Pipe#

Probelm description#

../../../_images/examplepipe0.png

Figure 45 Cross section of the pipe [YU2005].#

This example has the cross section as shown in Fig. 45 [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 27 and Table 28. Cross-sectional properties are given in Table 29 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.

../../../_images/examplepipe1.png

Figure 46 Base points and Base lines of the pipe cross section.#

../../../_images/examplepipe2.png

Figure 47 Segments of the pipe cross section.#

../../../_images/examplepipe.png

Figure 48 Meshed cross section viewed in Gmsh.#

Table 27 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 28 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 29 Results#

Component

Value

Reference [YU2005]

\(S_{11}\) [\(\mathrm{lb}\)]

\(\phantom{-}1.03892 \times 10^7\)

\(\phantom{-}1.03890 \times 10^7\)

\(S_{22}\) [\(\mathrm{lb}\)]

\(\phantom{-}7.85800 \times 10^5\)

\(\phantom{-}7.84299 \times 10^5\)

\(S_{33}\) [\(\mathrm{lb}\)]

\(\phantom{-}3.31330 \times 10^5\)

\(\phantom{-}3.29002 \times 10^5\)

\(S_{14}\) [\(\mathrm{lb \cdot in}\)]

\(\phantom{-}9.74568 \times 10^4\)

\(\phantom{-}9.82878 \times 10^4\)

\(S_{25}\) [\(\mathrm{lb \cdot in}\)]

\(-8.02785 \times 10^3\)

\(-8.18782 \times 10^3\)

\(S_{36}\) [\(\mathrm{lb \cdot in}\)]

\(-5.14533 \times 10^4\)

\(-5.18541 \times 10^4\)

\(S_{44}\) [\(\mathrm{lb \cdot in^2}\)]

\(\phantom{-}6.89600 \times 10^5\)

\(\phantom{-}6.86973 \times 10^5\)

\(S_{55}\) [\(\mathrm{lb \cdot in^2}\)]

\(\phantom{-}1.88230 \times 10^6\)

\(\phantom{-}1.88236 \times 10^6\)

\(S_{66}\) [\(\mathrm{lb \cdot in^2}\)]

\(\phantom{-}5.38985 \times 10^6\)

\(\phantom{-}5.38972 \times 10^6\)