From 779039e48d6b24f826792ef19ae639af9d4de6ee Mon Sep 17 00:00:00 2001
From: Jeremy Bleyer <jeremy.bleyer@enpc.fr>
Date: Fri, 6 Jul 2018 09:00:10 +0200
Subject: [PATCH] Published buckling example

---
 .../cantilever_modal.py.doctree               |   Bin 34213 -> 34201 bytes
 doc/_build/doctrees/environment.pickle        |   Bin 59083 -> 67456 bytes
 doc/_build/doctrees/index.doctree             |   Bin 4005 -> 3983 bytes
 .../html/_downloads/cantilever_modal.py       |    44 +-
 .../cantilever_modal.py.rst.txt               |    46 +-
 doc/_build/html/_sources/index.rst.txt        |     2 +-
 .../2D_plasticity/vonMises_plasticity.py.html |     9 +-
 .../cohesive_zone/cohesive_zone_crack.html    |     3 +-
 .../demo/elasticity/2D_elasticity.py.html     |     3 +-
 .../elasticity/axisymmetric_elasticity.html   |     3 +-
 .../elasticity/orthotropic_elasticity.py.html |     3 +-
 .../cantilever_modal.py.html                  |     5 +-
 .../periodic_homog_elas.html                  |     3 +-
 .../reissner_mindlin/reissner_mindlin.html    |    17 +-
 .../reissner_mindlin_dg.py.html               |     3 +-
 .../reissner_mindlin_quads.py.html            |     9 +-
 .../thermoelasticity/thermoelasticity.html    |     3 +-
 .../thermoelasticity_transient.html           |     3 +-
 doc/_build/html/genindex.html                 |     3 +-
 doc/_build/html/homogenization.html           |     3 +-
 doc/_build/html/index.html                    |     6 +-
 doc/_build/html/linear_problems.html          |     3 +-
 doc/_build/html/nonlinear_problems.html       |     3 +-
 doc/_build/html/objects.inv                   |   Bin 2306 -> 2652 bytes
 doc/_build/html/search.html                   |     3 +-
 doc/_build/html/searchindex.js                |     2 +-
 doc/beams_and_plates.rst                      |    19 +
 doc/index.rst                                 |     2 +-
 .../beam_buckling-checkpoint.ipynb            |    37 +-
 examples/timoshenko/beam_buckling.ipynb       |    45 +-
 .../linear_viscoelasticity-checkpoint.ipynb   | 11393 ----------------
 .../linear_viscoelasticity.ipynb              | 11393 ----------------
 32 files changed, 156 insertions(+), 22912 deletions(-)
 create mode 100644 doc/beams_and_plates.rst
 delete mode 100644 examples/viscoelasticity/.ipynb_checkpoints/linear_viscoelasticity-checkpoint.ipynb
 delete mode 100644 examples/viscoelasticity/linear_viscoelasticity.ipynb

diff --git a/doc/_build/doctrees/demo/modal_analysis_dynamics/cantilever_modal.py.doctree b/doc/_build/doctrees/demo/modal_analysis_dynamics/cantilever_modal.py.doctree
index 810391e221271b91b5ada187aa7b9756731cfbc1..760eb189abd4ac80dc1ff864ab66ec6debdcdc6a 100644
GIT binary patch
delta 32
jcmZ45%`~%{X~S1n#`T+Ddu?Kwyw1x8%G|uzpUDgW`3nw%

delta 46
qcmbQ)&9t<eX~S1n#;u#bxo%=%)6dUMO;4P>!pjC#Wb<@?CNlum2NMMV

diff --git a/doc/_build/doctrees/environment.pickle b/doc/_build/doctrees/environment.pickle
index 7e00a313900a20493bb9f2c6dbca8ea519c1dc7c..622e684106f5dc36166a609758ef5b9352dc6e0d 100644
GIT binary patch
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diff --git a/doc/_build/doctrees/index.doctree b/doc/_build/doctrees/index.doctree
index 2a91f760fd4323ed83d3460bee330be719b9525d..399aca990d53c9bb2b3d34faa378a2648b47f728 100644
GIT binary patch
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delta 55
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diff --git a/doc/_build/html/_downloads/cantilever_modal.py b/doc/_build/html/_downloads/cantilever_modal.py
index 468800f..ae6f541 100644
--- a/doc/_build/html/_downloads/cantilever_modal.py
+++ b/doc/_build/html/_downloads/cantilever_modal.py
@@ -10,8 +10,8 @@
 # -------------
 #
 # This program performs a dynamic modal analysis of an elastic cantilever beam
-# represented by a 3D solid continuum. The eigenmodes are computed using the 
-# **SLEPcEigensolver** and compared against an analytical solution of beam theory. 
+# represented by a 3D solid continuum. The eigenmodes are computed using the
+# **SLEPcEigensolver** and compared against an analytical solution of beam theory.
 # The corresponding file can be obtained from :download:`cantilever_modal.py`.
 #
 #
@@ -20,14 +20,14 @@
 # .. image:: vibration_modes.gif
 #    :scale: 80 %
 #
-# The first two fundamental modes are on top with bending along the weak axis (left) and along 
-# the strong axis (right), the next two modes are at the bottom. 
+# The first two fundamental modes are on top with bending along the weak axis (left) and along
+# the strong axis (right), the next two modes are at the bottom.
 #
 # ---------------
 # Implementation
 # ---------------
 #
-# After importing the relevant modules, the geometry of a beam of length :math:`L=20` 
+# After importing the relevant modules, the geometry of a beam of length :math:`L=20`
 # and rectangular section of size :math:`B\times H` with :math:`B=0.5, H=1` is first defined::
 
 from fenics import *
@@ -43,7 +43,7 @@ mesh = BoxMesh(Point(0.,0.,0.),Point(L,B,H), Nx, Ny, Nz)
 
