.. _v5.01.111-modelisation_A: Modeling A ============== Characteristics of modeling ----------------------------------- The modeling mesh is shown in the figure below: .. figure:: figures/v5.01.111_maillage.png :width: 70% :align: center Modeling A, Geometry mesh. Characteristics of the mesh ---------------------------- The dimensions of the geometry: * :math:`L_x = L_y = 10.0~cm`. * :math:`e_x = e_y = 0.2~cm`. * All the nodes are at :math:`z=0`, except for one of the nodes in :math:`\color{green}{\blacklozenge}` which is at :math:`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 :math:`\color{green}{\blacklozenge}`. 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. Loads ----------- Displacements imposed on solid :math:`A`: .. math:: \ left\ { \ begin {aligned} D_x =\ sum_ {i=1} ^3\ omega_ {x_i} sin (2\ pi f_ {x_i} t)\\ D_y =\ sum_ {i=1} ^3\ omega_ {y_i} sin (2\ pi f_ {y_i} t) \ end {aligned} \ right. with .. math:: \ 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. .. figure:: figures/v5.01.111_deplacement_A.png :width: 70% :align: center Modeling A, Displacement of the center of gravity of the solid A. .. figure:: figures/v5.01.111_trajectoire.png :width: 70% :align: center Modeling A, Trajectory of the centers of gravity of solids. Tested sizes and results ------------------------------ The quantities tested are the reactions to the nodes :math:`A` :math:`B`,, :math:`C`, :math:`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. .. csv-table:: :width: 50% :align: center **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, ... , ... ,...