:orphan:

Tutorials
=========

Numbered, deeply-narrated, multi-step walkthroughs that take a
new user from an empty :class:`~femorph_solver.Model` to a
designed structure.  Each tutorial builds on concepts from the
prior — modelled on the deal.II ``step-1`` … ``step-N`` family
that has trained two decades of finite-element practitioners.

The Tutorials live in the same gallery infrastructure as the
focused recipe :doc:`/gallery/post-processing/index` examples,
so every line of code runs on every documentation build —
nothing in this section is allowed to drift out of sync with the
library.

Where Tutorials differ from the focused gallery examples:

* **Prose-rich.**  Each step has design rationale, a recap of
  the FEM theory it exercises, and commentary on the result —
  not just a thin caption above the code.
* **End-to-end.**  Tutorials cover the complete workflow from
  geometry definition to a defensible engineering conclusion
  (mesh refinement, allowable check, design iteration).
* **Sequential.**  Tutorials assume you've worked the prior
  ones; they don't re-explain what was already taught.
* **Cross-linked.**  Each tutorial points back to the relevant
  theory chapters in :doc:`/reference/index` and the focused
  gallery recipes that demonstrate the same APIs in isolation.

If you want a 30-line snippet of one specific API, browse the
:doc:`/examples` gallery instead.  Tutorials are for learning
the workflow; the gallery is for copy-paste recipes.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="The earlier tutorials all built their meshes natively in pyvista.  Real engineering workflows rarely start that way: the geometry comes out of a CAD tool through a meshing pre-processor (HyperMesh, ANSA, Gmsh) and lands as a deck — almost always an MAPDL CDB or a NASTRAN BDF — that the analyst hands off to the solver, plus a snapshot of the solver-ready model that downstream consumers re-load.">

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  .. image:: /gallery/tutorials/images/thumb/sphx_glr_tutorial_06_cdb_to_results_thumb.png
    :alt:

  :doc:`/gallery/tutorials/tutorial_06_cdb_to_results`

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      <div class="sphx-glr-thumbnail-title">Tutorial 6 — End-to-end deliverable workflow</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Picking up from tutorial_01_cantilever_combined, the static analysis confirmed the bracket carries its design load with a comfortable safety margin.  But the equipment console it supports has variable-speed motors that excite the bracket at multiple harmonics across the operating band.  The next question is dynamic: do any of the bracket&#x27;s natural frequencies fall inside the excitation band, and if so which modes need to be included in a response-spectrum analysis to capture 90 % of the modal mass?">

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  .. image:: /gallery/tutorials/images/thumb/sphx_glr_tutorial_02_modal_survey_thumb.png
    :alt:

  :doc:`/gallery/tutorials/tutorial_02_modal_survey`

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      <div class="sphx-glr-thumbnail-title">Tutorial 2 — Modal survey of a cantilever bracket</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Picking up from tutorial_02_modal_survey, we now know the bracket&#x27;s natural frequencies and which modes carry the effective mass in each excitation direction.  The motors driving the equipment console aren&#x27;t a single sine, though — they sweep through their operating band as the production line ramps up and slows down, exciting the bracket at every frequency the sweep crosses.">

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  .. image:: /gallery/tutorials/images/thumb/sphx_glr_tutorial_04_harmonic_response_thumb.png
    :alt:

  :doc:`/gallery/tutorials/tutorial_04_harmonic_response`

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      <div class="sphx-glr-thumbnail-title">Tutorial 4 — Harmonic frequency response of a cantilever bracket</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Tutorials 1-3 walked the static + modal workflow on simply- shaped components.  Real rotating-equipment design has an extra wrinkle: the structure is cyclically symmetric.  An N-bladed rotor, an N-vaned diffuser, and an N-cylinder reciprocating engine all share the same algebraic property — the spectrum factors by harmonic index k \in \{0, 1, \ldots, \lfloor N / 2 \rfloor\}, and a single base sector plus the cyclic-pairing constraint recovers the full-rotor answer at a fraction of the DOF cost.">

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  .. image:: /gallery/tutorials/images/thumb/sphx_glr_tutorial_05_cyclic_rotor_thumb.png
    :alt:

  :doc:`/gallery/tutorials/tutorial_05_cyclic_rotor`

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      <div class="sphx-glr-thumbnail-title">Tutorial 5 — Cyclic-symmetry rotor design check</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="You&#x27;re sizing the wall of a small pressure vessel that operates at p = 10\,\text{MPa} internal pressure.  The preliminary design has bore radius a = 100\,\text{mm} and outer radius b = 200\,\text{mm} — a thick-walled geometry where the simpler thin-wall hoop-stress approximation \sigma_\theta = p\, r / t doesn&#x27;t apply.  ASME B31.3 §304.1 mandates that for r/t &lt; 6 you have to use either the full Lamé closed form or a numerical analysis.">

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  .. image:: /gallery/tutorials/images/thumb/sphx_glr_tutorial_03_pressure_vessel_thumb.png
    :alt:

  :doc:`/gallery/tutorials/tutorial_03_pressure_vessel`

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      <div class="sphx-glr-thumbnail-title">Tutorial 3 — Pressure-vessel design-by-analysis (Lamé thick cylinder)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="You&#x27;re tasked with sizing a steel cantilever bracket for an overhead-mounted equipment console.  The bracket carries the console&#x27;s dead weight (a uniform load along its span), an attached cable that pulls down at the tip, and a small applied moment from an off-axis fastener at the tip.  A preliminary cross-section is on the table; you need to confirm that">

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  .. image:: /gallery/tutorials/images/thumb/sphx_glr_tutorial_01_cantilever_combined_thumb.png
    :alt:

  :doc:`/gallery/tutorials/tutorial_01_cantilever_combined`

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      <div class="sphx-glr-thumbnail-title">Tutorial 1 — Cantilever beam under combined loading</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /gallery/tutorials/tutorial_06_cdb_to_results
   /gallery/tutorials/tutorial_02_modal_survey
   /gallery/tutorials/tutorial_04_harmonic_response
   /gallery/tutorials/tutorial_05_cyclic_rotor
   /gallery/tutorials/tutorial_03_pressure_vessel
   /gallery/tutorials/tutorial_01_cantilever_combined


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  .. container:: sphx-glr-footer sphx-glr-footer-gallery

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

      :download:`Download all examples in Python source code: tutorials_python.zip </gallery/tutorials/tutorials_python.zip>`

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

      :download:`Download all examples in Jupyter notebooks: tutorials_jupyter.zip </gallery/tutorials/tutorials_jupyter.zip>`


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

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