 
 # Material parameters and elastic constitutive relations are classical (here we
-# take :math:`\nu=0`) and we also introduce the material density :math:`\rho` for 
+# take :math:`\nu=0`) and we also introduce the material density :math:`\rho` for
 # later definition of the mass matrix::
 
 E, nu = 1e5, 0.
@@ -59,7 +59,7 @@ def sigma(v):
     dim = v.geometric_dimension()
     return 2.0*mu*eps(v) + lmbda*tr(eps(v))*Identity(dim)
 
-# Standard FunctionSpace is defined and boundary conditions correspond to a 
+# Standard FunctionSpace is defined and boundary conditions correspond to a
 # fully clamped support at :math:`x=0`::
 
 V = VectorFunctionSpace(mesh, 'Lagrange', degree=1)
@@ -73,7 +73,7 @@ def left(x, on_boundary):
 bc = DirichletBC(V, Constant((0.,0.,0.)), left)
 
 
-# The system stiffness matrix :math:`[K]` and mass matrix :math:`[M]` are 
+# The system stiffness matrix :math:`[K]` and mass matrix :math:`[M]` are
 # respectively obtained from assembling the corresponding variational forms::
 
 k_form = inner(sigma(du),eps(u_))*dx
@@ -86,14 +86,14 @@ m_form = rho*dot(du,u_)*dx
 M = PETScMatrix()
 assemble(m_form, tensor=M)
 
-# Matrices :math:`[K]` and :math:`[M]` are first defined as PETSc Matrix and 
+# Matrices :math:`[K]` and :math:`[M]` are first defined as PETSc Matrix and
 # forms are assembled into it to ensure that they have the right type.
 # Note that boundary conditions have been applied to the stiffness matrix using
 # ``assemble_system`` so as to preserve symmetry (a dummy ``l_form`` and right-hand side
-# vector have been introduced to call this function). 
+# vector have been introduced to call this function).
 #
 #
-# Modal dynamic analysis consists in solving the following generalized 
+# Modal dynamic analysis consists in solving the following generalized
 # eigenvalue problem :math:`[K]\{U\}=\lambda[M]\{U\}` where the eigenvalue
 # is related to the eigenfrequency :math:`\lambda=\omega^2`. This problem
 # can be solved using the ``SLEPcEigenSolver``. ::
@@ -121,7 +121,7 @@ eigensolver.parameters['spectral_shift'] = 0.
 # and extract the corresponding eigenpair (first two arguments of ``get_eigenpair``
 # correspond to the real and complex part of the eigenvalue, the last two to the
 # real and complex part of the eigenvector)::
- 
+
 N_eig = 6   # number of eigenvalues
 print "Computing %i first eigenvalues..." % N_eig
 eigensolver.solve(N_eig)
@@ -141,26 +141,26 @@ file_results.parameters["functions_share_mesh"] = True
 for i in range(N_eig):
     # Extract eigenpair
     r, c, rx, cx = eigensolver.get_eigenpair(i)
-    
+
     # 3D eigenfrequency
     freq_3D = sqrt(r)/2/pi
-    
+
     # Beam eigenfrequency
     if i % 2 == 0: # exact solution should correspond to weak axis bending
         I_bend = H*B**3/12.
     else:          #exact solution should correspond to strong axis bending
         I_bend = B*H**3/12.
     freq_beam = alpha(i/2)**2*sqrt(E*I_bend/(rho*B*H*L**4))/2/pi
-    
+
     print("Solid FE: {0:8.5f} [Hz]   Beam theory: {1:8.5f} [Hz]".format(freq_3D, freq_beam))
 
     # Initialize function and assign eigenvector (renormalize by stiffness matrix)
     eigenmode = Function(V,name="Eigenvector "+str(i))
-    eigenmode.vector()[:] = rx/omega
+    eigenmode.vector()[:] = rx
 
