.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/elements/mass21/example_mass21.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_mass21_example_mass21.py>`
        to download the full example code.

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

.. _sphx_glr_gallery_elements_mass21_example_mass21.py:


.. _ref_mass21_example:

POINT_MASS — single-DOF spring-mass oscillator
==============================================

Two nodes connected by a SPRING element. A POINT_MASS element sits on the
free node. The first modal frequency is compared to the textbook SDOF
result ``ω = √(k / m)``.

.. GENERATED FROM PYTHON SOURCE LINES 11-21

.. code-block:: Python


    from __future__ import annotations

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

    import femorph_solver
    from femorph_solver import ELEMENTS








.. GENERATED FROM PYTHON SOURCE LINES 22-26

Problem data
------------
``k = 1 kN/m``, ``m = 0.25 kg`` → ``ω = √(4000) ≈ 63.2456 rad/s``
(``f ≈ 10.065 Hz``).

.. GENERATED FROM PYTHON SOURCE LINES 26-31

.. code-block:: Python

    k = 1000.0
    mass = 0.25
    omega_expected = np.sqrt(k / mass)
    f_expected = omega_expected / (2.0 * np.pi)








.. GENERATED FROM PYTHON SOURCE LINES 32-39

Build the model
---------------
Two element types: SPRING (spring, TYPE 1) and POINT_MASS (point mass,
TYPE 2). Each gets its own REAL set. The grid carries per-cell
``ansys_elem_type_num`` / ``ansys_real_constant`` arrays that pin the
kernel + real-set down element-by-element — the same routing legacy APDL
uses but stamped on the grid up front.

.. GENERATED FROM PYTHON SOURCE LINES 39-55

.. code-block:: Python

    points = np.array([[0.0, 0.0, 0.0], [1.0, 0.0, 0.0]], dtype=np.float64)
    cells = np.array([2, 0, 1, 1, 1], dtype=np.int64)  # VTK_LINE(0,1) + VTK_VERTEX(1)
    cell_types = np.array([VTK_LINE, VTK_VERTEX], dtype=np.uint8)
    grid = pv.UnstructuredGrid(cells, cell_types, points)
    grid.cell_data["ansys_elem_type_num"] = np.array([1, 2], dtype=np.int32)
    grid.cell_data["ansys_real_constant"] = np.array([1, 2], dtype=np.int32)

    mdl = femorph_solver.Model.from_grid(grid)
    mdl.assign(ELEMENTS.SPRING, real=(k,), et_id=1, real_id=1)
    mdl.assign(ELEMENTS.POINT_MASS, real=(mass,), et_id=2, real_id=2)

    mdl.fix(nodes=[1], dof="ALL")  # clamp the spring base
    mdl.fix(nodes=[2], dof="UY")  # kill transverse rigid-body modes
    mdl.fix(nodes=[2], dof="UZ")
    m = mdl  # alias preserves later references in this script








.. GENERATED FROM PYTHON SOURCE LINES 56-60

Modal solve + analytical comparison
-----------------------------------
Only one physical DOF is free (UX at node 2). ``modal_solve`` returns
a single positive eigenvalue whose square root is ω.

.. GENERATED FROM PYTHON SOURCE LINES 60-68

.. code-block:: Python

    res = m.modal_solve(n_modes=1)
    omega_computed = float(np.sqrt(res.omega_sq[0]))
    f_computed = float(res.frequency[0])

    print(f"Expected ω = {omega_expected:.6f} rad/s, f = {f_expected:.6f} Hz")
    print(f"Computed ω = {omega_computed:.6f} rad/s, f = {f_computed:.6f} Hz")
    assert np.isclose(omega_computed, omega_expected, rtol=1e-10)





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

 .. code-block:: none

    Expected ω = 63.245553 rad/s, f = 10.065842 Hz
    Computed ω = 63.245553 rad/s, f = 10.065842 Hz




.. GENERATED FROM PYTHON SOURCE LINES 69-75

Plot the mode shape
-------------------
Dilate the mode shape for visualisation. With POINT_MASS being a
single-node element the mesh contains a VTK_LINE (the spring) and a
VTK_VERTEX (the mass) — pyvista happily draws the combined
unstructured grid.

.. GENERATED FROM PYTHON SOURCE LINES 75-101

.. code-block:: Python

    dof = m.dof_map()
    mode = res.mode_shapes[:, 0]
    grid = m.grid.copy()
    displacement = np.zeros((grid.n_points, 3), dtype=np.float64)
    for i, nn in enumerate(grid.point_data["ansys_node_num"]):
        rows = np.where(dof[:, 0] == int(nn))[0]
        for r in rows:
            displacement[i, int(dof[r, 1])] = mode[r]
    # Scale so the peak is 0.3 m for clarity.
    peak = float(np.max(np.abs(displacement))) or 1.0
    displacement *= 0.3 / peak
    grid.point_data["mode1"] = displacement

    warped = grid.warp_by_vector("mode1", factor=1.0)
    plotter = pv.Plotter(off_screen=True)
    plotter.add_mesh(grid, style="wireframe", color="gray", line_width=3)
    plotter.add_mesh(
        warped,
        color="tomato",
        line_width=6,
        render_points_as_spheres=True,
        point_size=18,
    )
    plotter.add_text(f"f1 = {f_computed:.3f} Hz", font_size=12)
    plotter.add_axes()
    plotter.show()



.. image-sg:: /gallery/elements/mass21/images/sphx_glr_example_mass21_001.png
   :alt: example mass21
   :srcset: /gallery/elements/mass21/images/sphx_glr_example_mass21_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.229 seconds)


.. _sphx_glr_download_gallery_elements_mass21_example_mass21.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: example_mass21.ipynb <example_mass21.ipynb>`

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

      :download:`Download Python source code: example_mass21.py <example_mass21.py>`

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

      :download:`Download zipped: example_mass21.zip <example_mass21.zip>`


.. only:: html

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

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