Analyses
========

Each analysis-type chapter answers the same five questions:

1. **When to use this analysis** — what problem class it
   solves, when to pick it over its siblings.
2. **Boundary conditions and loads** — what BCs / load types
   feed into it, with cross-references to
   :doc:`/best-practices/bc-pitfalls`.
3. **The math** — one paragraph, with a link to the full
   theory chapter under :doc:`/reference/theory/index`.
4. **Running the solve** — the high-level ``Model.*_solve()``
   call and the result object it returns.
5. **Common gotchas + post-processing recipes** — links
   into the focused gallery and the troubleshooting
   flowchart.

Pick the analysis type that matches your engineering question:

.. grid:: 1 2 2 2
    :gutter: 3

    .. grid-item-card:: :octicon:`grabber;1.5em;sd-mr-1` Linear static
        :link: linear-static
        :link-type: doc

        :math:`\mathbf{K}\, \mathbf{u} = \mathbf{f}` — the
        workhorse for >80 % of structural design.  Snapshot
        of displacement / stress / reaction under fixed loads.

    .. grid-item-card:: :octicon:`pulse;1.5em;sd-mr-1` Modal
        :link: modal
        :link-type: doc

        Natural frequencies and mode shapes.  The
        ``n_modes`` for a downstream response-spectrum
        analysis usually comes from the cumulative
        effective-mass curve here.

    .. grid-item-card:: :octicon:`graph;1.5em;sd-mr-1` Harmonic
        :link: harmonic
        :link-type: doc

        Steady-state response to sinusoidal forcing across a
        frequency sweep.  FRF curves for vibration-isolation
        / control-system design land here.

    .. grid-item-card:: :octicon:`hourglass;1.5em;sd-mr-1` Transient
        :link: transient
        :link-type: doc

        Time-history response under arbitrary time-varying
        loads.  Newmark-β implicit integrator; modal-
        superposition variant on the planned roadmap.

    .. grid-item-card:: :octicon:`infinity;1.5em;sd-mr-1` Cyclic-symmetry
        :link: cyclic-symmetry
        :link-type: doc

        Modal analysis on N-fold rotationally-symmetric
        structures (rotors, vaned diffusers).  Recovers the
        full-rotor spectrum at sector cost.

    .. grid-item-card:: :octicon:`alert;1.5em;sd-mr-1` Buckling (planned)
        :link: buckling
        :link-type: doc

        Linear bifurcation buckling load multiplier.  Not yet
        shipped — see the page for workarounds today.

.. toctree::
    :hidden:
    :maxdepth: 1

    linear-static
    modal
    harmonic
    transient
    cyclic-symmetry
    buckling