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[Getfem-commits] r5276 - in /trunk/getfem/doc/sphinx/source: ./ userdoc/
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From: |
Yves . Renard |
|
Subject: |
[Getfem-commits] r5276 - in /trunk/getfem/doc/sphinx/source: ./ userdoc/ userdoc/images/ |
|
Date: |
Fri, 01 Apr 2016 11:37:27 -0000 |
Author: renard
Date: Fri Apr 1 13:37:27 2016
New Revision: 5276
URL: http://svn.gna.org/viewcvs/getfem?rev=5276&view=rev
Log:
work in progress
Added:
trunk/getfem/doc/sphinx/source/userdoc/images/ALE_rotating_body.fig
trunk/getfem/doc/sphinx/source/userdoc/images/ALE_rotating_conf.fig
trunk/getfem/doc/sphinx/source/userdoc/model_ALE_rotating.rst
Removed:
trunk/getfem/doc/sphinx/source/userdoc/examples.rst
Modified:
trunk/getfem/doc/sphinx/source/biblio.rst
trunk/getfem/doc/sphinx/source/userdoc/images/Makefile
trunk/getfem/doc/sphinx/source/userdoc/index.rst
trunk/getfem/doc/sphinx/source/userdoc/model.rst
trunk/getfem/doc/sphinx/source/userdoc/model_nonlinear_elasticity.rst
Modified: trunk/getfem/doc/sphinx/source/biblio.rst
URL:
http://svn.gna.org/viewcvs/getfem/trunk/getfem/doc/sphinx/source/biblio.rst?rev=5276&r1=5275&r2=5276&view=diff
==============================================================================
--- trunk/getfem/doc/sphinx/source/biblio.rst (original)
+++ trunk/getfem/doc/sphinx/source/biblio.rst Fri Apr 1 13:37:27 2016
@@ -62,6 +62,11 @@
*A finite element method for Reissner-Mindlin plates*,
Math. Comp., 83:286, 701-733, 2014.
+.. [Dr-La-Ek2014] A. Draganis, F. Larsson, A. Ekberg,
+ *Finite element analysis of transient thermomechanical rolling contact using
+ an efficient arbitrary Lagrangian-Eulerian description*,
+ Comput. Mech., 54, 389-405, 2014.
+
.. [Fa-Po-Re2015] M. Fabre, J. Pousin, Y. Renard.
*A fictitious domain method for frictionless contact problems in elasticity
using Nitsche's method*. preprint,
https://hal.archives-ouvertes.fr/hal-00960996v1
@@ -112,7 +117,13 @@
*Optimal L2 error bounds for MITC3 type element.* Numer. Math. 91, 77-91,
2002.
.. [Xfem] N. |moes|, J. Dolbow and T. Belytschko,
- *A finite element method for crack growth without remeshing*, Internat. J.
Numer. Methods Engrg., 46, 131-150, 1999.
+ *A finite element method for crack growth without remeshing*,
+ Internat. J. Numer. Methods Engrg., 46, 131-150, 1999.
+
+.. [Nackenhorst2004] U. Nackenhorst,
+ *The ALE formulation of bodies in rolling contact. Theoretical foundation
+ and finite element approach*,
+ Comp. Meth. Appl. Mech. Engng., 193:4299-4322, 2004.
.. [nedelec1991] J.-C. Nedelec.
*Notions sur les techniques d'elements finis*, Ellipses, SMAI,
Mathematiques & Applications no 7, 1991.
Removed: trunk/getfem/doc/sphinx/source/userdoc/examples.rst
URL:
http://svn.gna.org/viewcvs/getfem/trunk/getfem/doc/sphinx/source/userdoc/examples.rst?rev=5275&view=auto
==============================================================================
--- trunk/getfem/doc/sphinx/source/userdoc/examples.rst (original)
+++ trunk/getfem/doc/sphinx/source/userdoc/examples.rst (removed)
@@ -1,29 +0,0 @@
-.. $Id$
-
-.. include:: ../replaces.txt
-
-.. highlightlang:: c++
-
-.. _ud-examples:
-
-Example: Laplacian program
-==========================
-
-The program ``laplacian`` is provided in the directory ``tests`` of |gf|
-distribution. This program computes the solution of the Poisson problem in a
-parellepiped domain in any dimension with various finite element methods and
-elements. This program can be used as a model to build application programs.
