Elas5

A cylindrical conduit exposed to uniform pressure.

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

Element type: TRI6
Ne = 438, Nn = 942

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

Isotropic:
E = 2.10e+05, v = 0.3
planeStress = False
thickness = 1.00e+02

solver : scipy

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

Unspecified.

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


W def = 0.03

Svm max = 2.59

Evm max = 0.00 %

Ux max = 6.69e-05
Ux min = 0.00e+00

Uy max = 6.68e-05
Uy min = 0.00e+00

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

Mesh : 26.954 ms
Boundary Conditions : 31.710 µs
Matrix : 16.222 ms
Solver : 24.723 ms
Display : 175.191 ms
PostProcessing : 1.303 ms

import matplotlib.pyplot as plt
import numpy as np

from EasyFEA import Display, Models, ElemType, Simulations
from EasyFEA.Geoms import Point, Line, Circle, CircleArc, Contour

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

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

    dim = 2
    isSymmetric = True
    openCrack = True

    # geom
    r = 10
    e = 5
    thickness = 100

    # load
    sig = 5  # bar
    sig *= 1e-1  # 1 bar = 0.1 MPa

    # ----------------------------------------------
    # Mesh
    # ----------------------------------------------
    meshSize = e / 5

    center = Point()
    if isSymmetric:
        p1 = Point(r, 0)
        p2 = Point(e + r, 0)
        p3 = Point(0, e + r)
        p4 = Point(0, r)

        line1 = Line(p1, p2, meshSize)
        line2 = CircleArc(p2, p3, center, meshSize=meshSize)
        line3 = Line(p3, p4, meshSize)
        line4 = CircleArc(p4, p1, center, meshSize=meshSize)

        contour = Contour([line1, line2, line3, line4])
        inclusions = []
    else:
        contour = Circle(center, (r + e) * 2, meshSize)
        inclusions = [Circle(center, 2 * r, meshSize, isHollow=True)]

    extrude = [0, 0, -thickness]

    l = e / 4
    p = r + e / 2
    alpha = np.pi / 3
    pc1 = Point((p - l / 2) * np.cos(alpha), (p - l / 2) * np.sin(alpha))
    pc2 = Point((p + l / 2) * np.cos(alpha), (p + l / 2) * np.sin(alpha))

    if dim == 2:
        crack = Line(pc1, pc2, meshSize / 6, isOpen=openCrack)
        mesh = contour.Mesh_2D(inclusions, elemType=ElemType.TRI6, cracks=[crack])
    else:
        pc3 = pc2.copy()
        pc3.Translate(*extrude)
        pc4 = pc1.copy()
        pc4.Translate(*extrude)
        l1 = Line(pc1, pc2, meshSize / 6, isOpen=openCrack)
        l2 = Line(pc2, pc3, meshSize / 6)
        l3 = Line(pc3, pc4, meshSize / 6, isOpen=openCrack)
        l4 = Line(pc4, pc1, meshSize / 6)
        crack = Contour([l1, l2, l3, l4], isOpen=openCrack)
        mesh = contour.Mesh_Extrude(
            inclusions, extrude, [], ElemType.TETRA4, cracks=[crack]
        )

    # ----------------------------------------------
    # Simulation
    # ----------------------------------------------
    material = Models.Elastic.Isotropic(
        dim, E=210000, v=0.3, planeStress=False, 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)
        simu.add_dirichlet(nodes_x0, [0], ["x"])
        simu.add_dirichlet(nodes_y0, [0], ["y"])

    nodes_load = mesh.Nodes_Cylinder(Circle(center, r * 2), direction=extrude)

    if dim == 2 and not isSymmetric:
        sig *= -1

    simu.add_pressureLoad(nodes_load, sig)

    simu.Solve()
    simu.Save_Iter()

    # ----------------------------------------------
    # Results
    # ----------------------------------------------
    factorDef = r / 5 / simu.Result("displacement_norm").max()

    Display.Plot_Mesh(simu, deformFactor=factorDef)
    Display.Plot_BoundaryConditions(simu)
    Display.Plot_Result(simu, "ux", ncolors=10, nodeValues=True)
    Display.Plot_Result(simu, "uy", ncolors=10, nodeValues=True)
    Display.Plot_Result(
        simu, "Svm", ncolors=10, nodeValues=True, deformFactor=factorDef, plotMesh=True
    )

    print(simu)

    # PyVista.Plot_BoundaryConditions(simu).show()

    plt.show()