1. Modeling A#
1.1. But#
In this modeling, we want to validate the modelling/characteristic pairs DIS_T /K_T_D_N and DIS_T /A_T_D_N as well as the pairs DIS_T /K_T_D_L and DIS_T /A_T_D_L, in coordinate system GLOBAL and in coordinate system LOCAL. To do this, the tests EPX bm_str_resl_nl (calculation 1) and bm_str_resg_nl (calculation 2) are reproduced. This modeling also validates the use of circular beams in CALC_EPX.
1.2. Description#
1.2.1. Geometry and modeling#
|
|
System 1 |
System 2 |
Two systems are compared. In both cases it is a \(\mathit{AB}\) (POU_D_E) beam of length \(1m\) connected to a spring in \(B\). A mass of \(1000\mathit{kg}\) is also added to point \(B\). In the first system, the beam is connected to a point spring (DIS_T /K_T_D_N+A_T_D_N), in the second to a line spring \(\mathit{BC}\) oriented along \(Y\) (DIS_T /K_T_D_L+A_T_D_L).
Circular cross section of the beam: R = 0.02
Correspondence of node groups to the points shown in the figure above.
Points |
System 1 |
System 2 |
|
A |
T_0_0_0 |
P_0_0_0 |
P_0_0 |
B |
T_1_0_0 |
P_1_0_0 |
|
C |
P_1_L_0 |
1.2.2. Material properties#
Beam:
Young’s module: \(2E11\mathit{Pa}\)
Poisson’s ratio: \(0.\)
Density: \(7800\mathit{kg}/{m}^{3}\)
Springs/ shock absorbers:
Elements in local coordinate system (DIS_T/SEG2 of calculation 1 only):
Stiffness according to \(X\): \(75000.N/m\)
Stiffness according to \(Y\): \(60000.N/m\)
Stiffness according to \(Z\): \(50000.N/m\)
Depreciation according to \(X\): \(7500.N/(m/s)\)
Depreciation according to \(Y\): \(6000.N/(m/s)\)
Depreciation according to \(Z\): \(5000.N/(m/s)\)
Global coordinate system elements (DIS_T of calculation 2 and DIS_T/POI1 of calculation 1):
Stiffness according to \(X\): \(60000.N/m\)
Stiffness according to \(Y\): \(75000.N/m\)
Stiffness according to \(Z\): \(50000.N/m\)
Depreciation according to \(X\): \(6000.N/(m/s)\)
Depreciation according to \(Y\): \(7500.N/(m/s)\)
Depreciation according to \(Z\): \(5000.N/(m/s)\)
1.2.3. Boundary conditions and loads#
Node \(A\) is embedded for both systems. For system 2, node \(C\) is also embedded. Two calculations are carried out.
Calculation 1:
In both systems, a constant force with a value of \(1000N\) is imposed in \(B\) according to \(Y\).
Calculation 2:
In both systems, constant forces with a value of \(1000N\) are imposed according to \(X\), \(Y\), and \(Z\) in \(B\).
1.2.4. Reference values#
The reference values are given by the EUROPLEXUS tests mentioned in 1.1.
1.3. Tested values#
1.3.1. Calculus 1#
GROUP_NO |
NUME_ORDRE |
Component |
Reference |
Reference Value |
|
P_1_0_0 |
91609 |
|
|
3.52220E-03 |
|
T_1_0_0 |
91609 |
|
\(\mathit{DY}\) |
|
1.29492E-02 |
1.3.2. Calcul2#
GROUP_NO |
NUME_ORDRE |
Component |
Reference |
Reference Value |
|
P_1_0_0 |
25064 |
|
|
-1.62766E-05 |
|
T_1_0_0 |
25064 |
|
|
-1.62766E-05 |
|
P_1_0_0 |
25064 |
|
|
3.67804E-03 |
|
T_1_0_0 |
25064 |
|
|
3.67804E-03 |
|
P_1_0_0 |
25064 |
|
|
4.58138E-03 |
|
T_1_0_0 |
25064 |
|
|
4.58138E-03 |