.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/WeakForms/LinearElasticity2.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_WeakForms_LinearElasticity2.py: LinearElasticity2 ================= A cantilever beam undergoing bending deformation in dynamic. Note that this simulation is also performed in `examples/Dynamic/Dynamic1.py`. .. GENERATED FROM PYTHON SOURCE LINES 14-144 .. image-sg:: /examples/WeakForms/images/sphx_glr_LinearElasticity2_001.gif :alt: LinearElasticity2 :srcset: /examples/WeakForms/images/sphx_glr_LinearElasticity2_001.gif :class: sphx-glr-single-img .. tab-set:: .. tab-item:: Static Scene .. image-sg:: /examples/WeakForms/images/sphx_glr_LinearElasticity2_002.png :alt: LinearElasticity2 :srcset: /examples/WeakForms/images/sphx_glr_LinearElasticity2_002.png :class: sphx-glr-single-img .. tab-item:: Interactive Scene .. offlineviewer:: /home/docs/checkouts/readthedocs.org/user_builds/easyfea/checkouts/v1.8.0/docs/examples/WeakForms/images/sphx_glr_LinearElasticity2_002.vtksz .. 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 01/52 (1.92 %) 5.30 s Generate movie 02/52 (3.85 %) 3.82 s Generate movie 03/52 (5.77 %) 3.90 s Generate movie 04/52 (7.69 %) 3.75 s Generate movie 05/52 (9.62 %) 3.62 s Generate movie 06/52 (11.54 %) 3.53 s Generate movie 07/52 (13.46 %) 3.39 s Generate movie 08/52 (15.38 %) 3.40 s Generate movie 09/52 (17.31 %) 3.28 s Generate movie 10/52 (19.23 %) 3.24 s Generate movie 11/52 (21.15 %) 3.11 s Generate movie 12/52 (23.08 %) 3.11 s Generate movie 13/52 (25.00 %) 3.10 s Generate movie 14/52 (26.92 %) 3.02 s Generate movie 15/52 (28.85 %) 2.84 s Generate movie 16/52 (30.77 %) 2.73 s Generate movie 17/52 (32.69 %) 2.70 s Generate movie 18/52 (34.62 %) 2.59 s Generate movie 19/52 (36.54 %) 2.52 s Generate movie 20/52 (38.46 %) 2.54 s Generate movie 21/52 (40.38 %) 2.46 s Generate movie 22/52 (42.31 %) 2.35 s Generate movie 23/52 (44.23 %) 2.21 s Generate movie 24/52 (46.15 %) 2.14 s Generate movie 25/52 (48.08 %) 2.04 s Generate movie 26/52 (50.00 %) 2.05 s Generate movie 27/52 (51.92 %) 1.90 s Generate movie 28/52 (53.85 %) 1.82 s Generate movie 29/52 (55.77 %) 1.77 s Generate movie 30/52 (57.69 %) 1.70 s Generate movie 31/52 (59.62 %) 1.66 s Generate movie 32/52 (61.54 %) 1.57 s Generate movie 33/52 (63.46 %) 1.48 s Generate movie 34/52 (65.38 %) 1.45 s Generate movie 35/52 (67.31 %) 1.37 s Generate movie 36/52 (69.23 %) 1.42 s Generate movie 37/52 (71.15 %) 1.20 s Generate movie 38/52 (73.08 %) 1.09 s Generate movie 39/52 (75.00 %) 1.03 s Generate movie 40/52 (76.92 %) 958.81 ms Generate movie 41/52 (78.85 %) 870.10 ms Generate movie 42/52 (80.77 %) 777.53 ms Generate movie 43/52 (82.69 %) 699.22 ms Generate movie 44/52 (84.62 %) 644.31 ms Generate movie 45/52 (86.54 %) 543.80 ms Generate movie 46/52 (88.46 %) 470.26 ms Generate movie 47/52 (90.38 %) 385.68 ms Generate movie 48/52 (92.31 %) 310.87 ms Generate movie 49/52 (94.23 %) 237.71 ms Generate movie 50/52 (96.15 %) 158.20 ms Generate movie 51/52 (98.08 %) 78.30 ms Generate movie 52/52 (100.00 %) 0.00 µs | .. code-block:: Python :lineno-start: 15 import matplotlib.pyplot as plt import numpy as np from EasyFEA import Folder, Display, ElemType, Models, Simulations, PyVista from EasyFEA.FEM import Field, BiLinearForm, FeArray, Sym_Grad, Trace from EasyFEA.Geoms import Domain if __name__ == "__main__": Display.Clear() # ---------------------------------------------- # Configuration # ---------------------------------------------- dim = 3 # outputs makeMovie = True folder = Folder.Results_Dir() # geom L = 120 # mm h = 13 # model elastic = Models.Elastic.Isotropic(dim, 210000, 0.3, planeStress=True, thickness=h) lmbda = elastic.get_lambda() mu = elastic.get_mu() rho = 8100 * 1e-9 # load Tmax = 0.5 N = 50 dt = Tmax / N time = -dt # ---------------------------------------------- # Mesh # ---------------------------------------------- contour = Domain((0, 0), (L, h), h / 3) if dim == 2: mesh = contour.Mesh_2D([], ElemType.QUAD4, isOrganised=True) else: mesh = contour.Mesh_Extrude( [], [0, 0, h], [3], ElemType.HEXA8, isOrganised=True ) nodesX0 = mesh.Nodes_Conditions(lambda x, y, z: x == 0) nodesXL = mesh.Nodes_Conditions(lambda x, y, z: x == L) # ---------------------------------------------- # Formulations # ---------------------------------------------- field = Field(mesh.groupElem, dim) def S(u: Field) -> FeArray: Eps = Sym_Grad(u) return 2 * mu * Eps + lmbda * Trace(Eps) * np.eye(dim) @BiLinearForm def computeK(u: Field, v: Field): Sig = S(u) Eps = Sym_Grad(v) return Sig.ddot(Eps) @BiLinearForm def computeM(u: Field, v: Field): return rho * u.dot(v) @BiLinearForm def computeC(u: Field, v: Field): K = computeK(u, v) M = computeM(u, v) C = K * 1e-3 + M * 1e-3 return C weakForms = Models.WeakForms(field, computeK, computeC, computeM) # ---------------------------------------------- # Simulations # ---------------------------------------------- simu = Simulations.WeakForms(mesh, weakForms) # static simulation simu.add_dirichlet(nodesX0, [0] * dim, simu.Get_unknowns()) simu.add_dirichlet(nodesXL, [-10], ["y"]) simu.Solve() # dynamic simulation simu.Solver_Set_Hyperbolic_Algorithm(dt) simu.Save_Iter() simu.Bc_Init() simu.add_dirichlet(nodesX0, [0] * dim, simu.Get_unknowns()) while time <= Tmax: time += dt simu.Solve() simu.Save_Iter() print(f"{time:.3f} s", end="\r") # ---------------------------------------------- # Results # ---------------------------------------------- if makeMovie: PyVista.Movie_simu( simu, "uy", folder, "uy.gif", deformFactor=1, plotMesh=True, N=400, nodeValues=True, ) simu.Set_Iter(0) PyVista.Plot(simu, "uy", 1, plotMesh=True).show() plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 8.379 seconds) .. _sphx_glr_download_examples_WeakForms_LinearElasticity2.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: LinearElasticity2.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: LinearElasticity2.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: LinearElasticity2.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_