Nonlinear static analysis with structsolve
==========================================

.. currentmodule:: bfscplate2d.bfscplate2d

The plate of :doc:`ex_nonlinear_static`, solved with ``structsolve.Analysis``
of `structsolve <https://saullocastro.github.io/structsolve/>`_, see
:ref:`solving-with-structsolve`. The four callables loop over
the elements with the functions of :doc:`ex_nonlinear_static` and work on
the unknown degrees of freedom ``bu``, the partition of the free degrees of
freedom; ``calc_fint`` also keeps the internal forces of each iteration:

.. literalinclude:: ../../tests/test_static_axial_load_nonlinear.py
    :pyobject: Callables

The analysis applies the load in equal increments, with
``Analysis.initialInc`` and ``Analysis.maxInc``, checks that none was cut,
and computes Crisfield's relative residual, the convergence criterion of
structsolve, at each iteration of the last increment:

.. literalinclude:: ../../tests/test_static_axial_load_nonlinear.py
    :pyobject: newton_raphson

A consistent tangent stiffness matrix squares the residual at the last
iteration:

.. literalinclude:: ../../tests/test_static_axial_load_nonlinear.py
    :pyobject: assert_quadratic_convergence

With a small transverse force the solution in one increment reproduces the
linearised one, `(\boldsymbol{K}_{C0} + \boldsymbol{K}_G)^{-1}\boldsymbol{F}_{ext}`, with `\boldsymbol{K}_G` of the axial
load:

.. literalinclude:: ../../tests/test_static_axial_load_nonlinear.py
    :pyobject: test_static


Follower pressure
-----------------

The callables of a follower pressure, ``FollowerCallables``, which receive
the load factor ``inc``, are given in :ref:`solving-with-structsolve`.
The cantilever of :doc:`ex_follower_pressure`, with free edges and an
unsymmetric load stiffness matrix, solved with these callables in five
load increments, against the reference values of panels:

.. literalinclude:: ../../tests/test_follower_pressure_structsolve.py
    :pyobject: test_cantilever_large_deflection_against_panels