Beam6

A cantilever beam undergoing bending deformation in dynamic.

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Generate movie 01/20 (5.00 %) 3.98 s
Generate movie 02/20 (10.00 %) 1.67 s
Generate movie 03/20 (15.00 %) 1.58 s
Generate movie 04/20 (20.00 %) 1.49 s
Generate movie 05/20 (25.00 %) 1.38 s
Generate movie 06/20 (30.00 %) 1.33 s
Generate movie 07/20 (35.00 %) 1.23 s
Generate movie 08/20 (40.00 %) 1.10 s
Generate movie 09/20 (45.00 %) 1.01 s
Generate movie 10/20 (50.00 %) 914.34 ms
Generate movie 11/20 (55.00 %) 819.75 ms
Generate movie 12/20 (60.00 %) 736.10 ms
Generate movie 13/20 (65.00 %) 669.95 ms
Generate movie 14/20 (70.00 %) 562.10 ms
Generate movie 15/20 (75.00 %) 466.53 ms
Generate movie 16/20 (80.00 %) 372.67 ms
Generate movie 17/20 (85.00 %) 278.02 ms
Generate movie 18/20 (90.00 %) 183.85 ms
Generate movie 19/20 (95.00 %) 92.78 ms
Generate movie 20/20 (100.00 %) 0.00 µs


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

Element type: SEG3
Ne = 10, Nn = 21

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

<EasyFEA.Models.Beam._beam.BeamStructure object at 0x74a3aab1b590>

solver:scipy

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

Unspecified.

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



Ux max = -0.00e+00
Ux min = -0.00e+00

Uy max = 0.00e+00
Uy min = -5.75e-01

=================== TicTac ===================

Mesh: 18.784 ms
Boundary Conditions: 29.564 µs
Matrix: 18.968 ms
Solver: 92.484 ms
Display: 14.690 ms
PyVista_Interface: 3.135 s

import matplotlib.pyplot as plt

from EasyFEA import Folder, Display, Models, Mesher, Simulations, Paraview, PyVista
from EasyFEA.Geoms import Domain, Line

if __name__ == "__main__":
    Display.Clear()

    # ----------------------------------------------
    # Configuration
    # ----------------------------------------------

    # outputs
    folder = Folder.Results_Dir()
    makeParaview = False
    makeMovie = True
    result = "uy"

    # geom
    L = 120
    nL = 10
    h = 13
    b = 13
    e = 3

    # model
    E = 210000
    v = 0.3
    rho = 7850 * 1e-9
    beamDim = 2  # must be >= 2

    # load
    load = 800

    # time
    Tmax = 1 / 2
    N = 50
    dt = Tmax / N

    # ----------------------------------------------
    # Mesh
    # ----------------------------------------------

    # Create a section object for the beam mesh
    domain1 = Domain((0, 0), (b, h), h / 10)
    domain2 = Domain((e, e), (b - e, h - e), h / 10)
    section = domain1.Mesh_2D([domain2])

    p1 = (0, 0)
    p2 = (L, 0)
    line = Line(p1, p2, L / nL)
    beam = Models.Beam.Isotropic(beamDim, line, section, E, v)

    mesh = Mesher().Mesh_Beams([beam])

    # ----------------------------------------------
    # Simulation
    # ----------------------------------------------

    # Initialize the beam structure with the defined beam segments
    beamStructure = Models.Beam.BeamStructure([beam])

    # Create the beam simulation
    simu = Simulations.Beam(mesh, beamStructure)
    simu.rho = rho
    dof_n = simu.Get_dof_n()

    # Apply boundary conditions
    simu.add_dirichlet(mesh.Nodes_Point(p1), [0] * dof_n, simu.Get_unknowns())
    simu.add_neumann(mesh.Nodes_Point(p2), [-load], ["y"])

    # Solve the beam problem and get displacement results
    sol = simu.Solve()
    simu.Save_Iter()

    simu.Solver_Set_Hyperbolic_Algorithm(dt)
    simu.Bc_Init()
    simu.add_dirichlet(mesh.Nodes_Point(p1), [0] * dof_n, simu.Get_unknowns())

    for _ in range(N):
        simu.Solve()
        simu.Save_Iter()

    # ----------------------------------------------
    # Results
    # ----------------------------------------------

    Display.Plot_BoundaryConditions(simu)

    if makeParaview:
        Paraview.Save_simu(simu, folder)

    deform = 10
    if makeMovie:
        PyVista.Movie_simu(
            simu,
            f"{result}",
            folder,
            f"{result}.gif",
            N=20,
            deformFactor=deform,
            plotMesh=True,
        )

    print(simu)

    Display.Plot_Result(simu, result, deformFactor=deform)
    ax = Display.Plot_Mesh(section)
    ax.set_title("Section")
    Display.Plot_Mesh(simu, deformFactor=deform)

    plt.show()