Thickwalled Cylinder Under Outer Surface Pressure

1
Thick-walled Cylinder Under Outer Surface Pressure

• Gang Cao
• Dept. of Civil Engineering
• Oregon State University
• 05/31/2005

2
Outline

• Model introduction
• Preliminary analysis
• h-refinement
• p-refinement
• Convergent rate
• Conclusion

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Model introduction
Thicker Cylinder (3D problem)
2D plane stress problem
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Model Description
5
FEM Model in ANSYS

• Q4 element type Plane 42
• Thickness t1
• E10e6 psi
• Poisson Ratio0.3
• P01000psi
• ro3.0
• ri1.0

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Analytical Solution
The analytical solution for the radius
displacement is
At Point A, r2.0
7
Preliminary Analysis
Mesh size

• The division number in radius and
  circumferential direction are
• hr6
• ht12

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Preliminary Analysis
ANSYS solution
Analytical solution
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h-refinement (Model)
hr112,ht124
hr224,ht248
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h-refinement (Model)
hr348,ht396
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h-refinement (Deformation)
hr112,ht124
hr224,ht248
hr348,ht396
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h-refinement (uA)
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p-refinement
hr112,ht124 Plane42 (Q4)
hr112,ht124 Plane82 (Q8)
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p-refinement (Q8 mesh)
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p-refinement
hr112,ht124 Plane42 (Q4)
hr112,ht124 Plane82 (Q8)
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p-refinement
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Convergent rate
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Convergent rate
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Convergent rate
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Convergent rate
The error is approximately O(h2)
Using Richardson extrapolation formula
We get
2.3062E-04 inch
which is very close to the analytical solution
2.3062e-4 inch
21
Conclusion

• The h-refinement by Q4 element converge slower
  than the p-refinement
• By Richardson extrapolation, we can get a
  solution which is very close to the analytical
  solution
• The error is approximately O(h2)