.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/LinearizedElasticity/Elas8.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_LinearizedElasticity_Elas8.py: Elas8 ===== A cantilever beam undergoing dynamic bending deformation. .. GENERATED FROM PYTHON SOURCE LINES 11-130 .. image-sg:: /examples/LinearizedElasticity/images/sphx_glr_Elas8_001.gif :alt: Elas8 :srcset: /examples/LinearizedElasticity/images/sphx_glr_Elas8_001.gif :class: sphx-glr-single-img .. rst-class:: sphx-glr-horizontal * .. image-sg:: /examples/LinearizedElasticity/images/sphx_glr_Elas8_002.png :alt: QUAD4: Ne = 230, Nn = 282 :srcset: /examples/LinearizedElasticity/images/sphx_glr_Elas8_002.png :class: sphx-glr-multi-img * .. image-sg:: /examples/LinearizedElasticity/images/sphx_glr_Elas8_003.png :alt: Boundary conditions :srcset: /examples/LinearizedElasticity/images/sphx_glr_Elas8_003.png :class: sphx-glr-multi-img * .. image-sg:: /examples/LinearizedElasticity/images/sphx_glr_Elas8_004.png :alt: $uy^{e}$ :srcset: /examples/LinearizedElasticity/images/sphx_glr_Elas8_004.png :class: sphx-glr-multi-img * .. image-sg:: /examples/LinearizedElasticity/images/sphx_glr_Elas8_005.png :alt: $\sigma_{vm}^{e}$ :srcset: /examples/LinearizedElasticity/images/sphx_glr_Elas8_005.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out .. code-block:: none 0.000 s 0.010 s 0.020 s 0.030 s 0.040 s 0.050 s 0.060 s 0.070 s 0.080 s 0.090 s 0.100 s 0.110 s 0.120 s 0.130 s 0.140 s 0.150 s 0.160 s 0.170 s 0.180 s 0.190 s 0.200 s 0.210 s 0.220 s 0.230 s 0.240 s 0.250 s 0.260 s 0.270 s 0.280 s 0.290 s 0.300 s 0.310 s 0.320 s 0.330 s 0.340 s 0.350 s 0.360 s 0.370 s 0.380 s 0.390 s 0.400 s 0.410 s 0.420 s 0.430 s 0.440 s 0.450 s 0.460 s 0.470 s 0.480 s 0.490 s 0.500 s Generate movie 0/51 Generate movie 1/51 (1.96 %) 9.10 s Generate movie 2/51 (3.92 %) 9.01 s Generate movie 3/51 (5.88 %) 8.88 s Generate movie 4/51 (7.84 %) 8.73 s Generate movie 5/51 (9.80 %) 8.60 s Generate movie 6/51 (11.76 %) 8.28 s Generate movie 7/51 (13.73 %) 8.05 s Generate movie 8/51 (15.69 %) 8.03 s Generate movie 9/51 (17.65 %) 7.76 s Generate movie 10/51 (19.61 %) 7.53 s Generate movie 11/51 (21.57 %) 7.40 s Generate movie 12/51 (23.53 %) 7.01 s Generate movie 13/51 (25.49 %) 7.10 s Generate movie 14/51 (27.45 %) 7.00 s Generate movie 15/51 (29.41 %) 6.77 s Generate movie 16/51 (31.37 %) 6.55 s Generate movie 17/51 (33.33 %) 6.36 s Generate movie 18/51 (35.29 %) 6.15 s Generate movie 19/51 (37.25 %) 6.05 s Generate movie 20/51 (39.22 %) 5.88 s Generate movie 21/51 (41.18 %) 5.60 s Generate movie 22/51 (43.14 %) 5.52 s Generate movie 23/51 (45.10 %) 5.25 s Generate movie 24/51 (47.06 %) 5.09 s Generate movie 25/51 (49.02 %) 4.86 s Generate movie 26/51 (50.98 %) 4.70 s Generate movie 27/51 (52.94 %) 4.54 s Generate movie 28/51 (54.90 %) 4.31 s Generate movie 29/51 (56.86 %) 4.17 s Generate movie 30/51 (58.82 %) 3.94 s Generate movie 31/51 (60.78 %) 3.73 s Generate movie 32/51 (62.75 %) 3.57 s Generate movie 33/51 (64.71 %) 3.32 s Generate movie 34/51 (66.67 %) 3.24 s Generate movie 35/51 (68.63 %) 3.02 s Generate movie 36/51 (70.59 %) 2.82 s Generate movie 37/51 (72.55 %) 2.61 s Generate movie 38/51 (74.51 %) 2.43 s Generate movie 39/51 (76.47 %) 2.25 s Generate movie 40/51 (78.43 %) 2.04 s Generate movie 41/51 (80.39 %) 1.87 s Generate movie 42/51 (82.35 %) 1.69 s Generate movie 43/51 (84.31 %) 1.51 s Generate movie 44/51 (86.27 %) 1.31 s Generate movie 45/51 (88.24 %) 1.13 s Generate movie 46/51 (90.20 %) 941.12 ms Generate movie 47/51 (92.16 %) 757.46 ms Generate movie 48/51 (94.12 %) 562.66 ms Generate movie 49/51 (96.08 %) 376.14 ms Generate movie 50/51 (98.04 %) 189.89 ms Generate movie 51/51 (100.00 %) 0.00 µs ==================== Mesh ==================== Element type: QUAD4 Ne = 230, Nn = 282 ==================== Model ==================== ElasIsot: E = 2.10e+05, v = 0.3 planeStress = True thickness = 1.30e+01 solver : pypardiso ============= Boundary Conditions ============= Unspecified. =================== Results =================== W def = 1.15 Svm max = 12.72 Evm max = 0.01 % Ux max = 3.73e-03 Ux min = -3.73e-03 Uy max = 0.00e+00 Uy min = -5.04e-02 =================== TicTac =================== Mesh : 2.529 s Boundary Conditions : 2.362 ms Matrix : 10.078 s Solver : 5.846 s Display : 1.570 s PostProcessing : 806.896 ms Resolution hyperelastic : 6.224 s PyVista_Interface : 49.392 s Paraview : 1.437 s | .. code-block:: Python :lineno-start: 12 from EasyFEA import ( Display, Folder, Models, plt, ElemType, Simulations, PyVista, Paraview, ) from EasyFEA.Geoms import Domain if __name__ == "__main__": Display.Clear() # ---------------------------------------------- # Configuration # ---------------------------------------------- dim = 2 # outputs folder = Folder.Join(Folder.RESULTS_DIR, "LinearizedElasticity", "Dynamic1") makeParaview = False makeMovie = True result = "uy" # geom L = 120 # mm h = 13 b = 13 # time Tmax = 0.5 N = 50 dt = Tmax / N time = -dt # Dumping coefM = 1e-3 coefK = 1e-3 # ---------------------------------------------- # Mesh # ---------------------------------------------- meshSize = h / 5 if dim == 2: domain = Domain((0, -h / 2), (L, h / 2), meshSize) mesh = domain.Mesh_2D([], ElemType.QUAD4, isOrganised=True) area = mesh.area - L * h elif dim == 3: domain = Domain((0, -h / 2, -b / 2), (L, h / 2, -b / 2), meshSize=meshSize) mesh = domain.Mesh_Extrude([], [0, 0, b], [3], ElemType.HEXA8, isOrganised=True) volume = mesh.volume - L * b * h area = mesh.area - (L * h * 4 + 2 * b * h) nodes_0 = mesh.Nodes_Conditions(lambda x, y, z: x == 0) nodes_L = mesh.Nodes_Conditions(lambda x, y, z: x == L) nodes_h = mesh.Nodes_Conditions(lambda x, y, z: y == h / 2) # ---------------------------------------------- # Simulation # ---------------------------------------------- material = Models.ElasIsot(dim, thickness=b) simu = Simulations.ElasticSimu(mesh, material) simu.rho = 8100 * 1e-9 # static simulation simu.Bc_Init() simu.add_dirichlet(nodes_0, [0] * dim, simu.Get_unknowns(), description="Fixed") simu.add_dirichlet(nodes_L, [-10], ["y"], description="dep") simu.Solve() simu.Save_Iter() Display.Plot_Mesh(simu, deformFactor=1) # dynamic simulation simu.Solver_Set_Hyperbolic_Algorithm(dt) simu.Set_Rayleigh_Damping_Coefs(coefM=coefM, coefK=coefK) simu.Bc_Init() simu.add_dirichlet(nodes_0, [0] * dim, simu.Get_unknowns(), description="Fixed") while time <= Tmax: time += dt simu.Solve() simu.Save_Iter() print(f"{time:.3f} s", end="\r") # ---------------------------------------------- # Results # ---------------------------------------------- Display.Plot_BoundaryConditions(simu) if makeParaview: Paraview.Save_simu(simu, folder) if makeMovie: PyVista.Movie_simu( simu, f"{result}", folder, f"{result}.gif", deformFactor=1, plotMesh=True, ) print(simu) Display.Plot_Result(simu, f"{result}", deformFactor=1, nodeValues=False) Display.Plot_Result(simu, "Svm", plotMesh=False, nodeValues=False) plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 16.743 seconds) .. _sphx_glr_download_examples_LinearizedElasticity_Elas8.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: Elas8.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: Elas8.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: Elas8.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_