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

.. currentmodule:: bfsccylinder.bfsccylinder

The callables of ``structsolve.Analysis``, of `structsolve
<https://saullocastro.github.io/structsolve/>`_, for the cylinder of
:doc:`ex_nonlinear_static`, see :ref:`solving-with-structsolve`. They loop
over the elements with :func:`.update_fint`, :func:`.update_KCNL` and
:func:`.update_KG`, assemble, and work on the unknown degrees of freedom
``bu``, the partition of the free degrees of freedom:

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

The analysis, at the end of the test of :doc:`ex_nonlinear_static`, applies
the load in one increment, ``Analysis.initialInc = 1.``, with at most seven
corrections, ``Analysis.maxNumIter = 7``, and checks that the increment was
not cut:

.. literalinclude:: ../../tests/test_nonlinear_axial_compression.py
    :pyobject: test_nonlinear_axial_compression_load_controlled
    :start-at: callables = Callables(
    :end-at: raise RuntimeError('Not converged!')
    :dedent: 4

The solution is ``u = callables.expand(cs[-1])``. With the default
convergence criterion of Crisfield, `\zeta \le 10^{-9}`, the iterations
give `\zeta` = 2.5e-2, 2.2e-4, 2.0e-9 and then the round-off, about
1e-15, the quadratic convergence of a consistent tangent stiffness matrix.


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

The callables of a follower pressure, ``FollowerCallables``, which receive
the load factor ``inc``, are given in :ref:`solving-with-structsolve`.
A cylinder clamped at one end and free at the other, with an unsymmetric
load stiffness matrix, solved with these callables for both kinematics,
checking the equilibrium with the whole follower pressure and the
quadratic convergence of the Newton-Raphson iterations:

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