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Elas8#
A cantilever beam undergoing dynamic bending deformation.
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==================== 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 : 6.160 ms
Boundary Conditions : 13.590 µs
Matrix : 4.816 ms
Solver : 121.066 ms
Display : 19.852 ms
PyVista_Interface : 6.253 s
PostProcessing : 535.965 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 7.612 seconds)