 # The beam analytical solution is obtained using the eigenfrequencies of a clamped
 # beam in bending given by :math:`\omega_n = \alpha_n^2\sqrt{\dfrac{EI}{\rho S L^4}}`
-# where :math:`S=BH` is the beam section, :math:`I` the bending inertia and 
+# where :math:`S=BH` is the beam section, :math:`I` the bending inertia and
 # :math:`\alpha_n` is the solution of the following nonlinear equation:
 #
 # .. math::
@@ -173,9 +173,9 @@ for i in range(N_eig):
 # for the considered numerical values, the strong axis bending frequency will be twice that corresponsing
 # to bending along the weak axis. The solution :math:`\alpha_n` are computed using the
 # ``scipy.optimize.root`` function with initial guess given by :math:`(2n+1)\pi/2`.
-#    
+#
 # With ``Nx=400``, we obtain the following comparison between the FE eigenfrequencies
-# and the beam theory eigenfrequencies : 
+# and the beam theory eigenfrequencies :
 #
 #
 # =====  =============  =================
@@ -184,11 +184,11 @@ for i in range(N_eig):
 #  #     Solid FE [Hz]   Beam theory [Hz]
 # =====  =============  =================
 #   1      2.04991           2.01925
-#   2      4.04854           4.03850 
+#   2      4.04854           4.03850
 #   3      12.81504         12.65443
-#   4      25.12717         25.30886 
+#   4      25.12717         25.30886
 #   5      35.74168         35.43277
-#   6      66.94816         70.86554 
+#   6      66.94816         70.86554
 # =====  =============  =================
 #
 #
diff --git a/doc/_build/html/_sources/demo/modal_analysis_dynamics/cantilever_modal.py.rst.txt b/doc/_build/html/_sources/demo/modal_analysis_dynamics/cantilever_modal.py.rst.txt
index 508fa5a..d52f9e8 100644
--- a/doc/_build/html/_sources/demo/modal_analysis_dynamics/cantilever_modal.py.rst.txt
+++ b/doc/_build/html/_sources/demo/modal_analysis_dynamics/cantilever_modal.py.rst.txt
@@ -10,8 +10,8 @@ Introduction
 -------------
 
 This program performs a dynamic modal analysis of an elastic cantilever beam
-represented by a 3D solid continuum. The eigenmodes are computed using the 
-**SLEPcEigensolver** and compared against an analytical solution of beam theory. 
+represented by a 3D solid continuum. The eigenmodes are computed using the
+**SLEPcEigensolver** and compared against an analytical solution of beam theory.
 The corresponding file can be obtained from :download:`cantilever_modal.py`.
 
 
@@ -20,14 +20,14 @@ The first four eigenmodes of this demo will look as follows:
 .. image:: vibration_modes.gif
    :scale: 80 %
 
-The first two fundamental modes are on top with bending along the weak axis (left) and along 
-the strong axis (right), the next two modes are at the bottom. 
+The first two fundamental modes are on top with bending along the weak axis (left) and along
+the strong axis (right), the next two modes are at the bottom.
 
 ---------------
 Implementation
 ---------------
 
-After importing the relevant modules, the geometry of a beam of length :math:`L=20` 
+After importing the relevant modules, the geometry of a beam of length :math:`L=20`
 and rectangular section of size :math:`B\times H` with :math:`B=0.5, H=1` is first defined::
 
  from fenics import *
@@ -43,7 +43,7 @@ and rectangular section of size :math:`B\times H` with :math:`B=0.5, H=1` is fir
 
 
 Material parameters and elastic constitutive relations are classical (here we
-take :math:`\nu=0`) and we also introduce the material density :math:`\rho` for 
+take :math:`\nu=0`) and we also introduce the material density :math:`\rho` for
 later definition of the mass matrix::
 
  E, nu = 1e5, 0.
@@ -59,7 +59,7 @@ later definition of the mass matrix::
      dim = v.geometric_dimension()
      return 2.0*mu*eps(v) + lmbda*tr(eps(v))*Identity(dim)
 
-Standard FunctionSpace is defined and boundary conditions correspond to a 
+Standard FunctionSpace is defined and boundary conditions correspond to a
 fully clamped support at :math:`x=0`::
 
  V = VectorFunctionSpace(mesh, 'Lagrange', degree=1)
@@ -73,7 +73,7 @@ fully clamped support at :math:`x=0`::
  bc = DirichletBC(V, Constant((0.,0.,0.)), left)
 
 
-The system stiffness matrix :math:`[K]` and mass matrix :math:`[M]` are 
+The system stiffness matrix :math:`[K]` and mass matrix :math:`[M]` are
 respectively obtained from assembling the corresponding variational forms::
 
  k_form = inner(sigma(du),eps(u_))*dx
@@ -86,14 +86,14 @@ respectively obtained from assembling the corresponding variational forms::
  M = PETScMatrix()
  assemble(m_form, tensor=M)
 
-Matrices :math:`[K]` and :math:`[M]` are first defined as PETSc Matrix and 
+Matrices :math:`[K]` and :math:`[M]` are first defined as PETSc Matrix and
 forms are assembled into it to ensure that they have the right type.
 Note that boundary conditions have been applied to the stiffness matrix using
 ``assemble_system`` so as to preserve symmetry (a dummy ``l_form`` and right-hand side
-vector have been introduced to call this function). 
+vector have been introduced to call this function).
 
