Nonlinear static analysis
=========================

.. currentmodule:: bfscplate2d.bfscplate2d

A rectangular isotropic plate, with `w` constrained at the nodes of the
four edges, compressed along `x` below its critical load, with a transverse force at the centre large enough to reach a
deflection of about 2.6 times the thickness. The model keeps the value
arrays of `\boldsymbol{K}_{CNL} + \boldsymbol{K}_{GNL}` and `\boldsymbol{K}_G`, which are zeroed and recomputed at each
iteration with :func:`.update_KCNL` and :func:`.update_KG`, and the
internal forces of :func:`.update_fint`:

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

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

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

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

The full Newton-Raphson method of structsolve, with the tangent stiffness
matrix `\boldsymbol{K}_{C0} + \boldsymbol{K}_{CNL} + \boldsymbol{K}_{GNL} + \boldsymbol{K}_G` rebuilt at every iteration and the
external forces applied in four increments, ``newton_raphson(m, fext + ftrans,
increments=4)``, see :doc:`ex_structsolve_nonlinear`. The test checks the
quadratic convergence and that the membrane stretching makes the plate
stiffer than the linearised prediction `(\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_large_deflection