Pipe

_images/examplepipe0.png

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.

_images/examplepipe1.png

Figure 26 Base points and Base lines of the pipe cross section.

_images/examplepipe2.png

Figure 27 Segments of the pipe cross section.

_images/examplepipe.png

Figure 28 Meshed cross section viewed in Gmsh.

Table 11 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 0.87 0.42 0.42 0.42
Table 12 Layups
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
Table 13 Results
Component Value Reference [YU2005]
\(S_{11}\), \(\mathrm{lb}\) \(\phantom{-}1.03892 \times 10^7\) \(\phantom{-}1.03890 \times 10^7\)
\(S_{22}\), \(\mathrm{lb}\) \(\phantom{-}7.85800 \times 10^5\) \(\phantom{-}7.84299 \times 10^5\)
\(S_{33}\), \(\mathrm{lb}\) \(\phantom{-}3.31330 \times 10^5\) \(\phantom{-}3.29002 \times 10^5\)
\(S_{14}\), \(\mathrm{lb \cdot in}\) \(\phantom{-}9.74568 \times 10^4\) \(\phantom{-}9.82878 \times 10^4\)
\(S_{25}\), \(\mathrm{lb \cdot in}\) \(-8.02785 \times 10^3\) \(-8.18782 \times 10^3\)
\(S_{36}\), \(\mathrm{lb \cdot in}\) \(-5.14533 \times 10^4\) \(-5.18541 \times 10^4\)
\(S_{44}\), \(\mathrm{lb \cdot in^2}\) \(\phantom{-}6.89600 \times 10^5\) \(\phantom{-}6.86973 \times 10^5\)
\(S_{55}\), \(\mathrm{lb \cdot in^2}\) \(\phantom{-}1.88230 \times 10^6\) \(\phantom{-}1.88236 \times 10^6\)
\(S_{66}\), \(\mathrm{lb \cdot in^2}\) \(\phantom{-}5.38985 \times 10^6\) \(\phantom{-}5.38972 \times 10^6\)