 
-Modal dynamic analysis consists in solving the following generalized 
+Modal dynamic analysis consists in solving the following generalized
 eigenvalue problem :math:`[K]\{U\}=\lambda[M]\{U\}` where the eigenvalue
 is related to the eigenfrequency :math:`\lambda=\omega^2`. This problem
 can be solved using the ``SLEPcEigenSolver``. ::
@@ -121,7 +121,7 @@ We now ask SLEPc to extract the first 6 eigenvalues by calling its solve functio
 and extract the corresponding eigenpair (first two arguments of ``get_eigenpair``
 correspond to the real and complex part of the eigenvalue, the last two to the
 real and complex part of the eigenvector)::
- 
+
  N_eig = 6   # number of eigenvalues
  print "Computing %i first eigenvalues..." % N_eig
  eigensolver.solve(N_eig)
@@ -136,31 +136,31 @@ real and complex part of the eigenvector)::
  file_results = XDMFFile("modal_analysis.xdmf")
  file_results.parameters["flush_output"] = True
  file_results.parameters["functions_share_mesh"] = True
- 
+
  # Extraction
  for i in range(N_eig):
      # Extract eigenpair
      r, c, rx, cx = eigensolver.get_eigenpair(i)
-     
+
      # 3D eigenfrequency
      freq_3D = sqrt(r)/2/pi
-     
+
      # Beam eigenfrequency
      if i % 2 == 0: # exact solution should correspond to weak axis bending
          I_bend = H*B**3/12.
      else:          #exact solution should correspond to strong axis bending
          I_bend = B*H**3/12.
      freq_beam = alpha(i/2)**2*sqrt(E*I_bend/(rho*B*H*L**4))/2/pi
-     
+
      print("Solid FE: {0:8.5f} [Hz]   Beam theory: {1:8.5f} [Hz]".format(freq_3D, freq_beam))
 
      # Initialize function and assign eigenvector (renormalize by stiffness matrix)
      eigenmode = Function(V,name="Eigenvector "+str(i))
-     eigenmode.vector()[:] = rx/omega
+     eigenmode.vector()[:] = rx
 
 The beam analytical solution is obtained using the eigenfrequencies of a clamped
 beam in bending given by :math:`\omega_n = \alpha_n^2\sqrt{\dfrac{EI}{\rho S L^4}}`
-where :math:`S=BH` is the beam section, :math:`I` the bending inertia and 
+where :math:`S=BH` is the beam section, :math:`I` the bending inertia and
 :math:`\alpha_n` is the solution of the following nonlinear equation:
 
 .. math::
@@ -173,9 +173,9 @@ and the other along the strong axis (:math:`I=I_{\text{strong}} = BH^3/12`). Sin
 for the considered numerical values, the strong axis bending frequency will be twice that corresponsing
 to bending along the weak axis. The solution :math:`\alpha_n` are computed using the
 ``scipy.optimize.root`` function with initial guess given by :math:`(2n+1)\pi/2`.
-    
+
 With ``Nx=400``, we obtain the following comparison between the FE eigenfrequencies
-and the beam theory eigenfrequencies : 
+and the beam theory eigenfrequencies :
 
 
 =====  =============  =================
@@ -184,11 +184,11 @@ Mode      Eigenfrequencies
  #     Solid FE [Hz]   Beam theory [Hz]
 =====  =============  =================
   1      2.04991           2.01925
-  2      4.04854           4.03850 
+  2      4.04854           4.03850
   3      12.81504         12.65443
-  4      25.12717         25.30886 
+  4      25.12717         25.30886
   5      35.74168         35.43277
-  6      66.94816         70.86554 
+  6      66.94816         70.86554
 =====  =============  =================
 
 
diff --git a/doc/_build/html/_sources/index.rst.txt b/doc/_build/html/_sources/index.rst.txt
index acb5462..e33a637 100644
--- a/doc/_build/html/_sources/index.rst.txt
+++ b/doc/_build/html/_sources/index.rst.txt
@@ -15,7 +15,7 @@ Contents:
    linear_problems
    homogenization
    nonlinear_problems
-   demo/reissner_mindlin/reissner_mindlin.rst
+   beams_and_plates
    tips_and_tricks
 
