Pipe

Probelm description

Figure 18 Cross section of the pipe [YU2005].

This example has the cross section as shown in Fig. 18 [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 9 and Table 10. Cross-sectional properties are given in Table 11 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, baselines.xml, materials.xml, and layups.xml.

Figure 19 Base points and Base lines of the pipe cross section.

Figure 20 Segments of the pipe cross section.

Figure 21 Meshed cross section viewed in Gmsh.

Table 9 Material properties

Name	Density	\(E_{1}\)	\(E_{2}\)	\(E_{3}\)	\(G_{12}\)	\(G_{13}\)	\(G_{23}\)	\(\nu_{12}\)	\(\nu_{13}\)	\(\nu_{23}\)
	\(\mathrm{lb\cdot sec^2/in^4}\)	\(10^6\ \mathrm{psi}\)	\(10^6\ \mathrm{psi}\)	\(10^6\ \mathrm{psi}\)	\(10^6\ \mathrm{psi}\)	\(10^6\ \mathrm{psi}\)	\(10^6\ \mathrm{psi}\)
mat_1	0.057	20.59	1.42	1.42	0.87	0.87	0.87	0.42	0.42	0.42

Table 10 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

Result

Table 11 Results

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