Finite Element Study of
Structural Discontinuities
Presented By: Ike Lee and Nick Lin
Project Advisor: Ioannis Korkolis
Presentation Objectives







Discuss background of structural
discontinuities
Introduce the finite element method
Explain how to generate a finite element
model
Review previous work
Present new work
Discuss possibilities for future work
Answer questions
What is a Structural
Discontinuity?

A break or gap within a structural
component that alters its behavior
under load
Examples of Structural
Discontinuities


Holes: Often used to lighten an
aerospace structure or to rivet
components together
Cracks: Usually a result of material
imperfections or areas of high
stress
Concerns

Uniform loading of a square plate results in
a uniform stress distribution
Concerns

Holes alter the
stress distribution
and induce stress
concentrations.
Study of Mesh Refinement
EM 360 Fall 2002
Concerns

Stress concentrations at crack tips

Crack propagation
Possible Consequences

Stress fields around discontinuities can
interact with each other and cause
failure.
Cessna 402C Mishap Investigation, 1999
Solution Method


Structural discontinuity problems are
often very difficult to solve analytically,
sometimes impossible.
Our method is to use ABAQUS, a finite
element program.
The Finite Element Method
(FEM)

General technique
for constructing
approximate
solutions to
boundary value
problems
Study of Mesh Refinement
EM 360 Fall 2002
How to Generate a Finite
Element Model

An input file must be written
containing the following two parts:


Model Data: This portion defines the
geometry of the model and
material properties.
History Data: This portion defines how the
model will be loaded and what
values should be outputted.
Some Important Factors to
Consider



Boundary
Conditions
Load Type and
Directions
Mesh Refinement
Study of Mesh Refinement
EM 360, Fall 2002
Some Important Factors to
Consider : Mesh Refinement
Peterson’s Stress Concentration Factors, 1997
11 Elements
1 Second
K=4.342
s max
K= ____
s
Finite Element Study of Structural Discontinuities, 2003
Some Important Factors to
Consider : Mesh Refinement
67 Elements
1 second
K=4.41
Finite Element Study of Structural Discontinuities, 2003
Some Important Factors to
Consider : Mesh Refinement
211 Elements
1 second
K=4.47
Finite Element Study of Structural Discontinuities, 2003
Some Important Factors to
Consider : Mesh Refinement
823 Elements
2 seconds
K=4.512
Finite Element Study of Structural Discontinuities, 2003
Some Important Factors to
Consider : Mesh Refinement
Approx. 3000 Elements
4 seconds
K=4.517
Finite Element Study of Structural Discontinuities, 2003
Some Important Factors to
Consider : Mesh Refinement
Approx. 19000 Elements
21 seconds
K=4.520
Finite Element Study of Structural Discontinuities, 2003
Mesh Convergence Curve
4.54
4.52
4.5
4.48
4.46
Ktg
4.44
4.42
4.4
4.38
4.36
4.34
4.32
0
2000
4000
6000
8000
10000
12000
14000
16000
Number of Elements
Mesh Convergence
Finite Element Study of Structural Discontinuities, 2003
18000
20000
Computation Time
25
Computation Time (sec)
20
15
10
5
0
0
2000
4000
6000
8000
10000
12000
14000
16000
Number of Elements
Effect of Number of Elements on Compuation Time
Finite Element Study of Structural Discontinuities, 2003
18000
20000
Mesh Convergence

Refining a coarse finite element mesh
will result in a more accurate solution
at the cost of computation time.
Caveat and Approach

Just because a solution is obtained does not
necessarily mean it is correct. Therefore, it
is important to study the results and
compare your solution with a known, correct
solution.
Previous Work

Model 1
Peterson’s Stress Concentration Factors, 1997
Finite Element Study of Structural Discontinuities, 2003
Previous Work
Model 1 (continued)
5
4.5
4
Ktg = smax /s
3.5
3
Ktg

2.5
2
1.5
ABAQUS
1
Peterson
0.5
0
0
0.1
0.2
0.3
0.4
0.5
d/H
Stress Concentration Factor (Model 1)
Finite Element Study of Structural Discontinuities, 2003
0.6
Previous Work

Model 2
Peterson’s Stress Concentration Factors, 1997
Finite Element Study of Structural Discontinuities, 2003
Previous Work
Model 2 (continued)
3.5
3
Ktg = smax /s1
2.5
2
Ktg

1.5
1
ABAQUS
0.5
Peterson
0
0
0.1
0.2
0.3
0.4
0.5
d/l
Stress Concentration Factor (Model 3)
Finite Element Study of Structural Discontinuities, 2003
0.6
0.7
New Work



Reduction of stress concentrations
from edges of holes
Finite element modeling of cracks
Reduction of crack stress intensity
factor
Reducing Stress
Concentrations from Holes

Method:
Add another hole to alleviate the stress
concentration.