 
diff --git a/doc/_build/html/demo/2D_plasticity/vonMises_plasticity.py.html b/doc/_build/html/demo/2D_plasticity/vonMises_plasticity.py.html
index c34cacb..332d907 100644
--- a/doc/_build/html/demo/2D_plasticity/vonMises_plasticity.py.html
+++ b/doc/_build/html/demo/2D_plasticity/vonMises_plasticity.py.html
@@ -24,7 +24,7 @@
     <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
-    <link rel="next" title="Reissner-Mindlin plates" href="../reissner_mindlin/reissner_mindlin.html" />
+    <link rel="next" title="Beams and plates" href="../../beams_and_plates.html" />
     <link rel="prev" title="Nonlinear problems in solid mechanics" href="../../nonlinear_problems.html" /> 
   </head>
   <body>
@@ -35,7 +35,7 @@
         <div class="rel" role="navigation" aria-label="related navigation">
           <a href="../../nonlinear_problems.html" title="Nonlinear problems in solid mechanics"
              accesskey="P">previous</a> |
-          <a href="../reissner_mindlin/reissner_mindlin.html" title="Reissner-Mindlin plates"
+          <a href="../../beams_and_plates.html" title="Beams and plates"
              accesskey="N">next</a> |
           <a href="../../genindex.html" title="General Index"
              accesskey="I">index</a>
@@ -431,7 +431,8 @@ when considering a zero hardening modulus.</p>
 <li class="toctree-l2 current"><a class="current reference internal" href="#">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
+<li class="toctree-l1"><a class="reference internal" href="../../beams_and_plates.html">Beams and plates</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="../timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
@@ -462,7 +463,7 @@ when considering a zero hardening modulus.</p>
           <div role="navigation" aria-label="related navigaton">
             <a href="../../nonlinear_problems.html" title="Nonlinear problems in solid mechanics"
               >previous</a> |
-            <a href="../reissner_mindlin/reissner_mindlin.html" title="Reissner-Mindlin plates"
+            <a href="../../beams_and_plates.html" title="Beams and plates"
               >next</a> |
             <a href="../../genindex.html" title="General Index"
               >index</a>
diff --git a/doc/_build/html/demo/cohesive_zone/cohesive_zone_crack.html b/doc/_build/html/demo/cohesive_zone/cohesive_zone_crack.html
index aa8f12a..2ece3a8 100644
--- a/doc/_build/html/demo/cohesive_zone/cohesive_zone_crack.html
+++ b/doc/_build/html/demo/cohesive_zone/cohesive_zone_crack.html
@@ -891,7 +891,8 @@ div.nboutput div.output_area.stderr {
 <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
+<li class="toctree-l1"><a class="reference internal" href="../../beams_and_plates.html">Beams and plates</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="../timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
diff --git a/doc/_build/html/demo/elasticity/2D_elasticity.py.html b/doc/_build/html/demo/elasticity/2D_elasticity.py.html
index 9d9c554..1276b7c 100644
--- a/doc/_build/html/demo/elasticity/2D_elasticity.py.html
+++ b/doc/_build/html/demo/elasticity/2D_elasticity.py.html
@@ -241,7 +241,8 @@ writing/reading. Prefered output format is now .xdmf:</p>
 <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
+<li class="toctree-l1"><a class="reference internal" href="../../beams_and_plates.html">Beams and plates</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="../timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
diff --git a/doc/_build/html/demo/elasticity/axisymmetric_elasticity.html b/doc/_build/html/demo/elasticity/axisymmetric_elasticity.html
index fd48282..4128caa 100644
--- a/doc/_build/html/demo/elasticity/axisymmetric_elasticity.html
+++ b/doc/_build/html/demo/elasticity/axisymmetric_elasticity.html
@@ -2826,7 +2826,8 @@ if (IPython.notebook.kernel != null) {
 <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
+<li class="toctree-l1"><a class="reference internal" href="../../beams_and_plates.html">Beams and plates</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="../timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
diff --git a/doc/_build/html/demo/elasticity/orthotropic_elasticity.py.html b/doc/_build/html/demo/elasticity/orthotropic_elasticity.py.html
index 9c1e72f..ab94a2b 100644
--- a/doc/_build/html/demo/elasticity/orthotropic_elasticity.py.html
+++ b/doc/_build/html/demo/elasticity/orthotropic_elasticity.py.html
@@ -219,7 +219,8 @@ that:</p>
 <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
+<li class="toctree-l1"><a class="reference internal" href="../../beams_and_plates.html">Beams and plates</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="../timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
diff --git a/doc/_build/html/demo/modal_analysis_dynamics/cantilever_modal.py.html b/doc/_build/html/demo/modal_analysis_dynamics/cantilever_modal.py.html
index a0231f9..f6b832f 100644
--- a/doc/_build/html/demo/modal_analysis_dynamics/cantilever_modal.py.html
+++ b/doc/_build/html/demo/modal_analysis_dynamics/cantilever_modal.py.html
@@ -188,7 +188,7 @@ real and complex part of the eigenvector):</p>
 
