4. B modeling#
4.1. Characteristics of modeling#
This is the section of a circle with an outer radius \(R\mathrm{=}\mathrm{0.025m}\) and a thickness of \(\mathrm{0.005m}\). We represent only a quarter of the section. This modeling makes it possible to test the CARA_GEOM keyword from POST_ELEM, which is also used by MACR_CARA_POUTRE to calculate the geometric characteristics of a flat area.
4.2. Characteristics of the mesh#
30 QUAD8 stitches.
4.3. Benchmark solution#
For the full section:
\(A=\pi \left[{R}^{2}-{(R-\mathrm{ep})}^{2}\right]=1.76714E\text{-}04{m}^{2}\)
\({I}_{y}={I}_{z}=\frac{\pi }{4}\left[{R}^{4}-{(R-\mathrm{ep})}^{4}\right]=1.81132E\text{-}7{m}^{4}\)
\({I}_{p}=2{I}_{y}=2{I}_{z}\)
4.4. Tested sizes and results#
Identification |
Reference |
% difference |
\({A}_{M}\) |
1.76714E—04 |
—7.76E—05 |
\({\mathit{CDG}}_{\text{Y-M}}\) |
1.438288E—02 |
—1.25E—04 |
\({\mathit{CDG}}_{\text{Z-M}}\) |
1.438288E—02 |
—1.25E—04 |
\({\mathit{IY}}_{\text{G-M}}\) |
8.7265757E—09 |
—2.78E—04 |
\({\mathit{IZ}}_{\text{G-M}}\) |
8.7265757E—09 |
—2.78E—04 |
\({\mathit{IYZ}}_{\text{G-M}}\) |
—7.72837E—09 |
—3.83E—04 |
\(A\) |
7.0685745E—04 |
—7.76E—05 |
\({\mathit{CDG}}_{Y}\) |
0.00000E+00 |
0 |
\({\mathit{CDG}}_{Z}\) |
0.00000E+00 |
0 |
\({\mathit{IY}}_{G}\) |
1.81132E—07 |
—4.19E—06 |
\({\mathit{IZ}}_{G}\) |
1.81132E—07 |
—4.19E—06 |
\({\mathit{IYZ}}_{G}\) |
0.00000E+00 |
|
\(\mathit{IY}\) |
1.81132E—07 |
—4.19E—06 |
\(\mathit{IZ}\) |
1.81132E—07 |
—4.19E—06 |
\({Y}_{\mathit{MIN}}\) |
—2.50000E—02 |
0.00E+00 |
\({Y}_{\mathit{MAX}}\) |
2.50000E—02 |
0.00E+00 |
\({Z}_{\mathit{MIN}}\) |
—2.50000E—02 |
0.00E+00 |
\({Z}_{\mathit{MAX}}\) |
2.50000E—02 |
0.00E+00 |