It is
-built when a ``make check`` is done on the root directory of |gf| (or just with
-``cd tests; make laplacian``).
-
-Once the program is compiled you can test it executing the command::
-
- $ cd tests
- $ ./laplacian laplacian.param
-
-The file ``laplacian.param`` is the parameter file. You can edit it and test
-various situation. The program prints the :math:`L^2` and :math:`H^1` error
from
-an exact solution.
-
-The program ``elastostatic`` is built in a same way and compute the solution of
-linear elasticity problem. Many more examples can be found in the tests
directory.
Added: trunk/getfem/doc/sphinx/source/userdoc/images/ALE_rotating_body.fig
URL:
http://svn.gna.org/viewcvs/getfem/trunk/getfem/doc/sphinx/source/userdoc/images/ALE_rotating_body.fig?rev=5276&view=auto
==============================================================================
--- trunk/getfem/doc/sphinx/source/userdoc/images/ALE_rotating_body.fig (added)
+++ trunk/getfem/doc/sphinx/source/userdoc/images/ALE_rotating_body.fig Fri Apr
1 13:37:27 2016
@@ -0,0 +1,38 @@
+#FIG 3.2 Produced by xfig version 3.2.5c
+Landscape
+Center
+Metric
+A4
+100.00
+Single
+-2
+1200 2
+5 1 0 1 0 7 50 -1 -1 0.000 0 1 0 1 1113.882 1747.765 1140 1050 540 1350 520
2115
+ 0 0 1.00 60.00 120.00
+1 3 0 2 0 7 50 -1 -1 0.000 1 0.0000 1125 1800 900 900 1125 1800 2025 1800
+1 3 0 2 0 7 60 -1 -1 0.000 1 0.0000 2025 1350 900 900 2025 1350 2925 1350
+1 3 2 2 0 7 53 -1 -1 4.500 1 0.0000 2025 1350 900 900 2025 1350 2925 1350
+2 1 0 2 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
+ 720 990 1715 505
+2 1 0 2 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
+ 1466 2637 2456 2142
+2 1 0 1 0 7 50 -1 -1 0.000 0 0 -1 1 0 2
+ 0 0 1.00 60.00 120.00
+ 2700 1575 4050 1575
+2 3 0 0 0 7 55 -1 20 0.000 0 0 -1 0 0 5
+ 1620 315 2520 2295 1125 3150 180 765 1620 315
+2 1 2 1 0 7 50 -1 -1 3.000 0 0 -1 1 0 2
+ 0 0 1.00 60.00 120.00
+ 2025 1350 2025 675
+2 1 2 1 0 7 50 -1 -1 3.000 0 0 -1 1 0 2
+ 0 0 1.00 60.00 120.00
+ 2025 1350 2700 1350
+2 1 2 1 0 7 50 -1 -1 3.000 0 0 -1 1 0 2
+ 0 0 1.00 60.00 120.00
+ 2025 1350 1530 1575
+4 0 0 50 -1 0 12 0.0000 6 180 810 3150 1485 $\\dot{z}$\001
+4 0 0 50 -1 0 12 0.0000 6 180 510 2070 765 $e_2$\001
+4 0 0 50 -1 0 12 0.0000 6 180 510 1530 1755 $e_3$\001
+4 0 0 50 -1 0 12 0.0000 6 180 510 2520 1530 $e_1$\001
+4 0 0 50 -1 0 12 0.0000 6 165 315 2025 1530 $0$\001
+4 0 0 50 -1 0 12 0.0000 6 180 1185 585 1575 $\\dot{\\theta}$\001
Added: trunk/getfem/doc/sphinx/source/userdoc/images/ALE_rotating_conf.fig
URL:
http://svn.gna.org/viewcvs/getfem/trunk/getfem/doc/sphinx/source/userdoc/images/ALE_rotating_conf.fig?rev=5276&view=auto
==============================================================================
--- trunk/getfem/doc/sphinx/source/userdoc/images/ALE_rotating_conf.fig (added)
+++ trunk/getfem/doc/sphinx/source/userdoc/images/ALE_rotating_conf.fig Fri Apr
1 13:37:27 2016
@@ -0,0 +1,73 @@
+#FIG 3.2 Produced by xfig version 3.2.5c
+Landscape
+Center
+Metric
