1. Reference problem#
1.1. Material properties#
The material properties and the characteristics specific to the RCC -M calculation are as follows:
Young’s modulus: \(E\mathrm{=}2.E+05\mathit{MPa}\);
material constants for the calculation of \(\mathrm{Ke}\): \(n=0.2\), \(m=\mathrm{2 }\);
Young’s modulus of reference: \({E}_{\mathit{REFE}}\mathrm{=}2.E+05\mathit{MPa}\);
allowable stress: \(\mathit{Sm}=200\mathit{MPa}\).
The Wöhler curve is defined analytically: \({N}_{\mathrm{adm}}=\frac{{5.10}^{5}}{{S}_{\mathrm{alt}}}\)
1.2. Evolution of constraints#
The constraints on the analysis segment are not calculated but read directly from a table. The only non-zero component of the stress tensor is \({\mathrm{\sigma }}_{\mathit{yy}}\). Several situations are considered. These situations do not aim to represent a specific real transient, but to cover all possible constraints (constant, linear or non-linear evolution of the stress in thickness).
Instant |
Thermal constraints of situations 1 and 2 |
Instant |
Thermal constraints of situation 3 |
||||
Abscissor |
Abscissor |
||||||
0 |
1 |
2 |
0 |
1 |
2 |
||
1 |
50 |
100 |
150 |
1, 5 |
50 |
100 |
150 |
2 |
0 |
50 |
-100 |
2, 5 |
0 |
50 |
-100 |
3 |
0 |
0 |
50 |
3, 5 |
0 |
0 |
50 |
4 |
0 |
0 |
0 |
||||
Table 1.2-1: Definition of constraints \({\mathrm{\sigma }}_{\mathit{yy}}\) (in \(\mathit{MPa}\)) for the moments of situation 1 and situation 2 as a function of the curvilinear abscissa
In this example, moments and pressure are defined by two torsors and four unit tensors. Again, only the \({\mathrm{\sigma }}_{\mathit{yy}}\) constraint is non-zero in these tensors.
Unit tensor |
\({\mathrm{\sigma }}_{\mathit{yy}}\) |
||
Abscissor |
|||
0 |
1 |
2 |
|
\({\mathit{Mom}}_{X}\) |
50 |
0 |
0 |
\({\mathit{Mom}}_{Y}\) |
0 |
50 |
0 |
\({\mathit{Mom}}_{Z}\) |
0 |
0 |
100 |
\(\mathit{Pres}\) |
50 |
0 |
0 |
\({P}_{A}\) |
|
|
|
|
|
|
|
|||
Situation 1 |
1 |
10 |
10 |
1 |
1 |
-1 |
-1.5 |
-10 |
1 |
0.1 |
Situation 2 |
1 |
10 |
10 |
1 |
1 |
-1 |
-1.5 |
-10 |
1 |
0.1 |
Situation 3 |
0.4 |
1 |
0.4 |
0.4 |
0 |
-0.6 |
1 |
-1 |
-1.5 |
Table 1.2-2: Definition of torsors on moments (in N.mm) and pressure (in MPa) for situations 1, 2 and 3