     <span class="c1"># Initialize function and assign eigenvector (renormalize by stiffness matrix)</span>
     <span class="n">eigenmode</span> <span class="o">=</span> <span class="n">Function</span><span class="p">(</span><span class="n">V</span><span class="p">,</span><span class="n">name</span><span class="o">=</span><span class="s2">&quot;Eigenvector &quot;</span><span class="o">+</span><span class="nb">str</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
-    <span class="n">eigenmode</span><span class="o">.</span><span class="n">vector</span><span class="p">()[:]</span> <span class="o">=</span> <span class="n">rx</span><span class="o">/</span><span class="n">omega</span>
+    <span class="n">eigenmode</span><span class="o">.</span><span class="n">vector</span><span class="p">()[:]</span> <span class="o">=</span> <span class="n">rx</span>
 </pre></div>
 </div>
 <p>The beam analytical solution is obtained using the eigenfrequencies of a clamped
@@ -282,7 +282,8 @@ and the beam theory eigenfrequencies :</p>
 <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
+<li class="toctree-l1"><a class="reference internal" href="../../beams_and_plates.html">Beams and plates</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="../timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
diff --git a/doc/_build/html/demo/periodic_homog_elas/periodic_homog_elas.html b/doc/_build/html/demo/periodic_homog_elas/periodic_homog_elas.html
index 00f0890..257d2cf 100644
--- a/doc/_build/html/demo/periodic_homog_elas/periodic_homog_elas.html
+++ b/doc/_build/html/demo/periodic_homog_elas/periodic_homog_elas.html
@@ -2162,7 +2162,8 @@ if (IPython.notebook.kernel != null) {
 <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
+<li class="toctree-l1"><a class="reference internal" href="../../beams_and_plates.html">Beams and plates</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="../timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
diff --git a/doc/_build/html/demo/reissner_mindlin/reissner_mindlin.html b/doc/_build/html/demo/reissner_mindlin/reissner_mindlin.html
index 0ecf804..6a811f6 100644
--- a/doc/_build/html/demo/reissner_mindlin/reissner_mindlin.html
+++ b/doc/_build/html/demo/reissner_mindlin/reissner_mindlin.html
@@ -23,9 +23,7 @@
     <script type="text/javascript" src="../../_static/doctools.js"></script>
     <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
     <link rel="index" title="Index" href="../../genindex.html" />
-    <link rel="search" title="Search" href="../../search.html" />
-    <link rel="next" title="Reissner-Mindlin plate with Quadrilaterals" href="reissner_mindlin_quads.py.html" />
-    <link rel="prev" title="Elasto-plastic analysis of a 2D von Mises material" href="../2D_plasticity/vonMises_plasticity.py.html" /> 
+    <link rel="search" title="Search" href="../../search.html" /> 
   </head>
   <body>
     <div class="header-wrapper" role="banner">
@@ -33,10 +31,6 @@
         <div class="headertitle"><a
           href="../../index.html">Numerical tours of continuum mechanics using FEniCS</a></div>
         <div class="rel" role="navigation" aria-label="related navigation">
-          <a href="../2D_plasticity/vonMises_plasticity.py.html" title="Elasto-plastic analysis of a 2D von Mises material"
-             accesskey="P">previous</a> |
-          <a href="reissner_mindlin_quads.py.html" title="Reissner-Mindlin plate with Quadrilaterals"
-             accesskey="N">next</a> |
           <a href="../../genindex.html" title="General Index"
              accesskey="I">index</a>
         </div>
@@ -69,7 +63,7 @@
         </div>
         <div class="sidebar">
           <h3>Table Of Contents</h3>
-          <ul class="current">
+          <ul>
 <li class="toctree-l1"><a class="reference internal" href="../../intro.html">Introduction</a><ul>
 <li class="toctree-l2"><a class="reference internal" href="../../intro.html#what-is-it-about">What is it about ?</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../../intro.html#how-do-i-get-started">How do I get started ?</a></li>
@@ -93,7 +87,8 @@
 <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1 current"><a class="current reference internal" href="#">Reissner-Mindlin plates</a><ul>
+<li class="toctree-l1"><a class="reference internal" href="../../beams_and_plates.html">Beams and plates</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="../timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
@@ -122,10 +117,6 @@
       <div class="footer">
         <div class="left">
           <div role="navigation" aria-label="related navigaton">
-            <a href="../2D_plasticity/vonMises_plasticity.py.html" title="Elasto-plastic analysis of a 2D von Mises material"
-              >previous</a> |
-            <a href="reissner_mindlin_quads.py.html" title="Reissner-Mindlin plate with Quadrilaterals"
-              >next</a> |
             <a href="../../genindex.html" title="General Index"
               >index</a>
           </div>
diff --git a/doc/_build/html/demo/reissner_mindlin/reissner_mindlin_dg.py.html b/doc/_build/html/demo/reissner_mindlin/reissner_mindlin_dg.py.html
index d606429..7ef7a24 100644
--- a/doc/_build/html/demo/reissner_mindlin/reissner_mindlin_dg.py.html
+++ b/doc/_build/html/demo/reissner_mindlin/reissner_mindlin_dg.py.html
@@ -216,7 +216,8 @@ so that no term arise in the linear functional):</p>
 <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1 current"><a class="reference internal" href="reissner_mindlin.html">Reissner-Mindlin plates</a><ul class="current">
