ioannis korkolis slide

areas of high stress