Constant: Radius of original hole = 2 in
Tensile Load = 1 psi in horizontal
direction

Variables: R = radius of added hole
L = distance between
centers of holes
Reducing Stress
Concentrations from Holes
Finite Element Study of Structural Discontinuities, 2003
Reducing Stress
Concentrations from Holes
Finite Element Study of Structural Discontinuities, 2003
Reducing Stress
Concentrations from Holes
Finite Element Study of Structural Discontinuities, 2003
Reducing Stress
Concentrations from Holes
Finite Element Study of Structural Discontinuities, 2003
Reducing Stress
Concentrations from Holes

Conclusion:
Adding holes in a plane perpendicular
to the loading direction does not
reduce the stress concentration factor.
Reducing Stress
Concentrations from Holes
Finite Element Study of Structural Discontinuities, 2003
Reducing Stress
Concentrations from Holes
Finite Element Study of Structural Discontinuities, 2003
Reducing Stress
Concentrations from Holes
Finite Element Study of Structural Discontinuities, 2003
Reducing Stress
Concentrations from Holes
3.1
2.9
2.7
SCF
2.5
2.3
2.1
1.9
1.7
1.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
R (in)
Variation of Stress Concentration Factor with Second Hole Radius
(L = 4 in)
Finite Element Study of Structural Discontinuities, 2003
2
Reducing Stress
Concentrations from Holes
3.2
3
SCF
2.8
2.6
2.4
2.2
2
0
0.5
1
1.5
2
R (in)
Variation of Stress Concentration Factor with Second Hole Radius
(L = 5 in)
Finite Element Study of Structural Discontinuities, 2003
2.5
Reducing Stress
Concentrations from Holes
2.9
2.7
SFC
2.5
2.3
2.1
1.9
1.7
1.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
R (in)
Variation of Stress Concentration Factor with Second Hole Radius
(L = 7.50 in)
Finite Element Study of Structural Discontinuities, 2003
2
Reducing Stress
Concentrations from Holes
2.6
Optimal SFC
2.55
2.5
2.45
2.4
2.35
0
1
2
3
4
5
6
L (in)
Effect of Hole Spacing on Stress Concentration Factor
Finite Element Study of Structural Discontinuities, 2003
7
8
Reducing Stress
Concentrations from Holes

Conclusion:
Adding holes in a plane parallel to the
loading direction does reduce the
stress concentration factor.
Finite Element Analysis of
Cracks

Crack configuration models:
Tada The Stress Analysis of
Cracks Handbook
Model 1
Model 2
Model 3
Finite Element Analysis of
Cracks
Crack Model 1 (Center Cracked Plate)
Finite Element Analysis of
Cracks
Crack Model 2 (Edge Cracked Plate)
Finite Element Analysis of
Cracks
Crack Model 3
Finite Element Analysis of
Cracks
Tada, The Stress Analysis of Cracks Handbook
Crack Model 3
Finite Element Analysis of
Crack Repair

Crack repair models:
Finite Element Study of Structural Discontinuities, 2003
Finite Element Analysis of
Cracks
Center Cracked Plate with Stop Holes
Finite Element Analysis of
Cracks
Center Cracked Plate with an Array of Holes Near the Crack Tip
Finite Element Analysis of
Cracks
Patch Repair of Center Cracked Plate
Finite Element Analysis of
Cracks
Arrester Repair of Center Cracked Plate
Finite Element Analysis of
Cracks
2.9
2.8
2.7
K (psi-in 0.5 )
2.6
2.5
2.4
2.3
2.2
2.1
2
0
1
2
3
4
5
6
L (in)
Variation in Stress Intensity Factor with Arrester Strip Distance
7
Summary of Work
Completed This Semester



Used the FEM to determine how holes
and cracks affect stress distributions.
Devised a method to alleviate stress
concentrations around holes.
Investigated crack repair methods.
Possibilities for Future Work



Finite element modeling of structural
discontinuities under cyclic loading
Finite element modeling of structural
discontinuities in more complex structures
Adaptation of scripting feature in ABAQUS
Questions?