3. Modeling A#
3.1. Characteristics of modeling#
The modeling mesh is shown in the figure below:
3.2. Characteristics of the mesh#
The dimensions of the geometry:
\(L_x = L_y = 10.0~cm\).
\(e_x = e_y = 0.2~cm\).
All the nodes are at \(z=0\), except for one of the nodes in \(\color{green}{\blacklozenge}\) which is at \(z = -1.0~cm\).
The mesh consists only of discrete ones:
« DIS_T_D_N » affected on solid corners
« DIS_T_D_L » assigned for the contact in the global coordinate system, or local..
« DIS_TR_D_L » affected on \(\color{green}{\blacklozenge}\).
3.3. Mechanical characteristics#
The only characteristics are for discrete elements. These characteristics are not physical, they only serve to give a certain stiffness to the system.
3.4. Loads#
Displacements imposed on solid \(A\):
- left{
right.
with
- left{
begin {aligned} f_x = [1.0, 1.5, 3.0] ~~en~ [Hz] ~~en~ [Hz] ~~and~~omega_x = [0.004, 0.0016, 0.00352] ~~en~ [m]\ f_y = [2.0, 3.0, 1.0] ~~en~ [Hz] ~~en~ [Hz] ~~and~~omega_y = [0.006, 0.0024, 0.00528] ~~en~ [m] end {aligned}
right.
3.5. Tested sizes and results#
The quantities tested are the reactions to the nodes \(A\) \(B\),, \(C\), \(D\) at a few moments. The values tested are those that are significant, i.e. sufficiently large in relation to the maximum effort used to calculate the residue.
Instant |
Node A: FX |
Node A: FX |
Node A: FY |
Node C: FX |
Node D: FX |
Node D: FX |
1.00000000e-01 |
… |
… |
-3.36488601e+01 |
-1.63414366e+01 |
-1.27649757e+01 |
|
2.33333333e-01 |
… |
… |
-1.06940776e+02 |
-2.66028238e+01 |
-2.07804949e+01 |
|
4.41666667e-01 |
… |
… |
5.02724631e+01 |
-1.64566044e+01 |
1.28142905e+01 |
|
8.66666667e-01 |
… |
-3.84275614e+05 |
… |
-2.65002717e+01 |
… |
|
1.20000000e+00 |
… |
-5.32150617e+05 |
-1.86168657e+02 |
-1.04159414e+02 |
… |
|
1.20833333e+00 |
… |
5.35867910e+05 |
-1.78399244e+02 |
-1.04411434e+02 |
… |
|
1.72500000e+00 |
5.30153032e+05 |
7.64914825e+05 |
-2.70948599e+01 |
2.67592384e+01 |
… |
|
2.05000000e+00 |
-6.30026951e+05 |
-9.09083998e+05 |
… |
… |
… |
|
2.05833333e+00 |
6.32592934e+05 |
9.12814600e+05 |
… |
… |
… |
|
2.06666667e+00 |
-6.35167998e+05 |
-9.16512651e+05 |
… |
… |
… |
|
2.07500000e+00 |
6.37696352e+05 |
9.20174770e+05 |
… |
… |
… |
|
2.08333333e+00 |
-6.40304070e+05 |
-9.23914488e+05 |
-3.34371231e+01 |
… |
… |
|
2.09166667e+00 |
6.42818982e+05 |
9.27574683e+05 |
-5.96794295e+01 |
-1.19380057e+01 |
-1.19380057e+01 |
… |
2.10000000e+00 |
-6.45412230e+05 |
-9.31292085e+05 |
-8.38400109e+01 |
-2.79445966e+01 |
-2.79445966e+01 |
… |
2.10833333e+00 |
6.47958993e+05 |
9.34976978e+05 |
-1.05693798e+02 |
-4.27956396e+01 |
… |
|
2.11666667e+00 |
-6.50517861e+05 |
-9.38674424e+05 |
-1.25057816e+02 |
-5.63467583e+01 |
… |
|
2.12500000e+00 |
6.53096602e+05 |
9.42374684e+05 |
-1.41791607e+02 |
-6.84781500e+01 |
… |
|
2.16666667e+00 |
-6.65849454e+05 |
-9.60844561e+05 |
-1.84000040e+02 |
-1.05390132e+02 |
-1.05390132e+02 |
… |
2.17500000e+00 |
6.68494718e+05 |
9.64546960e+05 |
-1.84294746e+02 |
-1.07873147e+02 |
… |
|
2.18333333e+00 |
-6.70964837e+05 |
-9.68239481e+05 |
-1.82086337e+02 |
-1.08778688e+02 |
-1.08778688e+02 |
… |
2.19166667e+00 |
6.73622587e+05 |
9.71933784e+05 |
-1.77526327e+02 |
-1.08171216e+02 |
… |
|
2.20000000e+00 |
-6.76082637e+05 |
-9.75635264e+05 |
-1.70790621e+02 |
-1.06132490e+02 |
-1.06132490e+02 |
… |
2.35000000e+00 |
-7.22218515e+05 |
-1.04206748e+06 |
… |
1.22029202e+01 |
-1.24934727e+01 |
|
2.40000000e+00 |
-7.37609448e+05 |
-1.06421815e+06 |
… |
1.76310802e+01 |
-1.28950605e+01 |
|
2.88333333e+00 |
-8.86135009e+05 |
-1.27857177e+06 |
… |
… |
… |
|
2.95000000e+00 |
-9.06578177e+05 |
-1.30808051e+06 |
… |
… |
… |
|
2.95833333e+00 |
9.09253750e+05 |
1.31207994e+06 |
… |
… |
… |
|
2.96666667e+00 |
-9.11697447e+05 |
-1.31547443e+06 |
… |
… |
… |
|
2.97500000e+00 |
9.14376717e+05 |
1.31946439e+06 |
… |
… |
… |
|
2.98333333e+00 |
-9.16821189e+05 |
-1.32287620e+06 |
… |
… |
… |
|
2.99166667e+00 |
9.19495195e+05 |
1.32684103e+06 |
… |
… |
… |
|
3.00000000e+00 |
-9.21949341e+05 |
-1.33028560e+06 |
… |
… |
… |
|
3.00833333e+00 |
9.24609434e+05 |
1.33421035e+06 |
… |
… |
… |
|
3.01666667e+00 |
-9.27081469e+05 |
-1.33770190e+06 |
… |
… |
… |
|
3.02500000e+00 |
9.29720049e+05 |
1.34157331e+06 |
… |
… |
… |
|
3.03333333e+00 |
-9.32216790e+05 |
-1.34512392e+06 |
… |
… |
… |
|
3.04166667e+00 |
9.34827975e+05 |
1.34893130e+06 |
… |
… |
… |
|
3.05000000e+00 |
-9.37354236e+05 |
-1.35255007e+06 |
… |
… |
… |
|
3.05833333e+00 |
9.39934386e+05 |
1.35628605e+06 |
… |
… |
… |
|
3.06666667e+00 |
-9.42492550e+05 |
-1.35997850e+06 |
… |
… |
… |
|
3.50833333e+00 |
1.07820043e+06 |
1.55587011e+06 |
… |
… |
… |
|
4.12500000e+00 |
1.26774800e+06 |
1.82932535e+06 |
… |
… |
… |
|
4.17500000e+00 |
1.28314238e+06 |
1.85152117e+06 |
… |
… |
… |
|
4.18333333e+00 |
-1.28565158e+06 |
-1.85513820e+06 |
… |
… |
… |
|
4.19166667e+00 |
1.28827122e+06 |
1.85891106e+06 |
… |
… |
… |
|
4.20000000e+00 |
-1.29076795e+06 |
-1.86253213e+06 |
… |
… |
… |
|
4.20833333e+00 |
1.29339850e+06 |
1.86629814e+06 |
… |
… |
… |
|
4.25000000e+00 |
-1.30612817e+06 |
-1.88472416e+06 |
… |
… |
… |
|
5.45833333e+00 |
… |
2.42075067e+06 |
… |
… |
… |