9. G modeling#
9.1. Characteristics of modeling#
Solid rectangular section, width \(\mathrm{0.02m}\) and height \(\mathrm{0.05m}\). It is divided into two rectangles of respective heights \(\mathrm{0.025m}\), in order to test the calculation of the characteristics on groups of cells for a network consisting here of two parallel beams, between two floors distant from \(L=\mathrm{0.0002m}\) (which makes it possible to obtain characteristics (shear coefficient) very close to that of the complete section).
with b = 0.01, h=0.025
9.2. Characteristics of the mesh#
Number of stitches: 32 QUAD8
9.3. Benchmark solution#
Geometric characteristics for the complete section and for each half-section:
LIEU A CDG_Y CDG_Z IY_G IZ_G IYZ_G
All 1.00E-03 0.0 0.0 2.08E-07 3.33E-08 0.0
GR1 5.00E-04 0.0 -1.25E-02 2.60E-08 1.67E-08 0.0
GR2 5.00E-04 0.0 1.25E-02 2.60E-08 1.67E-08 0.0
LIEU Y_P Z_P IY_P IZ_P IYZ_P IY IZ
All 0.00E+00 0.00E+00 2.08E-07 3.33E-08 0.0 3.33E-08 2.08E-07
GR1 0.00E+00 0.00E+00 1.04E-07 1.67E-07 1.67E-08 0.0 1.67E-08 1.04E-07
GR2 0.00E+00 0.00E+00 1.04E-07 1.67E-07 1.67E-08 0.0 1.67E-08 1.04E-07
Shear coefficients: for each rectangular section: \({A}_{y}={A}_{z}=1.2\)
9.4. Tested sizes and results#
For the complete section, the geometric and mechanical characteristics are:
Identification |
Reference |
% difference |
\(A\) |
1.0000000E—03 |
0.00E+00 |
\(\mathit{ALPHA}\) |
9.0000000E+01 |
0.00E+00 |
\(\mathit{AY}\) |
1.2000000E+00 |
—0.004 |
\(\mathit{AZ}\) |
1.2000000E+00 |
—0.065 |
\({\mathit{CDG}}_{Y}\) |
0.0000000E+00 |
—1.03E—19 |
\({\mathit{CDG}}_{Z}\) |
0.0000000E+00 |
—2.67E—19 |
\(\mathit{JX}\) |
9.9805000E—08 |
—0.124 |
\(\mathit{EY}\) |
0.0000000E+00 |
1.55E—18 |
\(\mathit{EZ}\) |
0.0000000E+00 |
—4.79E—18 |
\({\mathit{IY}}_{G}\) |
2.0833333E—07 |
1.60E—06 |
\({\mathit{IYZ}}_{G}\) |
0.0000000E+00 |
—1.40E—24 |
\({\mathit{IZ}}_{G}\) |
3.3333330E—08 |
1.00E—05 |
\(\mathit{PCTY}\) |
0.0000000E+00 |
4.90E—18 |
\(\mathit{PCTZ}\) |
0.0000000E+00 |
1.82E—18 |
\({Y}_{\mathit{MAX}}\) |
2.5000000E—02 |
0.00E+00 |
\({Y}_{\mathit{MIN}}\) |
—2.5000000E—02 |
0.00E+00 |
\({Z}_{\mathit{MAX}}\) |
1.0000000E—02 |
1.73E—14 |
\({Z}_{\mathit{MIN}}\) |
—1.0000000E—02 |
1.73E—14 |
For the two disjoint groups, we obtain:
Location |
Identification |
Reference |
% difference |
\(\mathit{GR2}\) |
|
5.00000E—04 |
2.17E—14 |
\(\mathit{GR1}\) |
|
5.00000E—04 |
4.34E—14 |
\(\mathit{TOUT}\) |
|
1.20000E+00 |
—0.064 |
\(\mathit{GR1}\) |
|
1.20000E+00 |
—0.065 |
\(\mathit{GR2}\) |
|
1.20000E+00 |
—0.065 |
\(\mathit{GR1}\) |
|
1.20000E+00 |
—0.065 |
\(\mathit{GR2}\) |
|
1.20000E+00 |
—0.065 |
\(\mathit{GR1}\) |
|
0.00000E+00 |
1.59E—19 |
\(\mathit{GR2}\) |
|
0.00000E+00 |
2.11E—19 |
\(\mathit{GR1}\) |
|
1.25000E—02 |
—1.39E—14 |
\(\mathit{GR2}\) |
|
—1.25000E—02 |
—4.16E—14 |
\(\mathit{GR1}\) |
|
2.60417E—08 |
—1.28E—04 |
\(\mathit{GR2}\) |
|
2.60417E—08 |
—1.28E—04 |
\(\mathit{GR1}\) |
|
0.00000E+00 |
—1.58E—24 |
\(\mathit{GR2}\) |
|
0.00000E+00 |
1.98E—24 |
\(\mathit{GR1}\) |
|
1.66667E—08 |
—2.00E—04 |
\(\mathit{GR2}\) |
|
1.66667E—08 |
—2.00E—04 |