Figure 22 Cross section of the box beam [YU2012].

This example is a thin-walled box beam whose cross section is depicted in Fig. 22 [YU2012]. The width \(a_2=0.953\) in, height \(a_3=0.530\) in, and thickness \(t=0.030\) in. Each wall has six plies of the same composite material and the same fiber orientation of \(15^\circ\). Material properties and layup scheme are listed in Table 8 and Table 9. Cross-sectional properties are given in Table 10 and compared with those in Ref. [YU2012]. The tiny differences are due to different meshes. Complete input files can be found in examples\ex_box\, including box.xml, basepoints.dat, baselines.xml, materials.xml, and layups.xml.


Figure 23 Base points, Base lines and Segments of the box beam cross section.


Figure 24 Meshed cross section viewed in Gmsh.

Table 8 Material properties
Name Type Density \(E_{1}\) \(E_{2}\) \(E_{3}\) \(G_{12}\) \(G_{13}\) \(G_{23}\) \(\nu_{12}\) \(\nu_{13}\) \(\nu_{23}\)
    \(10^3\ \mathrm{lb\cdot sec^2/in^4}\) \(10^6\ \mathrm{psi}\) \(10^6\ \mathrm{psi}\) \(10^6\ \mathrm{psi}\) \(10^6\ \mathrm{psi}\) \(10^6\ \mathrm{psi}\) \(10^6\ \mathrm{psi}\)      
mat_1 orthotropic 13.53 20.59 1.42 1.42 0.87 0.87 0.696 0.30 0.30 0.34
Table 9 Layups
Name Layer Material Ply thickness Orientation Number of plies
      \(\mathrm{in}\) \(\circ\)  
layup1 1 mat_1 0.05 -15 6
Table 10 Results
Component Value Reference [YU2012]
\(S_{11}\), \(\mathrm{lb}\) \(\phantom{-}1.437 \times 10^6\) \(\phantom{-}1.437 \times 10^6\)
\(S_{22}\), \(\mathrm{lb}\) \(\phantom{-}9.026 \times 10^4\) \(\phantom{-}9.027 \times 10^4\)
\(S_{33}\), \(\mathrm{lb}\) \(\phantom{-}3.941 \times 10^4\) \(\phantom{-}3.943 \times 10^4\)
\(S_{14}\), \(\mathrm{lb \cdot in}\) \(\phantom{-}1.074 \times 10^5\) \(\phantom{-}1.074 \times 10^5\)
\(S_{25}\), \(\mathrm{lb \cdot in}\) \(-5.201 \times 10^4\) \(-5.201 \times 10^4\)
\(S_{36}\), \(\mathrm{lb \cdot in}\) \(-5.635 \times 10^4\) \(-5.635 \times 10^4\)
\(S_{44}\), \(\mathrm{lb \cdot in^2}\) \(\phantom{-}1.679 \times 10^4\) \(\phantom{-}1.679 \times 10^4\)
\(S_{55}\), \(\mathrm{lb \cdot in^2}\) \(\phantom{-}6.621 \times 10^4\) \(\phantom{-}6.621 \times 10^4\)
\(S_{66}\), \(\mathrm{lb \cdot in^2}\) \(\phantom{-}1.725 \times 10^5\) \(\phantom{-}1.725 \times 10^5\)