Note

Go to the end to download the full example code.

Elas8#

A cantilever beam undergoing dynamic bending deformation.

Elas8
  • QUAD4: Ne = 230, Nn = 282
  • Boundary conditions
  • $uy^{e}$
  • $\sigma_{vm}^{e}$
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 %) 4.85 s
Generate movie 02/52 (3.85 %) 3.84 s
Generate movie 03/52 (5.77 %) 3.55 s
Generate movie 04/52 (7.69 %) 3.48 s
Generate movie 05/52 (9.62 %) 3.35 s
Generate movie 06/52 (11.54 %) 3.48 s
Generate movie 07/52 (13.46 %) 3.26 s
Generate movie 08/52 (15.38 %) 3.22 s
Generate movie 09/52 (17.31 %) 3.06 s
Generate movie 10/52 (19.23 %) 3.01 s
Generate movie 11/52 (21.15 %) 3.12 s
Generate movie 12/52 (23.08 %) 3.04 s
Generate movie 13/52 (25.00 %) 2.81 s
Generate movie 14/52 (26.92 %) 2.87 s
Generate movie 15/52 (28.85 %) 2.68 s
Generate movie 16/52 (30.77 %) 2.63 s
Generate movie 17/52 (32.69 %) 2.59 s
Generate movie 18/52 (34.62 %) 2.58 s
Generate movie 19/52 (36.54 %) 2.42 s
Generate movie 20/52 (38.46 %) 2.31 s
Generate movie 21/52 (40.38 %) 2.25 s
Generate movie 22/52 (42.31 %) 2.26 s
Generate movie 23/52 (44.23 %) 2.14 s
Generate movie 24/52 (46.15 %) 1.99 s
Generate movie 25/52 (48.08 %) 1.92 s
Generate movie 26/52 (50.00 %) 1.84 s
Generate movie 27/52 (51.92 %) 1.85 s
Generate movie 28/52 (53.85 %) 1.82 s
Generate movie 29/52 (55.77 %) 1.68 s
Generate movie 30/52 (57.69 %) 1.61 s
Generate movie 31/52 (59.62 %) 1.55 s
Generate movie 32/52 (61.54 %) 1.46 s
Generate movie 33/52 (63.46 %) 1.39 s
Generate movie 34/52 (65.38 %) 1.34 s
Generate movie 35/52 (67.31 %) 1.24 s
Generate movie 36/52 (69.23 %) 1.24 s
Generate movie 37/52 (71.15 %) 1.09 s
Generate movie 38/52 (73.08 %) 1.02 s
Generate movie 39/52 (75.00 %) 947.91 ms
Generate movie 40/52 (76.92 %) 888.34 ms
Generate movie 41/52 (78.85 %) 823.35 ms
Generate movie 42/52 (80.77 %) 751.83 ms
Generate movie 43/52 (82.69 %) 679.84 ms
Generate movie 44/52 (84.62 %) 595.80 ms
Generate movie 45/52 (86.54 %) 524.51 ms
Generate movie 46/52 (88.46 %) 459.00 ms
Generate movie 47/52 (90.38 %) 367.25 ms
Generate movie 48/52 (92.31 %) 300.73 ms
Generate movie 49/52 (94.23 %) 230.85 ms
Generate movie 50/52 (96.15 %) 157.91 ms
Generate movie 51/52 (98.08 %) 76.63 ms
Generate movie 52/52 (100.00 %) 0.00 µs


==================== Mesh ====================

Element type: QUAD4
Ne = 230, Nn = 282

==================== Model ====================

Isotropic:
E = 2.10e+05, v = 0.3
planeStress = True
thickness = 1.30e+01

solver : scipy

============= Boundary Conditions =============

Unspecified.

