I-beam¶
Figure 34 Meshed cross section viewed in Gmsh.
This example has an I-shape cross section. The dimensions shown in
Fig. 34 are \(w_1=2.0\) m, \(w_2=3.0\) m,
\(h=3.0\) m, \(t_1=0.11\) m, \(t_2=0.065\) m, \(t_w=0.08\) m.
Materials and layups are given in Table 21
and Table 22. The effective stiffness
matrix is listed in Table 23.
Complete input files can be found in examples\ex_ibeam\, including
ibeam.xml, basepoints.dat, baselines.xml, materials.xml,
and layups.xml.
Figure 35 Base points, Base lines and Segments of the I beam cross section.
Figure 36 Meshed cross section viewed in Gmsh.
| Name | Type | Density | \(E_{1}\) | \(E_{2}\) | \(E_{3}\) | \(G_{12}\) | \(G_{13}\) | \(G_{23}\) | \(\nu_{12}\) | \(\nu_{13}\) | \(\nu_{23}\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(10^3\ \mathrm{kg/m^3}\) | \(10^9\ \mathrm{Pa}\) | \(10^9\ \mathrm{Pa}\) | \(10^9\ \mathrm{Pa}\) | \(10^9\ \mathrm{Pa}\) | \(10^9\ \mathrm{Pa}\) | \(10^9\ \mathrm{Pa}\) | |||||
| iso5_1 | orthotropic | 1.86 | 37.00 | 9.00 | 9.00 | 4.00 | 4.00 | 4.00 | 0.28 | 0.28 | 0.28 |
| iso5_2 | orthotropic | 1.83 | 10.30 | 10.30 | 10.30 | 8.00 | 8.00 | 8.00 | 0.30 | 0.30 | 0.30 |
| iso5_3 | orthotropic | 1.83 | 1e-8 | 1e-8 | 1e-8 | 1e-9 | 1e-9 | 1e-9 | 0.30 | 0.30 | 0.30 |
| iso5_4 | orthotropic | 1.664 | 10.30 | 10.30 | 10.30 | 8.00 | 8.00 | 8.00 | 0.30 | 0.30 | 0.30 |
| iso5_5 | orthotropic | 0.128 | 0.01 | 0.01 | 0.01 | 2e-4 | 2e-4 | 2e-4 | 0.30 | 0.30 | 0.30 |
| Name | Layer | Material | Ply thickness | Orientation | Number of plies |
|---|---|---|---|---|---|
| \(\mathrm{m}\) | \(\circ\) | ||||
| layup1 | 1 | iso5_1 | 0.03 | 90 | 2 |
| 2 | iso5_2 | 0.05 | 0 | 1 | |
| layup2 | 1 | iso5_3 | 0.015 | 0 | 3 |
| 2 | iso5_4 | 0.02 | 90 | 1 | |
| layup_web | 1 | iso5_5 | 0.02 | 0 | 4 |
| \(\phantom{-}2.749\times 10^9\) | \(-4.763\times 10^{-8}\) | \(-1.505\times 10^{-14}\) | \(-5.734\times 10^{-8}\) | \(-1.945\times 10^9\) | \(\phantom{-}2.779\times 10^3\) |
| \(-4.763\times 10^{-8}\) | \(\phantom{-}1.362\times 10^9\) | \(\phantom{-}4.309\times 10^2\) | \(\phantom{-}1.645\times 10^9\) | \(\phantom{-}1.277\times 10^{-7}\) | \(-4.362\times 10^{-14}\) |
| \(-1.505\times 10^{-14}\) | \(\phantom{-}4.309\times 10^2\) | \(\phantom{-}4.729\times 10^4\) | \(\phantom{-}5.201\times 10^2\) | \(\phantom{-}4.038\times 10^{-14}\) | \(-4.775\times 10^{-13}\) |
| \(-5.734\times 10^{-8}\) | \(\phantom{-}1.645\times 10^9\) | \(\phantom{-}5.201\times 10^2\) | \(\phantom{-}1.990\times 10^9\) | \(\phantom{-}1.541\times 10^{-7}\) | \(\phantom{-}7.025\times 10^{-14}\) |
| \(-1.945\times 10^9\) | \(\phantom{-}1.277\times 10^{-7}\) | \(\phantom{-}4.038\times 10^{-14}\) | \(\phantom{-}1.541\times 10^{-7}\) | \(\phantom{-}5.376\times 10^9\) | \(-5.274\times 10^2\) |
| \(\phantom{-}2.779\times 10^3\) | \(-4.362\times 10^{-14}\) | \(-4.775\times 10^{-13}\) | \(\phantom{-}7.025\times 10^{-14}\) | \(-5.274\times 10^2\) | \(\phantom{-}1.173\times 10^9\) |