I-beam

_images/exampleibeam0.png

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.

_images/exampleibeam1.png

Figure 35 Base points, Base lines and Segments of the I beam cross section.

_images/exampleibeam.png

Figure 36 Meshed cross section viewed in Gmsh.

Table 21 Material properties
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
Table 22 Layups
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
Table 23 Results
\(\phantom{-}2.749\times 10^9\) \(-4.763\times 10^{-8}\) \(-1.505\times 10^{-14}\) \(-5.734\times 10^{-8}\) \(-1.945\times 10^9\) \(\phantom{-}2.779\times 10^3\)
\(-4.763\times 10^{-8}\) \(\phantom{-}1.362\times 10^9\) \(\phantom{-}4.309\times 10^2\) \(\phantom{-}1.645\times 10^9\) \(\phantom{-}1.277\times 10^{-7}\) \(-4.362\times 10^{-14}\)
\(-1.505\times 10^{-14}\) \(\phantom{-}4.309\times 10^2\) \(\phantom{-}4.729\times 10^4\) \(\phantom{-}5.201\times 10^2\) \(\phantom{-}4.038\times 10^{-14}\) \(-4.775\times 10^{-13}\)
\(-5.734\times 10^{-8}\) \(\phantom{-}1.645\times 10^9\) \(\phantom{-}5.201\times 10^2\) \(\phantom{-}1.990\times 10^9\) \(\phantom{-}1.541\times 10^{-7}\) \(\phantom{-}7.025\times 10^{-14}\)
\(-1.945\times 10^9\) \(\phantom{-}1.277\times 10^{-7}\) \(\phantom{-}4.038\times 10^{-14}\) \(\phantom{-}1.541\times 10^{-7}\) \(\phantom{-}5.376\times 10^9\) \(-5.274\times 10^2\)
\(\phantom{-}2.779\times 10^3\) \(-4.362\times 10^{-14}\) \(-4.775\times 10^{-13}\) \(\phantom{-}7.025\times 10^{-14}\) \(-5.274\times 10^2\) \(\phantom{-}1.173\times 10^9\)