Box beam#

Problem description#

../../../_images/examplebox0.png

Figure 42 Cross section of the box beam [YU2012].#

This example is a thin-walled box beam whose cross section is depicted in Fig. 42 [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 24 and Table 25. Cross-sectional properties are given in Table 26 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 and materials.xml.

../../../_images/examplebox1.png

Figure 43 Base points, Base lines and Segments of the box beam cross section.#

../../../_images/examplebox.png

Figure 44 Meshed cross section viewed in Gmsh.#

Table 24 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

0.0001353

20.59

1.42

1.42

0.87

0.87

0.696

0.30

0.30

0.34

Table 25 Layups#

Name

Layer

Material

Ply thickness

Orientation

Number of plies

\(\mathrm{in}\)

\(\circ\)

layup1

1

mat_1

0.05

-15

6

Result#

Table 26 Results#

Component

Value

Reference [YU2012]

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

\(\phantom{-}1.437 \times 10^6\)

\(\phantom{-}1.437 \times 10^6\)

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

\(\phantom{-}9.026 \times 10^4\)

\(\phantom{-}9.027 \times 10^4\)

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

\(\phantom{-}3.941 \times 10^4\)

\(\phantom{-}3.943 \times 10^4\)

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

\(\phantom{-}1.074 \times 10^5\)

\(\phantom{-}1.074 \times 10^5\)

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

\(-5.201 \times 10^4\)

\(-5.201 \times 10^4\)

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

\(-5.635 \times 10^4\)

\(-5.635 \times 10^4\)

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

\(\phantom{-}1.679 \times 10^4\)

\(\phantom{-}1.679 \times 10^4\)

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

\(\phantom{-}6.621 \times 10^4\)

\(\phantom{-}6.621 \times 10^4\)

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

\(\phantom{-}1.725 \times 10^5\)

\(\phantom{-}1.725 \times 10^5\)