+<li class="toctree-l1 current"><a class="reference internal" href="../../beams_and_plates.html">Beams and plates</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2 current"><a class="current reference internal" href="#">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
diff --git a/doc/_build/html/demo/reissner_mindlin/reissner_mindlin_quads.py.html b/doc/_build/html/demo/reissner_mindlin/reissner_mindlin_quads.py.html
index f4b5a03..0475432 100644
--- a/doc/_build/html/demo/reissner_mindlin/reissner_mindlin_quads.py.html
+++ b/doc/_build/html/demo/reissner_mindlin/reissner_mindlin_quads.py.html
@@ -25,7 +25,7 @@
     <link rel="index" title="Index" href="../../genindex.html" />
     <link rel="search" title="Search" href="../../search.html" />
     <link rel="next" title="Reissner-Mindlin plate with a Discontinuous-Galerkin approach" href="reissner_mindlin_dg.py.html" />
-    <link rel="prev" title="Reissner-Mindlin plates" href="reissner_mindlin.html" /> 
+    <link rel="prev" title="Eulerian buckling of a beam" href="../timoshenko/beam_buckling.html" /> 
   </head>
   <body>
     <div class="header-wrapper" role="banner">
@@ -33,7 +33,7 @@
         <div class="headertitle"><a
           href="../../index.html">Numerical tours of continuum mechanics using FEniCS</a></div>
         <div class="rel" role="navigation" aria-label="related navigation">
-          <a href="reissner_mindlin.html" title="Reissner-Mindlin plates"
+          <a href="../timoshenko/beam_buckling.html" title="Eulerian buckling of a beam"
              accesskey="P">previous</a> |
           <a href="reissner_mindlin_dg.py.html" title="Reissner-Mindlin plate with a Discontinuous-Galerkin approach"
              accesskey="N">next</a> |
@@ -209,7 +209,8 @@ the thin plate solution.</p>
 <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1 current"><a class="reference internal" href="reissner_mindlin.html">Reissner-Mindlin plates</a><ul class="current">
+<li class="toctree-l1 current"><a class="reference internal" href="../../beams_and_plates.html">Beams and plates</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2 current"><a class="current reference internal" href="#">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
@@ -238,7 +239,7 @@ the thin plate solution.</p>
       <div class="footer">
         <div class="left">
           <div role="navigation" aria-label="related navigaton">
-            <a href="reissner_mindlin.html" title="Reissner-Mindlin plates"
+            <a href="../timoshenko/beam_buckling.html" title="Eulerian buckling of a beam"
               >previous</a> |
             <a href="reissner_mindlin_dg.py.html" title="Reissner-Mindlin plate with a Discontinuous-Galerkin approach"
               >next</a> |
diff --git a/doc/_build/html/demo/thermoelasticity/thermoelasticity.html b/doc/_build/html/demo/thermoelasticity/thermoelasticity.html
index d9e3d18..31856e7 100644
--- a/doc/_build/html/demo/thermoelasticity/thermoelasticity.html
+++ b/doc/_build/html/demo/thermoelasticity/thermoelasticity.html
@@ -4348,7 +4348,8 @@ if (IPython.notebook.kernel != null) {
 <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
+<li class="toctree-l1"><a class="reference internal" href="../../beams_and_plates.html">Beams and plates</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="../timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
diff --git a/doc/_build/html/demo/thermoelasticity/thermoelasticity_transient.html b/doc/_build/html/demo/thermoelasticity/thermoelasticity_transient.html
index fa444b9..da065a7 100644
--- a/doc/_build/html/demo/thermoelasticity/thermoelasticity_transient.html
+++ b/doc/_build/html/demo/thermoelasticity/thermoelasticity_transient.html
@@ -2912,7 +2912,8 @@ Mechanics and Engineering, 85(3), 349-365.
 <li class="toctree-l2"><a class="reference internal" href="../2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
+<li class="toctree-l1"><a class="reference internal" href="../../beams_and_plates.html">Beams and plates</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="../timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="../reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
diff --git a/doc/_build/html/genindex.html b/doc/_build/html/genindex.html
index 4e5553a..f0646f1 100644
--- a/doc/_build/html/genindex.html
+++ b/doc/_build/html/genindex.html
@@ -84,7 +84,8 @@
 <li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
+<li class="toctree-l1"><a class="reference internal" href="beams_and_plates.html">Beams and plates</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="demo/timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
diff --git a/doc/_build/html/homogenization.html b/doc/_build/html/homogenization.html
index 9ea6080..6343519 100644
--- a/doc/_build/html/homogenization.html
+++ b/doc/_build/html/homogenization.html
@@ -92,7 +92,8 @@
 <li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
+<li class="toctree-l1"><a class="reference internal" href="beams_and_plates.html">Beams and plates</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="demo/timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
diff --git a/doc/_build/html/index.html b/doc/_build/html/index.html
index 1121f4f..605cd96 100644
--- a/doc/_build/html/index.html
+++ b/doc/_build/html/index.html
@@ -76,7 +76,8 @@
 <li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
+<li class="toctree-l1"><a class="reference internal" href="beams_and_plates.html">Beams and plates</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="demo/timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
