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Elas8#

A cantilever beam undergoing dynamic bending deformation.

Elas8
  • QUAD4: Ne = 230, Nn = 282
  • Boundary conditions
  • $uy^{e}$
  • $\sigma_{vm}^{e}$
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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 : 9.973 ms
Boundary Conditions : 25.749 µs
Matrix : 9.570 ms
Solver : 247.986 ms
Display : 35.676 ms
PyVista_Interface : 13.381 s
PostProcessing : 924.826 µs


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

Total running time of the script: (0 minutes 14.010 seconds)

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