5. C modeling#
5.1. Characteristics of modeling#
Hollow rectangular section of which a quarter is represented. 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.
\(\mathit{Hx}\mathrm{=}\mathrm{0.02m}\), \(\mathit{Hy}\mathrm{=}\mathrm{0.05m}\), \(\mathit{epx}\mathrm{=}\mathrm{0.002m}\), \(\mathit{epy}\mathrm{=}\mathrm{0.005m}\).
5.2. Characteristics of the mesh#
The coordinates of the nodes are:
\(\mathit{N1}\) 8.00E-03 0.00E+00 \(\mathit{N2}\) 8.00E-03 2.00E-03 2.00E-02 \(\mathit{N3}\) 0.00E-03 2.00E-02 \(\mathit{N4}\) 0.00E-02 \(\mathit{N5}\) 1.00E-02 2.50E-02 \(\mathit{N6}\) 1.00E-02 2.50E-02 1.00E-02 0.00E+00 E-02 0.00E+00 \(\mathit{N7}\) 8.00E-03 2.00E-03 6.6667E-03 6.6667E-03 6.6667E-03 6.6667E-03 \(\mathit{N8}\) 8.00E-03 1.3333E-02 \(\mathit{N9}\) 4.00E-03 2.00E-02 \(\mathit{N10}\) 5.00E-03 2.50E-02 \(\mathit{N11}\) 1.00E-02 1.66667E-02 \(\mathit{N12}\) 1.00E-02 8.3333E-03 |
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5.3. Benchmark solution#
\(A={h}_{y}{h}_{z}-({h}_{y}-2{\mathrm{ep}}_{y})({h}_{z}-2{\mathrm{ep}}_{z})=3.6E\text{-}04{m}^{2}\)
\({I}_{x}=\frac{1}{12}\left[{h}_{y}{h}_{z}^{3}-({h}_{y}-2{\mathrm{ep}}_{y}){({h}_{z}-2{\mathrm{ep}}_{z})}^{3}\right]=1.23E\text{-}7{m}^{4}\)
\({I}_{y}=\frac{1}{12}\left[{h}_{z}{h}_{y}^{3}-({h}_{z}-2{\mathrm{ep}}_{z}){({h}_{y}-2{\mathrm{ep}}_{y})}^{3}\right]=1.968E\text{-}8{m}^{4}\)
5.4. Tested sizes and results#
Identification |
Reference |
% difference |
\(A\) |
3.60000E—04 |
—2.26E—13 |
\(\mathit{ALPHA}\) |
9.00000E+01 |
0.00E+00 |
\({\mathit{CDG}}_{Y}\) |
0.00000E+00 |
0 |
\({\mathit{CDG}}_{Z}\) |
0.00000E+00 |
0.00E+00 |
\({\mathit{IY}}_{G}\) |
1.23000E—07 |
—6.46E—14 |
\({\mathit{IYZ}}_{\text{G-M}}\) |
—1.11111E—09 |
1.00E—04 |
\({\mathit{IZ}}_{G}\) |
1.96800E—08 |
—2.52E—13 |
\(\mathit{IY}\) |
1.96800E—08 |
—2.52E—13 |
\(\mathit{IZ}\) |
1.23000E—07 |
—6.46E—14 |
\({R}_{\mathit{MAX}}\) |
2.69258E—02 |
—6.54E—04 |
\({Y}_{\mathit{MAX}}\) |
2.50000E—02 |
0.00E+00 |
\({Y}_{\mathit{MIN}}\) |
—2.50000E—02 |
0.00E+00 |
\({Z}_{\mathit{MAX}}\) |
1.00000E—02 |
0.00E+00 |
\({Z}_{\mathit{MIN}}\) |
—1.00000E—02 |
0.00E+00 |