Pipe

The pipe section is circular and is characterized by its outer radius and its thickness (in that order). There are 8 integration points equally distributed along the circumference. In local coordinates, the radius at which the integration points are located is $\sqrt{(\xi^2+1)/2}$, where $\xi=r/R$, $r$ being the inner radius and $R$ the outer radius. The weight for each integration point is given by $\pi*(1-\xi^2)/8$ [12].