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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 ====================

ElasIsot:
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 : 1.036 s
Boundary Conditions : 948.429 µs
Matrix : 4.760 s
Solver : 1.892 m
Display : 613.304 ms
PostProcessing : 378.959 ms
Resolution hyperelastic : 3.863 s
PyVista_Interface : 18.129 s
Paraview : 829.406 ms


 12 from EasyFEA import (
 13     Display,
 14     Folder,
 15     Models,
 16     plt,
 17     ElemType,
 18     Simulations,
 19     PyVista,
 20     Paraview,
 21 )
 22 from EasyFEA.Geoms import Domain
 23
 24 if __name__ == "__main__":
 25     Display.Clear()
 26
 27     # ----------------------------------------------
 28     # Configuration
 29     # ----------------------------------------------
 30     dim = 2
 31
 32     # outputs
 33     folder = Folder.Join(Folder.RESULTS_DIR, "LinearizedElasticity", "Dynamic1")
 34     makeParaview = False
 35     makeMovie = True
 36     result = "uy"
 37
 38     # geom
 39     L = 120  # mm
 40     h = 13
 41     b = 13
 42
 43     # time
 44     Tmax = 0.5
 45     N = 50
 46     dt = Tmax / N
 47     time = -dt
 48
 49     # Dumping
 50     coefM = 1e-3
 51     coefK = 1e-3
 52
 53     # ----------------------------------------------
 54     # Mesh
 55     # ----------------------------------------------
 56     meshSize = h / 5
 57
 58     if dim == 2:
 59         domain = Domain((0, -h / 2), (L, h / 2), meshSize)
 60         mesh = domain.Mesh_2D([], ElemType.QUAD4, isOrganised=True)
 61
 62         area = mesh.area - L * h
 63
 64     elif dim == 3:
 65         domain = Domain((0, -h / 2, -b / 2), (L, h / 2, -b / 2), meshSize=meshSize)
 66         mesh = domain.Mesh_Extrude([], [0, 0, b], [3], ElemType.HEXA8, isOrganised=True)
 67
 68         volume = mesh.volume - L * b * h
 69         area = mesh.area - (L * h * 4 + 2 * b * h)
 70
 71     nodes_0 = mesh.Nodes_Conditions(lambda x, y, z: x == 0)
 72     nodes_L = mesh.Nodes_Conditions(lambda x, y, z: x == L)
 73     nodes_h = mesh.Nodes_Conditions(lambda x, y, z: y == h / 2)
 74
 75     # ----------------------------------------------
 76     # Simulation
 77     # ----------------------------------------------
 78
 79     material = Models.ElasIsot(dim, thickness=b)
 80     simu = Simulations.ElasticSimu(mesh, material)
 81     simu.rho = 8100 * 1e-9
 82
 83     # static simulation
 84     simu.Bc_Init()
 85     simu.add_dirichlet(nodes_0, [0] * dim, simu.Get_unknowns(), description="Fixed")
 86     simu.add_dirichlet(nodes_L, [-10], ["y"], description="dep")
 87     simu.Solve()
 88     simu.Save_Iter()
 89     Display.Plot_Mesh(simu, deformFactor=1)
 90
 91     # dynamic simulation
 92     simu.Solver_Set_Hyperbolic_Algorithm(dt)
 93     simu.Set_Rayleigh_Damping_Coefs(coefM=coefM, coefK=coefK)
 94
 95     simu.Bc_Init()
 96     simu.add_dirichlet(nodes_0, [0] * dim, simu.Get_unknowns(), description="Fixed")
 97
 98     while time <= Tmax:
 99         time += dt
100
101         simu.Solve()
102         simu.Save_Iter()
103
104         print(f"{time:.3f} s", end="\r")
105
106     # ----------------------------------------------
107     # Results
108     # ----------------------------------------------
109
110     Display.Plot_BoundaryConditions(simu)
111
112     if makeParaview:
113         Paraview.Save_simu(simu, folder)
114
115     if makeMovie:
116         PyVista.Movie_simu(
117             simu,
118             f"{result}",
119             folder,
120             f"{result}.gif",
121             deformFactor=1,
122             plotMesh=True,
123         )
124
125     print(simu)
126     Display.Plot_Result(simu, f"{result}", deformFactor=1, nodeValues=False)
127     Display.Plot_Result(simu, "Svm", plotMesh=False, nodeValues=False)
128
129     plt.show()

Total running time of the script: (0 minutes 7.472 seconds)

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