Elas7

Control lever for a molding machine used to blow plastic bottles.

References

This example comes from:

• A French research article: MMC et RDM comparées sur un cas de dimensionnement de levier

• The book: Mécanique des systèmes et des milieux déformables (3rd edition)

Static Scene

Interactive Scene

Static Scene

Interactive Scene

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

Element type: PRISM6
Ne = 6108, Nn = 4315

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

Isotropic:
E = 2.10e+05, v = 0.25

solver : scipy

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

Unspecified.

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


W def = 615.59

Svm max = 43.45

Evm max = 0.03 %

Ux max = 2.07e-02
Ux min = -2.05e-02

Uy max = 1.98e-03
Uy min = -1.13e-01

Uz max = 4.60e-04
Uz min = -4.60e-04

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

Mesh : 323.721 ms
Boundary Conditions : 167.608 µs
Matrix : 688.181 ms
Solver : 3.332 s
PostProcessing : 17.106 ms


Generate paraview 1/5 (20.00 %) 278.38 ms
Generate paraview 2/5 (40.00 %) 208.27 ms
Generate paraview 3/5 (60.00 %) 134.76 ms
Generate paraview 4/5 (80.00 %) 68.33 ms
Generate paraview 5/5 (100.00 %) 0.00 µs

import numpy as np

from EasyFEA import Display, Folder, Models, ElemType, Simulations, PyVista, Paraview
from EasyFEA.Geoms import Points, Point, Circle

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

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

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

    # geom
    dim = 3
    thickness = 25

    # sinusoidal load
    F = 13000  # N
    area = np.pi * 25 / 2 * thickness
    coefs = np.linspace(0, 1, 5)
    loads = F * np.sin(np.pi / 2 * coefs)

    # ----------------------------------------------
    # Mesh
    # ----------------------------------------------
    meshSize = 42 / 5

    # get the contour
    pt1 = Point(0, 80)
    pt2 = Point(-245, 21)
    pt3 = Point(-245, -21)
    pt4 = Point(0, -80)
    pt5 = Point(114, -80)
    pt6 = Point(114 + 13, -80 + 13)
    pt7 = Point(114 + 13, -67 / 2)
    pt8 = Point(114 + 13 + 25, -67 / 2)
    pt9 = Point(114 + 13 + 25, -34 / 2)
    pt10 = Point(114 + 13, -34 / 2, r=10)
    pt11 = Point(114 + 13, 34 / 2, r=10)
    pt12 = Point(114 + 13 + 25, 34 / 2)
    pt13 = Point(114 + 13 + 25, 67 / 2)
    pt14 = Point(114 + 13, 67 / 2)
    pt15 = Point(114 + 13, 80 - 13)
    pt16 = Point(114, 80)

    # fmt: off
    contour = Points([
            pt1, pt2, pt3, pt4, pt5, pt6, pt7, pt8, pt9, pt10,
            pt11, pt12, pt13, pt14, pt15, pt16,
        ],
        meshSize,
    )
    # fmt: on

    # get circles
    circle1 = Circle(Point(-220), 25, meshSize, isHollow=True)
    circle2 = Circle(Point(), 25, meshSize, isHollow=True)
    circle3 = Circle(Point(114 + 13 - 25, 80 - 25), 25, meshSize, isHollow=True)
    circle4 = Circle(Point(114 + 13 - 25, -80 + 25), 25, meshSize, isHollow=True)
    circle5 = Circle(Point(67), 84, meshSize, isHollow=True)

    inclusions = [circle1, circle2, circle3, circle4, circle5]

    # get the mesh
    if dim == 2:
        mesh = contour.Mesh_2D(inclusions, ElemType.TRI3)
    else:
        mesh = contour.Mesh_Extrude(inclusions, [0, 0, thickness], [4], ElemType.PRISM6)

    # get loading nodes
    nodesLoad = mesh.Nodes_Cylinder(circle1)
    nodesLoad = nodesLoad[mesh.coord[nodesLoad, 1] <= 0]

    # get fixed nodes
    nodesCircle2 = mesh.Nodes_Cylinder(circle2)
    nodesCircle3 = mesh.Nodes_Cylinder(circle3)
    nodesCircle4 = mesh.Nodes_Cylinder(circle4)
    fixedNodes = np.concat((nodesCircle2, nodesCircle3, nodesCircle4))

    # PyVista.Plot_Mesh(mesh).show()

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

    material = Models.Elastic.Isotropic(
        dim, E=210000, v=0.25, planeStress=True, thickness=thickness
    )

    simu = Simulations.Elastic(mesh, material)

    fixed = [0] * dim
    unknowns = simu.Get_unknowns()

    # loop over the load
    for load in loads:
        # Apply boundary conditions
        simu.Bc_Init()
        simu.add_dirichlet(fixedNodes, fixed, unknowns)
        simu.add_surfLoad(nodesLoad, [-load / area], ["y"])

        # Solve the simulation
        simu.Solve()

        # Save the iteration results
        simu.Save_Iter()

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

    print(simu)

    PyVista.Plot_BoundaryConditions(simu).show()

    PyVista.Plot(simu, "Svm", deformFactor=200, plotMesh=True, nodeValues=False).show()

    if makeMovie:
        PyVista.Movie_simu(
            simu,
            "Svm",
            folder,
            "Svm.gif",
            deformFactor=200,
            nodeValues=False,
            plotMesh=True,
        )

    if makeParaview:
        Paraview.Save_simu(
            simu, folder, elementFields=["Svm", "Stress", "Strain", "Wdef_e"]
        )