Sampling / Interpolation along points

[m-vik]

Hello,
I made an elastic simulation. I would like to know if it is possible to sample the strain along defined points (so basically interpolated between the elements/nodes). Because i need to investigate specific areas of my model.

Thank you!

[matnoel]

Hello @m-vik,

Does this kind of tool meet your expectations?

import numpy as np

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

if __name__ == "__main__":

    Display.Clear()

    # mesh --------------------------------------------

    result = "Exx"

    domain = Domain((0, 0), (1, 1))
    mesh = domain.Mesh_2D(elemType=ElemType.TRI3)

    coords_p = np.array(
        [
            [0.5, 0.5, 0.0],
            [0.8, 0.95, 0.0],
            [0.08, 0.95, 0.0],
        ]
    )

    ax = Display.Plot_Mesh(mesh)
    ax.plot(
        *coords_p[:, : mesh.inDim].T,
        ls="",
        marker="s",
        color="red",
    )

    # simu --------------------------------------------

    simu = Simulations.Elastic(
        mesh,
        Models.Elastic.Isotropic(2, E=1, v=0.3),
    )
    simu.add_dirichlet(
        mesh.Nodes_Conditions(lambda x, y, z: x == 0), [0, 0], ["x", "y"]
    )
    simu.add_dirichlet(mesh.Nodes_Conditions(lambda x, y, z: x == 1), [0.1], ["x"])

    simu.Solve()

    Display.Plot_Result(simu, "ux", plotMesh=True)

    # get values --------------------------------------------

    groupElem = mesh.groupElem

    detectedNodes, detectedElements_e, connect_e_n, coordInElem_n = (
        groupElem.Get_Mapping(
            coords_p,
            needCoordinates=(groupElem.order > 1),
        )
    )

    values_p = np.zeros(len(coords_p))

    if groupElem.order == 1:
        result_e = simu.Result(result, nodeValues=False)  # (Ne,)
        for element, pidx in zip(detectedElements_e, connect_e_n):
            values_p[pidx] = result_e[element]
        useNodeValues = False

    else:
        Eps_n = simu.Result(result, nodeValues=True)  # (Nn,)
        Eps_e = groupElem.Locates_sol_e(Eps_n, 1)  # (Ne, nPe)
        for element, pidx in zip(detectedElements_e, connect_e_n):
            xi = coordInElem_n[pidx]  # (n_pts_in_e, dim)
            N_pg = groupElem._Eval_Functions(groupElem._N(), xi)  # (n_pts_in_e, 1, nPe)
            values_p[pidx] = np.einsum("pin,n->p", N_pg, Eps_e[element])
        useNodeValues = True

    ax = Display.Plot_Result(
        simu,
        result,
        nodeValues=useNodeValues,
        plotMesh=True,
        ncolors=11,
    )

    for p in detectedNodes:
        ax.scatter(
            *coords_p[p, : mesh.inDim],
            marker="o",
            label=f"{values_p[p]:.3f}",
        )
    ax.legend()

    Display.plt.show()

[m-vik]

Thank you very much!