2. Benchmark solution#
2.1. Calculation method used for the reference solution#
The reference solutions selected to verify Code_Aster models are as follows:
for POUTRE models: comparison with the codes: \(\text{POUX}\), \(\text{ADL}\) and \(\text{TITUS-T}\) [1], using beam-type modeling,
for TUYAU models: comparison with the :math:`text{ABAQUS}` code, using pipe-type modeling. The Fourier mode number (:math:`M`) used when calculating the reference is the same as that used when calculating with*Code_Aster.
for beam models, a moment equivalent to point \(T1\) is also defined as \({M}_{\mathit{eq}}=\sqrt{({\mathit{MT}}^{2}+{\mathit{MFY}}^{2}+{\mathit{MFZ}}^{2})}\). The reference value is that obtained by hand with the results of modeling A (reference AUTRE_ASTER).
2.2. Benchmark results#
Load Case |
Move to point 3 (T3 node group) |
Beam Modeling |
Beam Modeling (\(\text{POUX}\), \(\text{ADL}\), \(\text{TITUS}\)) |
Pipe Modeling: \(M=3\) (\(\text{ABAQUS}\)) |
Pipe Modeling: \(M=6\) (\(\text{ABAQUS}\)) |
\(\mathrm{DX}\) |
—0.1658E—3 |
—0.16517E—3 |
—0.16512E—3 |
||
Own weight |
\(\mathrm{DY}\) |
—0.2040E—4 |
—0.13870E—4 |
—0.13946E—4 |
|
\(\mathrm{DZ}\) |
—0.8010E—5 |
—0.80376E—5 |
—0.80369E—5 |
||
\(\mathrm{DX}\) |
—0.1651E—3 |
—0.16445E—3 |
—0.16441E—3 |
||
Nodal force |
\(\mathrm{DY}\) |
—0.2080E—4 |
—0.14245E—4 |
—0.14320E—4 |
|
\(\mathrm{DZ}\) |
—0.9516E—5 |
—0.10047E—4 |
—0.10047E—4 |
||
\(\mathrm{DX}\) |
—6.1418E—3 |
—6.3277E—3 |
—6.3236E—3 |
||
Expansion |
\(\mathrm{DY}\) |
—13.090E—3 |
—13.092E—3 |
—13.093E—3 |
|
\(\mathrm{DZ}\) |
16.799E—3 |
16.798E—3 |
16.798E—3 |
Load case |
Moment equivalent to point \(T1\) |
Reference AUTRE_ASTER (modeling A) |
Own weight |
\({M}_{\mathit{eq}}\) |
189.76886594440944 |
2.3. Uncertainty about the solution#
The uncertainty on the reference solution is set to \(\text{2\%}\).
2.4. Bibliographical references#
M.W. KELLOG Co. Design of Piping Systems. New York, 1956 - Problem #5.9