=================== Results ===================


W def = 1.15

Svm max = 12.78

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 : 6.189 ms
Boundary Conditions : 12.875 µs
Matrix : 4.749 ms
Solver : 120.715 ms
Display : 19.720 ms
PyVista_Interface : 6.188 s
PostProcessing : 540.018 µs


 13 import matplotlib.pyplot as plt
 14
 15 from EasyFEA import Display, Folder, Models, ElemType, Simulations, PyVista, Paraview
 16 from EasyFEA.Geoms import Domain
 17
 18 if __name__ == "__main__":
 19     Display.Clear()
 20
 21     # ----------------------------------------------
 22     # Configuration
 23     # ----------------------------------------------
 24     dim = 2
 25
 26     # outputs
 27     folder = Folder.Results_Dir()
 28     makeParaview = False
 29     makeMovie = True
 30     result = "uy"
 31
 32     # geom
 33     L = 120  # mm
 34     h = 13
 35     b = 13
 36
 37     # time
 38     Tmax = 0.5
 39     N = 50
 40     dt = Tmax / N
 41     time = -dt
 42
 43     # Dumping
 44     coefM = 1e-3
 45     coefK = 1e-3
 46
 47     # ----------------------------------------------
 48     # Mesh
 49     # ----------------------------------------------
 50     meshSize = h / 5
 51
 52     if dim == 2:
 53         domain = Domain((0, -h / 2), (L, h / 2), meshSize)
 54         mesh = domain.Mesh_2D([], ElemType.QUAD4, isOrganised=True)
 55
 56         area = mesh.area - L * h
 57
 58     elif dim == 3:
 59         domain = Domain((0, -h / 2, -b / 2), (L, h / 2, -b / 2), meshSize=meshSize)
 60         mesh = domain.Mesh_Extrude([], [0, 0, b], [3], ElemType.HEXA8, isOrganised=True)
 61
 62         volume = mesh.volume - L * b * h
 63         area = mesh.area - (L * h * 4 + 2 * b * h)
 64
 65     nodes_0 = mesh.Nodes_Conditions(lambda x, y, z: x == 0)
 66     nodes_L = mesh.Nodes_Conditions(lambda x, y, z: x == L)
 67     nodes_h = mesh.Nodes_Conditions(lambda x, y, z: y == h / 2)
 68
 69     # ----------------------------------------------
 70     # Simulation
 71     # ----------------------------------------------
 72
 73     material = Models.Elastic.Isotropic(dim, thickness=b)
 74     simu = Simulations.Elastic(mesh, material)
 75     simu.rho = 8100 * 1e-9
 76
 77     # static simulation
 78     simu.Bc_Init()
 79     simu.add_dirichlet(nodes_0, [0] * dim, simu.Get_unknowns(), description="Fixed")
 80     simu.add_dirichlet(nodes_L, [-10], ["y"], description="dep")
 81     simu.Solve()
 82     simu.Save_Iter()
 83     Display.Plot_Mesh(simu, deformFactor=1)
 84
 85     # dynamic simulation
 86     simu.Solver_Set_Hyperbolic_Algorithm(dt)
 87     simu.Set_Rayleigh_Damping_Coefs(coefM=coefM, coefK=coefK)
 88
 89     simu.Bc_Init()
 90     simu.add_dirichlet(nodes_0, [0] * dim, simu.Get_unknowns(), description="Fixed")
 91
 92     while time <= Tmax:
 93         time += dt
 94
 95         simu.Solve()
 96         simu.Save_Iter()
 97
 98         print(f"{time:.3f} s", end="\r")
 99
100     # ----------------------------------------------
101     # Results
102     # ----------------------------------------------
103
104     Display.Plot_BoundaryConditions(simu)
105
106     if makeParaview:
107         Paraview.Save_simu(simu, folder)
108
109     if makeMovie:
110         PyVista.Movie_simu(
111             simu,
112             f"{result}",
113             folder,
114             f"{result}.gif",
115             deformFactor=1,
116             plotMesh=True,
117         )
118
119     print(simu)
120     Display.Plot_Result(simu, f"{result}", deformFactor=1, nodeValues=False)
121     Display.Plot_Result(simu, "Svm", plotMesh=False, nodeValues=False)
122
123     plt.show()

Total running time of the script: (0 minutes 7.524 seconds)

Gallery generated by Sphinx-Gallery