-
Notifications
You must be signed in to change notification settings - Fork 13
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
* Add `SolidBodyCauchyStress` * Update test_mechanics.py * Update mechanics.rst * remove `cauchy_stress`-arg from `SolidBodyCauchyStress._gradient` * Update test_mechanics.py * Update test_mechanics.py
- Loading branch information
Showing
6 changed files
with
214 additions
and
1 deletion.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,162 @@ | ||
| # -*- 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/>. | ||
| """ | ||
| import numpy as np | ||
|
|
||
| from ..assembly import IntegralForm | ||
| from ..constitution import AreaChange | ||
| from ..math import dot | ||
| from ._helpers import Assemble, Results | ||
|
|
||
|
|
||
| class SolidBodyCauchyStress: | ||
| r"""A Cauchy stress boundary on a solid body. | ||
| Parameters | ||
| ---------- | ||
| field : FieldContainer | ||
| A field container with fields created on a boundary region. | ||
| stress : ndarray of shape (3, 3, ...) or None, optional | ||
| The prescribed Cauchy stress components :math:`\sigma_{ij}` (default is None). | ||
| If None, all Cauchy stress components are set to zero. | ||
| Notes | ||
| ----- | ||
| .. math:: | ||
| \delta W_{ext} = \int_{\partial V} | ||
| \delta \boldsymbol{u} \cdot \boldsymbol{\sigma}\ d\boldsymbol{a} = | ||
| \int_{\partial V} | ||
| \delta \boldsymbol{u} \cdot \boldsymbol{\sigma} 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_stress = 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_stress, dim=2)]) | ||
| >>> stress = fem.SolidBodyCauchyStress(field=field_boundary) | ||
| >>> | ||
| >>> table = fem.math.linsteps([0, 1], num=5, axis=0, axes=9).reshape(-1, 3, 3) | ||
| >>> step = fem.Step( | ||
| ... items=[solid, stress], ramp={stress: 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, cauchy_stress=None): | ||
| self.field = field | ||
| self._normals = self.field.region.normals | ||
|
|
||
| self.results = Results() | ||
| self.results.kinematics = self._extract(self.field) | ||
|
|
||
| self.results.cauchy_stress = np.zeros((3, 3)) | ||
| if cauchy_stress is not None: | ||
| self.results.cauchy_stress = cauchy_stress | ||
|
|
||
| self.assemble = Assemble( | ||
| vector=self._vector, matrix=self._matrix, multiplier=-1.0 | ||
| ) | ||
| self._area_change = AreaChange() | ||
|
|
||
| def update(self, cauchy_stress): | ||
| self.__init__(self.field, cauchy_stress) | ||
|
|
||
| def _extract(self, field): | ||
| self.field = field | ||
| self.results.kinematics = self.field.extract() | ||
|
|
||
| return self.results.kinematics | ||
|
|
||
| def _vector(self, field=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, | ||
| ) | ||
|
|
||
| fun[0] = dot(self.results.cauchy_stress, fun[0], mode=(2, 2), out=fun[0]) | ||
|
|
||
| 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, 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, | ||
| ) | ||
|
|
||
| fun[0] = dot(self.results.cauchy_stress, fun[0], mode=(2, 4), out=fun[0]) | ||
|
|
||
| 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 |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters