10. H modeling#
10.1. Characteristics of modeling#
The model is composed of 21 TUYAU_3M elements based on SEG4 meshes. The section is hollow circular with radius \(\mathrm{0,1}\) and thickness \(\mathrm{0,01}\).
The distributed effort is imposed according to axis \(y\). So the flexure takes place around \(z\).
10.2. Characteristics of the mesh#
It consists of 21 SEG3 stitches, transformed into SEG4 meshes. The length of the pipe is \(L=6m\).
10.3. Tested sizes and results#
10.3.1. Travel#
Analytical Results |
|
\({D}_{y}\mathit{maxi}\) at point \(x=3.115977734\) |
9.38888E-03 |
10.3.2. Cross-sectional reactions#
Analytical Results |
|
\({R}_{\mathit{Oy}}\) |
-6.0000E+03 |
\({R}_{\mathit{By}}\) |
-1.2000E+04 |
10.3.3. Internal efforts#
Analytical Results |
|
\({V}_{y}(x=0)\) |
6.0000E+03 |
\({V}_{y}(x=L=6)\) |
-1.2000E+04 |
\(\mathrm{MFZ}\) in \(x=2\sqrt{3}\) |
-1.3856E+04 |
10.3.4. Constraints#
They are calculated at the abscissa point \(x=\frac{L\sqrt{3}}{3}\) which corresponds to the maximum moment: \({M}_{z}(x)=\frac{-1000}{9\sqrt{(3)}}{L}^{3}=-13856.41\mathrm{N.m}\)
For the angle 0° on the circumference of the pipe (the origin of the angles being the \(z\) axis), the constraints are zero, and for the 90° angle, they are maximum: \({\sigma }_{\mathrm{xx}}^{\mathrm{max}}=\frac{{M}_{z}^{\mathrm{max}}(R-e/2)}{{I}_{z}}=-4.87363E+07\mathrm{Pa}\)
Reference |
Tolerance |
|
\({\sigma }_{\mathrm{xx}}(\alpha =0)\) |
0 |
|
\({\sigma }_{\mathrm{xx}}(\alpha =90)\) |
-4.87363E+07 |
|
\(\mathrm{MFZ}\) |
-1.3856E+04 |
|