# -*- coding: utf-8 -*-
"""
This file is part of FElupe.
FElupe is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
FElupe is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FElupe. If not, see <http://www.gnu.org/licenses/>.
"""
from ..assembly import IntegralForm
from ..constitution import AreaChange
from ._helpers import Assemble, Results
[docs]
class SolidBodyPressure:
r"""A hydrostatic pressure boundary on a solid body.
Parameters
----------
field : FieldContainer
A field container with fields created on a boundary region.
pressure : float or ndarray or None, optional
A scaling factor for the prescribed pressure :math:`p` (default is None). If
None, the pressure is set to zero.
Notes
-----
.. hint::
The pressure is always given as normal force per deformed **area**. This is
important for axisymmetric problems.
.. math::
\delta W_{ext} = \int_{\partial V}
\delta \boldsymbol{u} \cdot (-p) J \boldsymbol{F}^{-T} \ d\boldsymbol{A}
Examples
--------
.. pyvista-plot::
>>> import felupe as fem
>>>
>>> mesh = fem.Rectangle(n=6)
>>> region = fem.RegionQuad(mesh)
>>> field = fem.FieldContainer([fem.FieldAxisymmetric(region, dim=2)])
>>> boundaries = fem.dof.symmetry(field[0])
>>> umat = fem.NeoHooke(mu=1, bulk=2)
>>> solid = fem.SolidBody(umat, field)
>>>
>>> region_pressure = fem.RegionQuadBoundary(
... mesh=mesh,
... only_surface=True, # select only faces on the outline
... mask=mesh.points[:, 0] == 1, # select a subset of faces on the surface
... ensure_3d=True, # requires True for axisymmetric/plane strain, otherwise False
... )
>>> field_boundary = fem.FieldContainer([fem.FieldAxisymmetric(region_pressure, dim=2)])
>>> pressure = fem.SolidBodyPressure(field=field_boundary)
>>>
>>> table = fem.math.linsteps([0, 1], num=5)
>>> step = fem.Step(
... items=[solid, pressure], ramp={pressure: 1 * table}, boundaries=boundaries
... )
>>>
>>> job = fem.Job(steps=[step]).evaluate()
>>> solid.plot(
... "Principal Values of Cauchy Stress", component=2, clim=[-1.01, -0.99]
... ).show()
"""
def __init__(self, field, pressure=None):
self.field = field
self._normals = self.field.region.normals
self.results = Results()
self.results.kinematics = self._extract(self.field)
self.results.pressure = 0
if pressure is not None:
self.results.pressure = pressure
self.assemble = Assemble(
vector=self._vector, matrix=self._matrix, multiplier=-1.0
)
self._area_change = AreaChange()
[docs]
def update(self, pressure):
self.__init__(self.field, pressure)
def _extract(self, field):
self.field = field
self.results.kinematics = self.field.extract()
return self.results.kinematics
def _vector(self, field=None, pressure=None, parallel=False, resize=None):
if field is not None:
self._update(field)
self.results.kinematics = self._extract(self.field)
fun = self._area_change.function(
self.results.kinematics,
self._normals,
parallel=parallel,
)
if pressure is not None:
self.results.pressure = pressure
fun[0] *= -self.results.pressure
self.results.force = IntegralForm(
fun=fun, v=self.field, dV=self.field.region.dV, grad_v=[False]
).assemble(parallel=parallel)
if resize is not None:
self.results.force.resize(*resize.shape)
return self.results.force
def _matrix(self, field=None, pressure=None, parallel=False, resize=None):
if field is not None:
self._update(field)
self.results.kinematics = self._extract(self.field)
fun = self._area_change.gradient(
self.results.kinematics,
self._normals,
parallel=parallel,
)
if pressure is not None:
self.results.pressure = pressure
fun[0] *= -self.results.pressure
self.results.stiffness = IntegralForm(
fun=fun,
v=self.field,
u=self.field,
dV=self.field.region.dV,
grad_v=[False],
grad_u=[True],
).assemble(parallel=parallel)
if resize is not None:
self.results.stiffness.resize(*resize.shape)
return self.results.stiffness
def _update(self, other_field, field=None):
if field is not None:
self.field = field
self.field[0].values = other_field[0].values
self.results.kinematics = self._extract(self.field)
return self.field
