.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/elements/link180/example_link180.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_gallery_elements_link180_example_link180.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_gallery_elements_link180_example_link180.py:


.. _ref_link180_example:

TRUSS2 — axial truss under end load
====================================

Single TRUSS2 spar fixed at node 1 and pulled along the x-axis at
node 2. The tip displacement is compared to the closed-form rod
solution ``u = P L / (E A)`` and the axial stress is plotted on the
deformed mesh.

.. GENERATED FROM PYTHON SOURCE LINES 12-22

.. code-block:: Python


    from __future__ import annotations

    import numpy as np
    import pyvista as pv
    from vtkmodules.util.vtkConstants import VTK_LINE

    import femorph_solver
    from femorph_solver import ELEMENTS








.. GENERATED FROM PYTHON SOURCE LINES 23-26

Problem data
------------
Steel rod, 1 m long, 100 mm² cross-section, pulled with a 1 kN tip load.

.. GENERATED FROM PYTHON SOURCE LINES 26-31

.. code-block:: Python

    E = 2.1e11  # Pa
    A = 1.0e-4  # m² (100 mm²)
    L = 1.0  # m
    P = 1.0e3  # N (tensile)








.. GENERATED FROM PYTHON SOURCE LINES 32-38

Build the model
---------------
``femorph_solver.Model.assign`` collapses the legacy ``et / mp / r``
trio into one call.  A TRUSS2 has three translational DOFs per node,
so we only fix UX at node 2's support and zero-out the transverse
DOFs to kill the transverse rigid modes.

.. GENERATED FROM PYTHON SOURCE LINES 38-55

.. code-block:: Python

    points = np.array([[0.0, 0.0, 0.0], [L, 0.0, 0.0]], dtype=np.float64)
    cells = np.array([2, 0, 1], dtype=np.int64)
    cell_types = np.array([VTK_LINE], dtype=np.uint8)
    grid = pv.UnstructuredGrid(cells, cell_types, points)

    m = femorph_solver.Model.from_grid(grid)
    m.assign(
        ELEMENTS.TRUSS2,
        material={"EX": E, "DENS": 7850.0},
        real=(A,),
    )

    m.fix(nodes=[1], dof="ALL")  # clamp all translational DOFs at node 1
    m.fix(nodes=[2], dof="UY")  # suppress transverse rigid-body motion
    m.fix(nodes=[2], dof="UZ")
    m.apply_force(2, fx=P)








.. GENERATED FROM PYTHON SOURCE LINES 56-61

Static solve + analytical comparison
------------------------------------
The rod equation gives ``u_tip = P L / (E A)``. With a single TRUSS2
this is exact (linear shape functions are sufficient for a prismatic
bar under end load).

.. GENERATED FROM PYTHON SOURCE LINES 61-72

.. code-block:: Python

    res = m.solve()

    dof = m.dof_map()
    tip_ux_row = np.where((dof[:, 0] == 2) & (dof[:, 1] == 0))[0][0]
    u_tip = res.displacement[tip_ux_row]
    u_expected = P * L / (E * A)

    print(f"TRUSS2 tip UX        = {u_tip:.6e} m")
    print(f"Analytical PL/(EA)    = {u_expected:.6e} m")
    assert np.isclose(u_tip, u_expected, rtol=1e-10)





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    TRUSS2 tip UX        = 4.761905e-05 m
    Analytical PL/(EA)    = 4.761905e-05 m




.. GENERATED FROM PYTHON SOURCE LINES 73-78

Post-processing: axial stress
-----------------------------
For a single TRUSS2 the axial stress is uniform: ``σ = E · (Δu / L)``
where ``Δu`` is the elongation. Carry it as cell data on the mesh for
plotting.

.. GENERATED FROM PYTHON SOURCE LINES 78-90

.. code-block:: Python

    sigma_axial = E * (u_tip / L)
    print(f"Axial stress          = {sigma_axial:.3e} Pa (= P/A = {P / A:.3e})")

    grid = m.grid.copy()
    displacement = np.zeros((grid.n_points, 3), dtype=np.float64)
    for i, node_num in enumerate(grid.point_data["ansys_node_num"]):
        rows = np.where(dof[:, 0] == int(node_num))[0]
        for r in rows:
            displacement[i, int(dof[r, 1])] = res.displacement[r]
    grid.point_data["displacement"] = displacement
    grid.cell_data["sigma_axial"] = np.array([sigma_axial])





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Axial stress          = 1.000e+07 Pa (= P/A = 1.000e+07)




.. GENERATED FROM PYTHON SOURCE LINES 91-93

Plot the deformed truss coloured by axial stress
------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 93-112

.. code-block:: Python

    warped = grid.warp_by_vector("displacement", factor=1.0e5)
    plotter = pv.Plotter(off_screen=True)
    plotter.add_mesh(
        grid,
        style="wireframe",
        color="gray",
        line_width=3,
        label="undeformed",
    )
    plotter.add_mesh(
        warped,
        scalars="sigma_axial",
        line_width=6,
        scalar_bar_args={"title": "axial stress [Pa]"},
        label="deformed (×1e5)",
    )
    plotter.add_legend()
    plotter.add_axes()
    plotter.show()



.. image-sg:: /gallery/elements/link180/images/sphx_glr_example_link180_001.png
   :alt: example link180
   :srcset: /gallery/elements/link180/images/sphx_glr_example_link180_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.185 seconds)


.. _sphx_glr_download_gallery_elements_link180_example_link180.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: example_link180.ipynb <example_link180.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: example_link180.py <example_link180.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: example_link180.zip <example_link180.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_