Elas4

Plate with a hole subjected to uniform tensile loading.

• 
• 
• 
• 
• 

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

Element type: TRI10
Ne = 104, Nn = 511

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

Isotropic:
E = 2.10e+05, v = 0.3
planeStress = True
thickness = 1.00e+00

solver:scipy

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

Unspecified.

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


W def = 5.04

Svm max = 127.24

Evm max = 0.07 %

Ux max = 1.27e-02
Ux min = 0.00e+00

Uy max = 0.00e+00
Uy min = -4.89e-03

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

Mesh: 11.694 ms
Boundary Conditions: 14.782 µs
Matrix: 7.452 ms
Solver: 4.315 ms
Display: 69.976 ms
PostProcessing: 590.801 µs

import matplotlib.pyplot as plt

from EasyFEA import Display, ElemType, Models, Simulations
from EasyFEA.Geoms import Point, Points, Domain, Circle

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

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

    dim = 2
    isSymmetric = True

    # geom
    a = 10
    l = 50
    h = 20
    thickness = 1

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

    meshSize = h / 4

    if isSymmetric:
        p0 = Point(0, 0, r=-a)
        p1 = Point(l, 0)
        p2 = Point(l, h)
        p3 = Point(0, h)
        contour = Points([p0, p1, p2, p3], meshSize)
        inclusions = []
    else:
        p0 = Point(-l, -h)
        p1 = Point(l, h)
        contour = Domain(p0, p1, meshSize)
        inclusions = [Circle(Point(), 2 * a, meshSize)]

    if dim == 2:
        mesh = contour.Mesh_2D(inclusions, elemType=ElemType.TRI10)
    else:
        mesh = contour.Mesh_Extrude(
            inclusions, [0, 0, thickness], [1], ElemType.PRISM18
        )

    # ----------------------------------------------
    # Simu
    # ----------------------------------------------
    material = Models.Elastic.Isotropic(
        dim, E=210000, v=0.3, planeStress=True, thickness=thickness
    )
    simu = Simulations.Elastic(mesh, material)

    if isSymmetric:
        nodes_x0 = mesh.Nodes_Conditions(lambda x, y, z: x == 0)
        nodes_y0 = mesh.Nodes_Conditions(lambda x, y, z: y == 0)
        nodes_xl = mesh.Nodes_Conditions(lambda x, y, z: x == l)
        simu.add_dirichlet(nodes_x0, [0], ["x"])
        simu.add_dirichlet(nodes_y0, [0], ["y"])
        simu.add_surfLoad(nodes_xl, [800 / 20], ["x"])
    else:
        nodes_pl = mesh.Nodes_Conditions(lambda x, y, z: x == l)
        nodes_ml = mesh.Nodes_Conditions(lambda x, y, z: x == -l)
        nodes_y0 = mesh.Nodes_Conditions(lambda x, y, z: y == 0)
        simu.add_dirichlet(nodes_y0, [0], ["y"])
        simu.add_surfLoad(nodes_pl, [800 / 20], ["x"])
        simu.add_surfLoad(nodes_ml, [-800 / 20], ["x"])

    simu.Solve()

    # ----------------------------------------------
    # Results
    # ----------------------------------------------
    uxMax = simu.Result("ux").max()
    Display.Plot_Mesh(simu, deformFactor=2 / uxMax)
    Display.Plot_BoundaryConditions(simu)

    Display.Plot_Result(simu, "ux", ncolors=10)
    Display.Plot_Result(simu, "uy", ncolors=10)
    Display.Plot_Result(simu, "Svm", ncolors=10, nodeValues=False, plotMesh=True)

    print(simu)

    plt.show()