+A4
+100.00
+Single
+-2
+1200 2
+1 3 0 2 0 7 50 -1 -1 0.000 1 0.0000 1125 1800 900 900 1125 1800 2025 1800
+1 3 2 2 0 7 53 -1 -1 4.500 1 0.0000 2025 1350 900 900 2025 1350 2925 1350
+1 3 0 2 0 7 50 -1 -1 0.000 1 0.0000 5850 1800 900 900 5850 1800 6750 1800
+1 3 2 2 0 7 53 -1 -1 4.500 1 0.0000 6750 1350 900 900 6750 1350 7650 1350
+1 3 0 2 0 7 60 -1 -1 0.000 1 0.0000 2025 1350 900 900 2025 1350 2925 1350
+1 2 0 2 4 7 50 -1 -1 0.000 1 0.0000 5850 1777 1035 517 4815 1777 6885 1777
+1 3 0 2 0 7 60 -1 -1 0.000 1 0.0000 6750 1350 900 900 6750 1350 7650 1350
+1 2 0 2 4 7 60 -1 -1 0.000 1 0.0000 6739 1332 1035 517 5704 1332 7774 1332
+1 2 2 2 4 7 50 -1 -1 4.500 1 0.0000 6739 1333 1035 517 5704 1333 7774 1333
+2 1 0 2 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
+ 720 990 1715 505
+2 1 0 2 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
+ 1466 2637 2456 2142
+2 1 2 1 0 7 50 -1 -1 3.000 0 0 -1 1 0 2
+ 0 0 1.00 60.00 120.00
+ 2025 1350 2025 675
+2 1 2 1 0 7 50 -1 -1 3.000 0 0 -1 1 0 2
+ 0 0 1.00 60.00 120.00
+ 2025 1350 2700 1350
+2 1 2 1 0 7 50 -1 -1 3.000 0 0 -1 1 0 2
+ 0 0 1.00 60.00 120.00
+ 2025 1350 1530 1575
+2 1 0 2 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
+ 5445 990 6440 505
+2 1 0 2 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
+ 6191 2637 7181 2142
+2 1 2 1 0 7 50 -1 -1 3.000 0 0 -1 1 0 2
+ 0 0 1.00 60.00 120.00
+ 6750 1350 6750 675
+2 1 2 1 0 7 50 -1 -1 3.000 0 0 -1 1 0 2
+ 0 0 1.00 60.00 120.00
+ 6750 1350 7425 1350
+2 1 2 1 0 7 50 -1 -1 3.000 0 0 -1 1 0 2
+ 0 0 1.00 60.00 120.00
+ 6750 1350 6255 1575
+2 1 0 2 4 7 50 -1 -1 0.000 0 0 -1 0 0 2
+ 6582 2140 7572 1643
+2 3 0 0 0 7 55 -1 20 0.000 0 0 -1 0 0 10
+ 6345 315 6480 630 6120 810 6300 1035 7515 1710 7065 2070
+ 7245 2295 5850 3150 4905 765 6345 315
+2 1 0 2 4 7 50 -1 -1 0.000 0 0 -1 0 0 2
+ 5209 1372 6204 887
+2 1 0 2 9 7 50 -1 -1 0.000 0 0 -1 1 0 2
+ 0 0 2.00 90.00 120.00
+ 5409 2560 5499 2267
+2 3 0 0 0 7 55 -1 20 0.000 0 0 -1 0 0 5
+ 1620 315 2520 2295 1125 3150 180 765 1620 315
+3 2 0 1 0 7 50 -1 -1 0.000 0 1 0 3
+ 0 0 1.00 60.00 120.00
+ 2840 772 4190 502 5450 682
+ 0.000 -1.000 0.000
+4 0 0 50 -1 0 12 0.0000 6 180 540 1530 1755 $E_3$\001
+4 0 0 50 -1 0 12 0.0000 6 165 315 2025 1530 $0$\001
+4 0 0 50 -1 0 12 0.0000 6 180 1035 6795 765 $\\bar{E}_2$\001
+4 0 0 50 -1 0 12 0.0000 6 180 1035 6255 1755 $\\bar{E}_3$\001
+4 0 0 50 -1 0 12 0.0000 6 180 1035 7245 1530 $\\bar{E}_1$\001
+4 0 0 50 -1 0 12 0.0000 6 165 315 6750 1530 $0$\001
+4 0 0 50 -1 0 12 0.0000 6 180 540 2520 1530 $E_1$\001
+4 0 0 50 -1 0 12 0.0000 6 180 540 2070 765 $E_2$\001
+4 0 0 50 -1 0 12 0.0000 6 195 3750 3157 862 $\\varphi(t,X) =
\\bar{\\varphi}(t,\\bar{X}) + z(t)$\001
+4 0 4 50 -1 0 12 0.0000 6 195 1005 4958 1822 $\\Omega_t$\001
+4 0 9 50 -1 0 12 0.0000 6 180 1665 5521 2543 $\\bar{u}(t,\\bar{X})$\001
+4 0 0 50 -1 0 12 0.0000 6 195 1035 510 1365 $\\Omega^0$\001
+4 0 0 50 -1 0 12 0.0000 6 195 1530 5325 1245 $\\bar{\\Omega}^0$\001
Modified: trunk/getfem/doc/sphinx/source/userdoc/images/Makefile
