Pipe

Pipe cross-section example with straight and arc baselines.

Overview

Figure 23 Cross section of the pipe [YU2005].

This example has the cross-section as shown in Figure 23 [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 Material properties and Layups.

Table 18 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 19 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

Figure 24 Base points and Base lines of the pipe cross section.

Figure 25 Segments of the pipe cross section.

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Input

• pipe.xml

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Run the example

prevabs -i pipe.xml --hm

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Output

Figure 26 Cross section viewed in gmsh.

• pipe.png

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Analysis Result

Table 20 Results

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