Pipe¶
Figure 25 Cross section of the pipe [YU2005].
This example has the cross section as shown in
Fig. 25 [YU2005]. This cross section has two
straight walls and two half circular walls. \(r=1.0\) in. and other
dimensions are shown in the figure. Each wall has the layup having two
layers made from one material. Fiber orientations for each layer are
also given in the figure. Material properties and layups are given in
Table 11 and
Table 12. Cross-sectional properties are
given in Table 13 and compared with the
results from [YU2005]. The tiny differences are due to different meshes.
Complete input files can be found in examples\ex_pipe\, including
pipe.xml, basepoints.dat, baselines.xml, materials.xml,
and layups.xml.
Figure 26 Base points and Base lines of the pipe cross section.
Figure 27 Segments of the pipe cross section.
Figure 28 Meshed cross section viewed in Gmsh.
| Name | Type | Density | \(E_{1}\) | \(E_{2}\) | \(E_{3}\) | \(G_{12}\) | \(G_{13}\) | \(G_{23}\) | \(\nu_{12}\) | \(\nu_{13}\) | \(\nu_{23}\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(10^3\ \mathrm{lb\cdot sec^2/in^4}\) | \(10^6\ \mathrm{psi}\) | \(10^6\ \mathrm{psi}\) | \(10^6\ \mathrm{psi}\) | \(10^6\ \mathrm{psi}\) | \(10^6\ \mathrm{psi}\) | \(10^6\ \mathrm{psi}\) | |||||
| mat_1 | orthotropic | 13.53 | 20.59 | 1.42 | 1.42 | 0.87 | 0.87 | 0.87 | 0.42 | 0.42 | 0.42 |
| Name | Layer | Material | Ply thickness | Orientation | Number of plies |
|---|---|---|---|---|---|
| \(\mathrm{in}\) | \(\circ\) | ||||
| layup_1 | 1 | mat_1 | 0.1 | 0 | 1 |
| 2 | mat_1 | 0.1 | 90 | 1 | |
| layup_2 | 1 | mat_1 | 0.1 | -45 | 1 |
| 2 | mat_1 | 0.1 | 45 | 1 |
| Component | Value | Reference [YU2005] |
|---|---|---|
| \(S_{11}\), \(\mathrm{lb}\) | \(\phantom{-}1.03892 \times 10^7\) | \(\phantom{-}1.03890 \times 10^7\) |
| \(S_{22}\), \(\mathrm{lb}\) | \(\phantom{-}7.85800 \times 10^5\) | \(\phantom{-}7.84299 \times 10^5\) |
| \(S_{33}\), \(\mathrm{lb}\) | \(\phantom{-}3.31330 \times 10^5\) | \(\phantom{-}3.29002 \times 10^5\) |
| \(S_{14}\), \(\mathrm{lb \cdot in}\) | \(\phantom{-}9.74568 \times 10^4\) | \(\phantom{-}9.82878 \times 10^4\) |
| \(S_{25}\), \(\mathrm{lb \cdot in}\) | \(-8.02785 \times 10^3\) | \(-8.18782 \times 10^3\) |
| \(S_{36}\), \(\mathrm{lb \cdot in}\) | \(-5.14533 \times 10^4\) | \(-5.18541 \times 10^4\) |
| \(S_{44}\), \(\mathrm{lb \cdot in^2}\) | \(\phantom{-}6.89600 \times 10^5\) | \(\phantom{-}6.86973 \times 10^5\) |
| \(S_{55}\), \(\mathrm{lb \cdot in^2}\) | \(\phantom{-}1.88230 \times 10^6\) | \(\phantom{-}1.88236 \times 10^6\) |
| \(S_{66}\), \(\mathrm{lb \cdot in^2}\) | \(\phantom{-}5.38985 \times 10^6\) | \(\phantom{-}5.38972 \times 10^6\) |