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

0.10%

\({\sigma }_{\mathrm{xx}}(\alpha =90)\)

-4.87363E+07

1.00%

\(\mathrm{MFZ}\)

-1.3856E+04

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