Beam1

Beam subjected to pure tensile loading.

• 
• 
• 
• 

err ux: 3.05e-14 %

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

Element type: SEG2
Ne = 10, Nn = 11

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

<EasyFEA.Models.Beam._beam.BeamStructure object at 0x763ba46ab5d0>

solver : scipy

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

Unspecified.

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



Ux max = 4.45e-05
Ux min = 0.00e+00

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

Mesh : 9.046 ms
Boundary Conditions : 20.742 µs
Matrix : 4.448 ms
Solver : 734.329 µs
Display : 28.686 ms

import matplotlib.pyplot as plt
import numpy as np

from EasyFEA import Display, Models, Mesher, ElemType, Simulations
from EasyFEA.Geoms import Domain, Line

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

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

    # geom
    L = 10
    nL = 10
    h = 0.1
    b = 0.1

    # model
    E = 200000e6
    ro = 7800
    v = 0.3

    # load
    g = 10
    q = ro * g * (h * b)
    load = 5000

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

    elemType = ElemType.SEG2
    beamDim = 1

    # Create a section for the beam
    mesher = Mesher()
    section = mesher.Mesh_2D(Domain((0, 0), (b, h)))

    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], elemType=elemType)

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

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

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

    # Apply boundary conditions
    simu.add_dirichlet(mesh.Nodes_Point(p1), [0] * dof_n, simu.Get_unknowns())
    simu.add_lineLoad(mesh.nodes, [q], ["x"])
    simu.add_neumann(mesh.Nodes_Point(p2), [load], ["x"])

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

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

    Display.Plot_Mesh(simu, deformFactor=L / 10 / sol.max())
    Display.Plot_BoundaryConditions(simu)
    Display.Plot_Result(simu, "ux")

    ux = simu.Result("ux")

    x_array = np.linspace(0, L, 100)
    u_x = (load * x_array / (E * (section.area))) + (
        ro * g * x_array / 2 / E * (2 * L - x_array)
    )
    err_ux = np.abs(u_x[-1] - ux.max()) / ux.max()
    Display.MyPrint(f"err ux: {err_ux * 100:.2e} %")

    # Plot the analytical and finite element solutions for displacement (u)
    ax = Display.Init_Axes()
    ax.plot(x_array, u_x, label="Analytical", c="blue")
    ax.scatter(mesh.coord[:, 0], ux, label="FE", c="red", marker="x", zorder=2)
    ax.set_title("$u_x(x)$")
    ax.legend()

    print(simu)

    plt.show()