1. Reference problem#

1.1. Geometry#

The study concerns a pipe comprising two straight pipes and an elbow [Figure 1.1-a].

The geometric data for the problem is as follows:

  • the length \({L}_{G}\) of the two straight pipes is \(3m\),

  • the initial radius \(\mathrm{Rc}\) of the elbow is \(0.3m\),

  • Elbow angle \(\theta\) is 90 degrees,

  • the thickness of the straight pipes and the elbow is \(0.02m\),

  • and the outside radius \(\text{Re}\) of the straight pipes and the elbow is \(0.2m\).

_images/100013EA0000288400001F36789D77AD3C40BA9C.svg

Figure 1.1-a

Note:

The geometry of the problem is symmetric with respect to the plane \((A,X,Y)\) .

1.2. Material properties#

Isotropic linear elastic material. The properties of the material are those of \(\mathrm{A42}\) steel:

  • Young’s modulus:

\(E=1.8{10}^{11}\mathrm{Pa}\)

  • Poisson’s ratio:

\(\nu =0.3\)

1.3. Boundary conditions and loads#

  • Boundary conditions: embedding at the level of section \(A\),

  • Loading: constant force \(\mathrm{FY}\) directed along the \(Y\) axis and applied to section \(B\).

The value of \(\mathrm{FY}\) is calculated from:

  • of the average radius: \(\mathrm{RMOY}=0.19\),

  • of the total force applied: \(\mathrm{FTOT}=500000N/{m}^{2}\),

His expression is as follows:

\(\mathrm{FY}=\mathrm{FTOT}/(2\pi \mathrm{RMOY})(\simeq 418828.8)\)

  • The Von Mises limit constraint is \(2.0E+09N/{m}^{2}\)