8. F modeling#
8.1. Characteristics of modeling#
Full circular section, radius \(\mathrm{0.025m}\). The calculated characteristics are then used directly in a calculation of a straight beam (of length \(L\mathrm{=}\mathrm{1m}\)), in pure tension (\(F\mathrm{=}\mathrm{1000N}\)). Young’s modulus is \(2.E11\mathit{Pa}\). The characteristics of the section are given to AFFE_CARA_ELEM using the TABLE_CARA keyword.
8.2. Characteristics of the mesh#
Number of meshes: 52 TRIA6, 299 QUAD8
8.3. Benchmark solution#
\(A=\pi {R}^{2}=1.9635E\text{-}3{m}^{2}\); \({I}_{y}={I}_{z}=\frac{\pi }{4}{R}^{4}=3.06796E\text{-}7{m}^{4}\); \({A}_{y}={A}_{z}=\frac{10}{9}\); \(C={I}_{x}=2{I}_{y}=2{I}_{z}\)
Pure traction of a beam with a solid circular section, of length \(L\mathrm{=}\mathrm{1m}\), subjected to a force \(F\mathrm{=}\mathrm{1000N}\): \(u(x)=\frac{Fx}{EA}\) \(u(L)=\frac{FL}{EA}=2.54648E\text{-}6m\)
8.4. Tested sizes and results#
For the symmetrized section following \(\mathrm{OY}\), the geometric characteristics are:
Identification |
Reference |
Value |
Tolerance |
\(A\) |
|
1.96E-03 |
|
\({\mathrm{CDG}}_{Y}\) |
|
0.00E+00 |
|
\({\mathrm{CDG}}_{Z}\) |
|
0.00E+00 |
|
\({\mathrm{IY}}_{G}\) |
|
3.07E-07 |
|
\({\mathrm{IZ}}_{G}\) |
|
3.07E-07 |
|
\({\mathrm{IYZ}}_{G}\) |
|
0.00E+00 |
|
\(\mathrm{IY}\) |
|
3.07E-07 |
|
\(\mathrm{IZ}\) |
|
3.07E-07 |
|
\({Y}_{\mathrm{MIN}}\) |
|
-2.50E-02 |
|
\({Y}_{\mathrm{MAX}}\) |
|
2.50E-02 |
|
\({Z}_{\mathrm{MIN}}\) |
|
-2.50E-02 |
|
\({Z}_{\mathrm{MAX}}\) |
|
2.50E-02 |
|
\(\mathrm{JX}\) |
|
6.14E-07 |
|
\(\mathrm{AY}\) |
|
1.17E+00 |
|
\(\mathrm{AZ}\) |
|
1.17E+00 |
|
\(\mathrm{EY}\) |
|
0.00E+00 |
|
\(\mathrm{EZ}\) |
|
0.00E+00 |
|
\(\mathrm{JG}\) |
|
0.00E+00 |
|
For the beam tension calculation, the result is:
Identification |
Reference |
Value |
Tolerance |
DEPL |
|
2.55E-06 |
1.00E-03 |
Forc_noda |
ANALYTIQUE |
1.00E+03 |
1.00E-03 |