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Elas9#
A cantilever beam undergoing dynamic bending deformation.
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==================== Mesh ====================
elemType: 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: 8.683 ms
Boundary Conditions: 16.520 µs
Matrix: 6.739 ms
Solver: 151.555 ms
Matplotlib: 24.094 ms
PyVista_Interface: 8.461 s
PostProcessing: 479.833 µs
13 import matplotlib.pyplot as plt
14
15 from EasyFEA import (
16 Terminal,
17 Matplotlib,
18 Folder,
19 Models,
20 ElemType,
21 Simulations,
22 PyVista,
23 Paraview,
24 )
25 from EasyFEA.Geoms import Domain
26
27 if __name__ == "__main__":
28 Terminal.Clear()
29
30 # ----------------------------------------------
31 # Configuration
32 # ----------------------------------------------
33 dim = 2
34
35 # outputs
36 folder = Folder.Results_Dir()
37 makeParaview = False
38 makeMovie = True
39 result = "uy"
40
41 # geom
42 L = 120 # mm
43 h = 13
44 b = 13
45
46 # time
47 Tmax = 0.5
48 N = 50
49 dt = Tmax / N
50 time = -dt
51
52 # Dumping
53 coefM = 1e-3
54 coefK = 1e-3
55
56 # ----------------------------------------------
57 # Mesh
58 # ----------------------------------------------
59 meshSize = h / 5
60
61 if dim == 2:
62 domain = Domain((0, -h / 2), (L, h / 2), meshSize)
63 mesh = domain.Mesh_2D([], ElemType.QUAD4, isOrganised=True)
64
65 area = mesh.area - L * h
66
67 elif dim == 3:
68 domain = Domain((0, -h / 2, -b / 2), (L, h / 2, -b / 2), meshSize=meshSize)
69 mesh = domain.Mesh_Extrude([], [0, 0, b], [3], ElemType.HEXA8, isOrganised=True)
70
71 volume = mesh.volume - L * b * h
72 area = mesh.area - (L * h * 4 + 2 * b * h)
73
74 nodes_0 = mesh.Nodes_Conditions(lambda x, y, z: x == 0)
75 nodes_L = mesh.Nodes_Conditions(lambda x, y, z: x == L)
76 nodes_h = mesh.Nodes_Conditions(lambda x, y, z: y == h / 2)
77
78 # ----------------------------------------------
79 # Simulation
80 # ----------------------------------------------
81
82 material = Models.Elastic.Isotropic(dim, thickness=b)
83 simu = Simulations.Elastic(mesh, material)
84 simu.rho = 8100 * 1e-9
85
86 # static simulation
87 simu.Bc_Init()
88 simu.add_dirichlet(nodes_0, [0] * dim, simu.Get_unknowns(), description="Fixed")
89 simu.add_dirichlet(nodes_L, [-10], ["y"], description="dep")
90 simu.Solve()
91 simu.Save_Iter()
92 Matplotlib.Plot_Mesh(simu, deformFactor=1)
93
94 # dynamic simulation
95 simu.Solver_Set_Hyperbolic_Algorithm(dt)
96 simu.Set_Rayleigh_Damping_Coefs(coefM=coefM, coefK=coefK)
97
98 simu.Bc_Init()
99 simu.add_dirichlet(nodes_0, [0] * dim, simu.Get_unknowns(), description="Fixed")
100
101 while time <= Tmax:
102 time += dt
103
104 simu.Solve()
105 simu.Save_Iter()
106
107 print(f"{time:.3f} s", end="\r")
108
109 # ----------------------------------------------
110 # Results
111 # ----------------------------------------------
112
113 Matplotlib.Plot_BoundaryConditions(simu)
114
115 if makeParaview:
116 Paraview.Save_simu(simu, folder)
117
118 if makeMovie:
119 PyVista.Movie_simu(
120 simu,
121 f"{result}",
122 folder,
123 f"{result}.gif",
124 deformFactor=1,
125 plotMesh=True,
126 )
127
128 print(simu)
129 Matplotlib.Plot(simu, f"{result}", deformFactor=1, nodeValues=False)
130 Matplotlib.Plot(simu, "Svm", plotMesh=False, nodeValues=False)
131
132 plt.show()
Total running time of the script: (0 minutes 9.371 seconds)