2. • 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
2
3. • A break or gap within a structural component that
alters its behavior under load. Structural or material
discontinuity which affects the stress or strain
distribution across the entire wall thickness over a
region of significant area. EXAMPLE End-to-pipe
junction, connector-to-pipe junction, the junction of two
pipes of different diameters, thickness or material, or a
stiffener-to-pipe junction.
3
4. • 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. The pressure vessel codes define
two important ‘classes’ of stress. A primary stress is
related to mechanical loading directly and satisfies
force and moment equilibrium. Primary stress that
exceeds the yield stress by some margin will result in
failure. By contrast, secondary stresses are those
arising from geometric discontinuities or stress
concentrations. For an increasing external load, at any
point, both primary and secondary stresses increase in
proportion to this load, until the yield point is reached.
But secondary stresses are termed self-limiting by the
ASME code.
4
5. • Uniform loading of a square plate
results in a uniform stress
distribution
5
6. • Holes alter the stress distribution
and induce stress concentrations.
6
Study of Mesh Refinement
EM 360 Fall 2002
7. • Stress concentrations at crack tips
• Crack propagation
• The method of digital image correlation (DIC) was applied to the digital
image of orthogonal cutting parallel to the grain of hinoki, and the strain
distribution near the cutting edge was evaluated. The wood fracture
associated with chip generation was considered as mode I fracture, and the
stress intensity factor KI for fracture mode I was calculated from the strain
distribution according to the theory of linear elastic fracture mechanics for
the anisotropic material. The calculated KI increased prior to crack
propagation and decreased just after the crack propagation. The change
in KI before and after crack propagation, ΔKI, decreased in accordance with
the crack propagation length, although the variance in ΔKI should depend
on the relationships between the resolution of DIC method and the
dimensions of cellular structure.
7
8. 8
• Stress fields around discontinuities can interact with each other
and cause failure.
9. • Structural discontinuity problems are often very difficult to solve
analytically, sometimes impossible.
• Our method is to use ABAQUS, a finite element program.
9
10. • General technique for constructing
approximate solutions to boundary
value problems
10
Study of Mesh Refinement
EM 360 Fall 2002
11. • 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.
11
12. • Boundary Conditions
• Load Type and
Directions
• Mesh Refinement
12
Study of Mesh Refinement
EM 360, Fall 2002
13. 13
Peterson’s Stress Concentration Factors, 1997
11 Elements
1 Second
K=4.342
Finite Element Study of Structural
Discontinuities, 2003 K= s
max
____
s
20. 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
Computation
Time
(sec)
Finite Element Study of Structural Discontinuities, 2003
20
21. • Refining a coarse finite element mesh will result in a
more accurate solution at the cost of computation time.
21
22. • 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.
22
23. Model 1
Finite Element Study of Structural Discontinuities, 2003
Peterson’s Stress Concentration Factors, 1997
23
25. • Model 2
Finite Element Study of Structural Discontinuities, 2003
Peterson’s Stress Concentration Factors, 1997
25
26. • 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
K
tg
ABAQUS
Peterson
Ktg = smax/s1
Finite Element Study of Structural Discontinuities, 2003
26
27. • Reduction of stress concentrations from edges of holes
• Finite element modeling of cracks
• Reduction of crack stress intensity factor
27
28. • 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
28
53. • 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.
53
54. • 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
54
