Òåñò 5.5 Hovgaard's task
Verification of the LIRA-FEM software / Òåñò 5.5 Hovgaard's task / Analytical solution: W. Hovgaard, “Stress in three dimensional pipe-bends”, Transactions of ASME, vol. 57, FSP 75 – 12, p. 401 – 416.
Analytical solution: W. Hovgaard, “Stress in three dimensional pipe-bends”, Transactions of ASME, vol. 57, FSP 75 – 12, p. 401 – 416.
Geometry:
 | Circular cross-section:
Square: A = 0.3439 x 10-2 ì2 bending radius: R = 0.922 ì thickness: e = 0.00612 ì outer radius: Re = 0.0925 ì inner radius: Ri = 0.08638 ì moments of inertia: IY = IZ = 0.1377 x 10-4 ì4 (straight elements) IY = IZ = 0.5887 x 10-5 ì4 (curved elements) |
Point coordinates, ì
|
|
A |
B |
C |
D |
|
x |
0 |
1.96 |
0 |
0 |
|
y |
-2.75 |
0 |
-2.75 |
0 |
|
z |
-3.69 |
0 |
0 |
0 |
Material characteristics: Å = 1.658 õ 1011 Ïà, v = 0.3, ρ = 13404.106 êã/ì3 (pipe filled with water).
Boundary conditions: Points A and B are pinched.
Loads: For modal analysis.
CALCULATION RESULTS:
|
Order of form |
Frequency, Hz |
Uncertainty,% | |
|
Analytical solution |
Calculation results (LIRA) | ||
|
1 |
10,18 |
10,25 |
0,7 |
|
2 |
19,54 |
20,02 |
2,46 |
|
3 |
25,47 |
25,171 |
1,17 |
|
4 |
48,09 |
48,073 |
0,03 |
|
5 |
52,86 |
52,676 |
0,35 |
|
6 |
75,94 |
85 |
11,93 |
|
7 |
80,11 |
87,19 |
8,84 |
|
8 |
122,34 |
129,29 |
5,68 |
|
9 |
123,15 |
132,552 |
7,63 |
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