1. Reference problem#
1.1. Device description, A and B models#
The system studied is represented by the rheological model below. It is composed of a non-linear element M1 affected by behavior CHOC_ELAS_TRAC (between nodes N1 and N2), a linear element M2 (between nodes N1 and N2) affected by behavior ELAS and a mass Mass.
Figure 1.1-a : Device, **A and B models
Mesh characteristic: \(\Vert N1N2\Vert =0.10m\).
The equations governing the behavior of the nonlinear element are in [R5.03.17].
1.2. Device description, C and D models#
The system studied is represented by the rheological model below. It is composed of a non-linear element M2 affected by behavior CHOC_ELAS_TRAC (between nodes N2 and N3), linear elements M2, M3 (between nodes N1 and N2, N2 and N3) affected by behavior ELAS (between nodes N1 and N2, N2 and N3) affected by behavior and a mass Mass.
Figure 1.2-a: Device, C and D models.
Mesh characteristic: \(\Vert N1N2\Vert =\Vert N2N3\Vert =0.10m\).
The equations governing the behavior of the nonlinear element are in [R5.03.17].
1.3. Modellations#
The models tested are on elements DIS_T, mesh SEG2. The characteristics of the discrete elements are of the type: K_T_D_L.
Note: The units of the parameters must agree with the unit of effort, the unit of lengths [R5.03.17]. For all models the units are homogeneous to [N], [m].
1.3.1. A, B models#
This modeling makes it possible to test the nonlinear behavior of the isotropic work hardening type, in the local x-direction of the discrete, of the CHOC_ELAS_TRAC behavior with the DYNA_NON_LINE operator.
1.3.2. C, D modeling#
This modeling makes it possible to test the nonlinear behavior of the isotropic work hardening type, in the local x-direction of the discrete, of the CHOC_ELAS_TRAC behavior with the DYNA_VIBRA operator.
1.4. Properties of the elements#
1.4.1. A, B, C, D models#
The properties common to the models are those of the non-linear function [R5.03.17].
The table shows the x-axis and ordinate values of the function. It is extended linearly to the right.
X [m] |
0.00 |
0.200 |
0.200 |
0.500 |
0.700 |
0.950 |
1.000 |
Force [N] |
0.00 |
400.0 |
400.0 |
450.0 |
600.0 |
700.0 |
1000.0 |
Table 1.4.1-a ****: ******Axes and ordinates of the function. **
The figure shows the non-linear behavior used in the test cases.
1.4.2. A, B modeling#
Characteristics of the elements:
Modeling Behavior |
Types |
Values |
|
M1 |
D IS_T |
K_T_D_L |
Not applicable |
M_T_D_L |
\(0.0\) |
||
DIS_XXX_XXX |
Nonlinear function, array. |
||
\(\mathit{DIST}1=\mathit{DIST}2=0.0\) |
|||
M2 |
D IS_T |
K_T_D_L |
\({k}_{x}=300.0\), \({k}_{y}=300.0\), \({k}_{z}=300.0\) |
M_T_D_L |
\(m=50.0\) |
||
ELAS |
Not applicable |
1.4.3. C modeling#
Characteristics of the elements:
Modeling Behavior |
Types |
Values |
|
M2 |
D IS_T |
K_T_D_L |
Not applicable |
M_T_D_L |
\(0.0\) |
||
DIS_XXX_XXX |
Nonlinear function, array. |
||
\(\mathit{DIST}1=\mathit{DIST}2=0.0\) |
|||
M1, M3 |
D IS_T |
K_T_D_L |
\({k}_{x}=300.0\), \({k}_{y}=300.0\), \({k}_{z}=300.0\) |
M_T_D_L |
\(m=3.0\) |
||
ELAS |
Not applicable |
1.4.4. D modeling#
Characteristics of the elements:
Modeling Behavior |
Types |
Values |
|
M2 |
D IS_T |
K_T_D_L |
Not applicable |
M_T_D_L |
\(0.0\) |
||
DIS_XXX_XXX |
Nonlinear function, array. |
||
\(\textcolor[rgb]{0,0,1}{\mathit{DIST}1=0.50L;\mathit{DIST}2=0.25L}\) |
|||
M1, M3 |
D IS_T |
K_T_D_L |
\({k}_{x}=300.0\), \({k}_{y}=300.0\), \({k}_{z}=300.0\) |
M_T_D_L |
\(m=3.0\) |
||
ELAS |
Not applicable |
1.5. Boundary conditions and loads#
1.5.1. Modellations A#
Node N2 is stuck: \(\mathit{DX}=\mathit{DY}=\mathit{DZ}=0\).
Node N1 is free in the X direction and locked in y and z direction: \(\mathit{DY}=\mathit{DZ}=0\).
A displacement as a function of time is imposed on the node N 1 in the direction X. This load is a composition of 3 sines with 3 frequencies and 3 different amplitudes.
# Signal frequencies
f1, f2, f3 = 1.0*Hz, 1.5*Hz, 3.0*Hz
# Signal amplitudes
Rating = 2.5
a1, a2, a3 = 0.25*Coeff, 0.10*Coeff, 0.22*Coeff
def PyDepl (Inst):
w1, w2, w3 = 2.0*pi*f1, 2.0*pi*f2, 2.0*pi*f3
depl1, depl2, depl3 = a1*sin (W1*inst), a2*sin (W2*inst), a3*sin (W3*inst)
Return depl1+depl2+depl3
1.5.2. B models#
Node N2 is stuck: \(\mathit{DX}=\mathit{DY}=\mathit{DZ}=0\).
Node N1 is free in the X direction: \(\mathit{DY}=\mathit{DZ}=0\).
A displacement is imposed on the node N 1 in the direction X. This load is a ramp that allows the node to be moved and then to simulate a release attempt.
DePLT = DEFI_FONCTION ()
NOM_PARA = « INST « ,
VALE =(
0.0, 0.00,
1.0, -0.30,
),
)
1.5.3. C, D models#
Nodes N1, N3 are blocked: \(\mathit{DX}=\mathit{DY}=\mathit{DZ}=0\).
Displacement, speed, and acceleration are defined as follows:
# Signal frequencies
f1, f2, f3 = 1.0*Hz, 1.5*Hz, 3.0*Hz
w1, w2, w3 = 2.0*pi*f1, 2.0*pi*f2, 2.0*pi*f3
# Signal amplitudes
Coeff = 2.0
a1, a2, a3 = 0.25*Coeff, 0.10*Coeff, 0.22*Coeff
def PyDepl (Inst):
depl1, depl2, depl3 = a1*sin (W1*inst), a2*sin (W2*inst), a3*sin (W3*inst)
Return depl1+depl2+depl3
from PyVite (Inst):
vite1, speed2, speed3 = a1*w1*cos (W1*inst), a2*w2*cos (W2*inst), a3*w3*cos (W3*inst)
Return speed1+speed2+speed3
from PyAcce (Inst):
acce1 = -a1*w1*w1*w1*sin (W1*inst)
acce2 = -a2*w2*w2*sin (W2*inst)
acce3 = -a3*w3*w3*w3*sin (W3*inst)
Return acce1+acce2+acce3