URL:
http://svn.gna.org/viewcvs/getfem/trunk/getfem/doc/sphinx/source/userdoc/images/Makefile?rev=5276&r1=5275&r2=5276&view=diff
==============================================================================
--- trunk/getfem/doc/sphinx/source/userdoc/images/Makefile (original)
+++ trunk/getfem/doc/sphinx/source/userdoc/images/Makefile Fri Apr 1
13:37:27 2016
@@ -76,7 +76,9 @@
getfemusermodelmasterslave.fig \
getfemusermodeldetectcontact.fig \
getfemusermodelfalsecontact1.fig \
- getfemusermodelfalsecontact2.fig
+ getfemusermodelfalsecontact2.fig \
+ ALE_rotating_body.fig \
+ ALE_rotating_conf.fig
EPSFIGS=$(FIGS:.fig=.eps)
PNGFIGS=$(FIGS:.fig=.png)
Modified: trunk/getfem/doc/sphinx/source/userdoc/index.rst
URL:
http://svn.gna.org/viewcvs/getfem/trunk/getfem/doc/sphinx/source/userdoc/index.rst?rev=5276&r1=5275&r2=5276&view=diff
==============================================================================
--- trunk/getfem/doc/sphinx/source/userdoc/index.rst (original)
+++ trunk/getfem/doc/sphinx/source/userdoc/index.rst Fri Apr 1 13:37:27 2016
@@ -33,8 +33,10 @@
export
convect
model
- examples
-
+ model_continuation
+ model_nonlinear_elasticity
+ model_ALE_rotating
+
appendixA
appendixB
Modified: trunk/getfem/doc/sphinx/source/userdoc/model.rst
URL:
http://svn.gna.org/viewcvs/getfem/trunk/getfem/doc/sphinx/source/userdoc/model.rst?rev=5276&r1=5275&r2=5276&view=diff
==============================================================================
--- trunk/getfem/doc/sphinx/source/userdoc/model.rst (original)
+++ trunk/getfem/doc/sphinx/source/userdoc/model.rst Fri Apr 1 13:37:27 2016
@@ -8,9 +8,9 @@
.. _ud-model:
-=====================
-The model description
-=====================
+============================================
+The model description and basic model bricks
+============================================
The model description of |gf| allows
@@ -55,8 +55,7 @@
model_bilaplacian
model_Mindlin_plate
model_time_integration
- model_nonlinear_elasticity
model_contact_friction
model_contact_friction_large_sliding
model_elastoplasticity
- model_continuation
+
Added: trunk/getfem/doc/sphinx/source/userdoc/model_ALE_rotating.rst
URL:
http://svn.gna.org/viewcvs/getfem/trunk/getfem/doc/sphinx/source/userdoc/model_ALE_rotating.rst?rev=5276&view=auto
==============================================================================
--- trunk/getfem/doc/sphinx/source/userdoc/model_ALE_rotating.rst (added)
+++ trunk/getfem/doc/sphinx/source/userdoc/model_ALE_rotating.rst Fri Apr
1 13:37:27 2016
@@ -0,0 +1,126 @@
+.. $Id: model.rst 3655 2010-07-17 20:42:08Z renard $
+
+.. include:: ../replaces.txt
+
+.. highlightlang:: c++
+
+.. index:: models, model bricks
+
+.. _ud-model-ALE_rotating:
+
+ALE terms for rotating objects
+------------------------------
+
+This section present a set of bricks facilitating the use of an ALE
formulation for rotating bodies having a rotational symmetry (typically a train
wheel).
+
+
+Theoretical background
+++++++++++++++++++++++
+
+This strategy consists in adopting an intermediary description between an
Eulerian and a Lagrangian ones for a rotating body having a rotational
symmetry. This intermediary description consist in a rotating axes with respect
to the reference configuration. See for instance [Dr-La-Ek2014]_ and
[Nackenhorst2004]_.
+
+It is supposed that the considered body is submitted approximately to a rigid
body motion
+
+.. math::
+ \tau(X) = R(t)X + z(t)
+
+and may have additonal deformation (exptected smaller) with respect to this
rigid motion, where :math:`R(t)` is a rotation matrix
+
+.. math::
+ R(t) = \left(\begin{array}{ccc}
+ \cos(\theta(t)) & \sin(\theta(t)) & 0 \\
+ -\sin(\theta(t)) & \cos(\theta(t)) & 0 \\
+ 0 & 0 & 1
+ \end{array} \right),
+
+and :math:`z(t)` is a translation. This illustrated in the following figure:
+
+.. _ud-fig-rotating_cylinder:
+
+.. figure:: images/ALE_rotating_body.png
+ :align: center
+ :scale: 80
+
+Note that the description is given for a three-dimensional body. For
two-dimensional bodies, the third axes is neglected so that :math:`R(t)` is a
:math:`2\times 2` rotation matrix.
+
+Denoting :math:`r(t)` the rotation
+
+.. math::
+ r(t,X) = R(t)X, ~~~~~~~~~
+ A(t) = \left(\begin{array}{ccc}
+ 0 & -1 & 0 \\
+ 1 & 0 & 0 \\
+ 0 & 0 & 0
+ \end{array} \right), ~~~~~~~~~
+ \mbox{ and } B(t) = A^2(t) = \left(\begin{array}{ccc}
+ -1 & 0 & 0 \\
+ 0 & -1 & 0 \\
+ 0 & 0 & 0
+ \end{array} \right),
+
+such that
+
+.. math::
+ \dot{r}(t,X) = \dot{\theta}A(t)R(t)X
+
+
+
+The ALE description consists in the decomposition of the motion of the
cylinder :math:`\varphi(t, X)` in
+
+.. math::
+ \varphi(t, X) = (\tau(t) \circ \bar{\varphi}(t) \circ r(t))(X) =
\bar{\varphi}(t, r(t, X)) + z(t)
+
+With :math:`\bar{X} = R(t)X` the new considered deformation is
+
+.. math::
+ \bar{\varphi}(\bar{X}) = \varphi(X) - z(t)
+
+
+.. _ud-fig-rotating_cylinder_conf:
+
+.. figure:: images/ALE_rotating_conf.png
+ :align: center
+ :scale: 80
+
+
++ analyse ... et graphique eventuel
+
+
+Main invariants and derivatives
+###############################
+
+
+
+
+the available bricks ...
+++++++++++++++++++++++++
+
+This brick represents a large strain elasticity problem. It is defined in the
files :file:`getfem/getfem_nonlinear_elasticity.h` and
:file:`getfem/getfem_nonlinear_elasticity.cc`. The function adding this brick
to a model is ::
+
+ ind = getfem::add_nonlinear_elasticity_brick
+ (md, mim, varname, AHL, dataname, region = -1);
+
+where ``AHL`` is an object of type ``getfem::abstract_hyperelastic_law`` which
represents the considered hyperelastic law. It has to be chosen between: ::
+
+ getfem::SaintVenant_Kirchhoff_hyperelastic_law AHL;
+ getfem::Ciarlet_Geymonat_hyperelastic_law AHL;
+ getfem::Mooney_Rivlin_hyperelastic_law AHL(compressible, neohookean);
+ getfem::plane_strain_hyperelastic_law AHL(pAHL);
+ getfem::generalized_Blatz_Ko_hyperelastic_law AHL;
+
+The Saint-Venant Kirchhoff law is a linearized law defined with the two Lame
coefficients, Ciarlet Geymonat law is defined with the two Lame coefficients
and an additional coefficient (:math:`\lambda, \mu, a`).
+
+
+
+Here is the list of nonlinear operators in the language which can be useful
for nonlinear elasticity::
+
+ Det(M) % determinant of the matrix M
+ Trace(M) % trace of the matrix M
+ Matrix_i2(M) % second invariant of M (in 3D):
(sqr(Trace(m)) - Trace(m*m))/2
+ Matrix_j1(M) % modified first invariant of M:
Trace(m)pow(Det(m),-1/3).
+ Matrix_j2(M) % modified second invariant of M:
Matrix_I2(m)*pow(Det(m),-2/3).
+ Right_Cauchy_Green(F) % F' * F
+ Left_Cauchy_Green(F) % F * F'
+ Green_Lagrangian(F) % (F'F - Id(meshdim))/2
+ Cauchy_stress_from_PK2(sigma, Grad_u) %
(Id+Grad_u)*sigma*(I+Grad_u')/det(I+Grad_u)
+
Modified: trunk/getfem/doc/sphinx/source/userdoc/model_nonlinear_elasticity.rst
URL:
http://svn.gna.org/viewcvs/getfem/trunk/getfem/doc/sphinx/source/userdoc/model_nonlinear_elasticity.rst?rev=5276&r1=5275&r2=5276&view=diff
==============================================================================
--- trunk/getfem/doc/sphinx/source/userdoc/model_nonlinear_elasticity.rst
(original)
+++ trunk/getfem/doc/sphinx/source/userdoc/model_nonlinear_elasticity.rst
Fri Apr 1 13:37:27 2016
@@ -8,13 +8,13 @@
.. _ud-model-nonlinear-elasticity:
-Nonlinear Elasticity brick
---------------------------
+Finite strain Elasticity bricks
+-------------------------------
This brick implements some classical hyperelastic constitutive law for large
deformation elasticity.
-Some recalls on nonlinear elasticity
-++++++++++++++++++++++++++++++++++++
+Some recalls on finite strain elasticity
+++++++++++++++++++++++++++++++++++++++++
Let :math:`\Omega` be the reference configuration and :math:`\Omega_t` the
deformed configuration of an elastic media. Then for :math:`X \in \Omega` we
will denote by :math:`\Phi(x) = u(X) + X` the deformation. the vector field
:math:`u` is the displacement with respect to the initial position.
@@ -40,12 +40,12 @@
C = \nabla\Phi^T\nabla\Phi = 2 E + I.
-Both tensors :math:`E` and :math:`C` are used to describe nonlinear elasticity
constitutive laws.
+Both tensors :math:`E` and :math:`C` are used to describe finite strain
elasticity constitutive laws.
Main invariants and derivatives
###############################
-The description of nonlinear elasticity constitutive laws often requires the
principal invariants of the deformation tensors:
+The description of finite strain elasticity constitutive laws often requires
the principal invariants of the deformation tensors:
:math:`i_1,i_2,i_3` are the invariants of orders :math:`1,2` and :math:`3`:
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