LinearElasticity2

A cantilever beam undergoing bending deformation in dynamic.

Note that this simulation is also performed in examples/Dynamic/Dynamic1.py.

Static Scene

Interactive Scene

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import matplotlib.pyplot as plt
import numpy as np

from EasyFEA import Folder, Display, ElemType, Models, Simulations, PyVista
from EasyFEA.FEM import Field, BiLinearForm, FeArray, Sym_Grad, Trace
from EasyFEA.Geoms import Domain

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

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

    dim = 3

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

    # geom
    L = 120  # mm
    h = 13

    # model
    elastic = Models.Elastic.Isotropic(dim, 210000, 0.3, planeStress=True, thickness=h)
    lmbda = elastic.get_lambda()
    mu = elastic.get_mu()
    rho = 8100 * 1e-9

    # load
    Tmax = 0.5
    N = 50
    dt = Tmax / N
    time = -dt

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

    contour = Domain((0, 0), (L, h), h / 3)

    if dim == 2:
        mesh = contour.Mesh_2D([], ElemType.QUAD4, isOrganised=True)
    else:
        mesh = contour.Mesh_Extrude(
            [], [0, 0, h], [3], ElemType.HEXA8, isOrganised=True
        )

    nodesX0 = mesh.Nodes_Conditions(lambda x, y, z: x == 0)
    nodesXL = mesh.Nodes_Conditions(lambda x, y, z: x == L)

    # ----------------------------------------------
    # Formulations
    # ----------------------------------------------

    field = Field(mesh.groupElem, dim)

    def S(u: Field) -> FeArray:
        Eps = Sym_Grad(u)
        return 2 * mu * Eps + lmbda * Trace(Eps) * np.eye(dim)

    @BiLinearForm
    def computeK(u: Field, v: Field):
        Sig = S(u)
        Eps = Sym_Grad(v)
        return Sig.ddot(Eps)

    @BiLinearForm
    def computeM(u: Field, v: Field):
        return rho * u.dot(v)

    @BiLinearForm
    def computeC(u: Field, v: Field):
        K = computeK(u, v)
        M = computeM(u, v)
        C = K * 1e-3 + M * 1e-3
        return C

    weakForms = Models.WeakForms(field, computeK, computeC, computeM)

    # ----------------------------------------------
    # Simulations
    # ----------------------------------------------

    simu = Simulations.WeakForms(mesh, weakForms)

    # static simulation
    simu.add_dirichlet(nodesX0, [0] * dim, simu.Get_unknowns())
    simu.add_dirichlet(nodesXL, [-10], ["y"])

    simu.Solve()

    # dynamic simulation
    simu.Solver_Set_Hyperbolic_Algorithm(dt)
    simu.Save_Iter()

    simu.Bc_Init()
    simu.add_dirichlet(nodesX0, [0] * dim, simu.Get_unknowns())

    while time <= Tmax:

        time += dt

        simu.Solve()
        simu.Save_Iter()

        print(f"{time:.3f} s", end="\r")

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

    if makeMovie:
        PyVista.Movie_simu(
            simu,
            "uy",
            folder,
            "uy.gif",
            deformFactor=1,
            plotMesh=True,
            N=400,
            nodeValues=True,
        )

    simu.Set_Iter(0)
    PyVista.Plot(simu, "uy", 1, plotMesh=True).show()

    plt.show()