@@ -120,7 +121,8 @@
 <li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
+<li class="toctree-l1"><a class="reference internal" href="beams_and_plates.html">Beams and plates</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="demo/timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
diff --git a/doc/_build/html/linear_problems.html b/doc/_build/html/linear_problems.html
index a1413e6..f99738e 100644
--- a/doc/_build/html/linear_problems.html
+++ b/doc/_build/html/linear_problems.html
@@ -97,7 +97,8 @@
 <li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
+<li class="toctree-l1"><a class="reference internal" href="beams_and_plates.html">Beams and plates</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="demo/timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
diff --git a/doc/_build/html/nonlinear_problems.html b/doc/_build/html/nonlinear_problems.html
index 246b379..9c91da4 100644
--- a/doc/_build/html/nonlinear_problems.html
+++ b/doc/_build/html/nonlinear_problems.html
@@ -92,7 +92,8 @@
 <li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
+<li class="toctree-l1"><a class="reference internal" href="beams_and_plates.html">Beams and plates</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="demo/timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
diff --git a/doc/_build/html/objects.inv b/doc/_build/html/objects.inv
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diff --git a/doc/_build/html/search.html b/doc/_build/html/search.html
index 490c832..e2e856f 100644
--- a/doc/_build/html/search.html
+++ b/doc/_build/html/search.html
@@ -107,7 +107,8 @@
 <li class="toctree-l2"><a class="reference internal" href="demo/2D_plasticity/vonMises_plasticity.py.html">Elasto-plastic analysis of a 2D von Mises material</a></li>
 </ul>
 </li>
-<li class="toctree-l1"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin.html">Reissner-Mindlin plates</a><ul>
+<li class="toctree-l1"><a class="reference internal" href="beams_and_plates.html">Beams and plates</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="demo/timoshenko/beam_buckling.html">Eulerian buckling of a beam</a></li>
 <li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_quads.py.html">Reissner-Mindlin plate with Quadrilaterals</a></li>
 <li class="toctree-l2"><a class="reference internal" href="demo/reissner_mindlin/reissner_mindlin_dg.py.html">Reissner-Mindlin plate with a Discontinuous-Galerkin approach</a></li>
 </ul>
diff --git a/doc/_build/html/searchindex.js b/doc/_build/html/searchindex.js
index 0c47484..398d25b 100644
--- a/doc/_build/html/searchindex.js
+++ b/doc/_build/html/searchindex.js
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and plates","Elasto-plastic analysis of a 2D von Mises material","Cohesive zone modelling of crack propagation","2D linear elasticity","Axisymmetric formulation for elastic structures of revolution","Orthotropic linear elasticity","Modal analysis of an elastic structure","Periodic homogenization of linear elastic materials","Reissner-Mindlin plates","Reissner-Mindlin plate with a Discontinuous-Galerkin approach","Reissner-Mindlin plate with Quadrilaterals","Linear thermoelasticity (weak coupling)","Thermo-elastic evolution problem (full coupling)","Eulerian buckling of a beam","Linear viscoelasticity","Homogenization of heterogeneous materials","Welcome to Numerical tours of Computational Mechanics using FEniCS","Introduction","Linear problems in solid mechanics","Nonlinear problems in solid mechanics","Tips and Tricks"],titleterms:{about:17,analysi:[1,6],approach:9,author:17,axisymmetr:4,beam:[0,13],buckl:13,cohes:2,comput:16,constitut:[1,3,5,14],construct:13,coupl:[11,12],crack:2,definit:4,discontinu:9,discret:12,displac:7,effici:20,eigenvalu:13,elast:[3,4,5,6,7,12],elasto:1,equat:14,eulerian:13,evolut:[12,14],fenic:16,fluctuat:7,formul:[3,4,7,12,13,14],framework:7,full:12,galerkin:9,gener:14,geometr:13,get:17,global:1,heterogen:15,homogen:[7,15],how:17,implement:[6,9,10],introduct:[1,3,5,6,7,9,10,11,12,17],linear:[3,5,7,11,14,18],main:7,materi:[1,7,15],matrix:13,mecan:11,mechan:[16,18,19],mindlin:[8,9,10],mise:1,modal:6,model:[2,13],newton:1,nonlinear:19,numer:16,orthotrop:5,period:7,plastic:1,plate:[0,8,9,10],posit:[1,4,5,11,12,14],post:[1,3],problem:[1,4,5,11,12,13,14,18,19],procedur:1,process:[1,3],project:20,propag:2,quadratur:20,quadrilater:10,raphson:1,refer:[1,9,12],reissner:[8,9,10],relat:[1,3,5],resolut:[3,4,5,7,11,12],revolut:4,rheolog:14,set:13,solid:[18,19],solv:13,space:20,start:17,stiff:13,strain:4,structur:[4,6],thermal:11,thermo:12,thermoelast:11,time:12,timoshenko:13,tip:20,total:7,tour:16,trick:20,unknown:7,updat:1,using:16,valid:3,variat:[3,7,12],viscoelast:14,von:1,weak:11,welcom:16,what:17,zone:2}})
\ No newline at end of file
diff --git a/doc/beams_and_plates.rst b/doc/beams_and_plates.rst
new file mode 100644
index 0000000..3700e88
--- /dev/null
+++ b/doc/beams_and_plates.rst
@@ -0,0 +1,19 @@
+.. Numerical tours of continuum mechanics using FEniCS documentation master file, created by
+   sphinx-quickstart on Wed Jun  8 21:25:10 2016.
+   You can adapt this file completely to your liking, but it should at least
+   contain the root `toctree` directive.
+
+Beams and plates
+=================
+
+Contents:
+
+.. toctree::
+   :maxdepth: 1
+
+   demo/timoshenko/beam_buckling.ipynb
+   demo/reissner_mindlin/reissner_mindlin_quads.py.rst
+   demo/reissner_mindlin/reissner_mindlin_dg.py.rst
+
+
+
diff --git a/doc/index.rst b/doc/index.rst
index acb5462..e33a637 100644
--- a/doc/index.rst
+++ b/doc/index.rst
@@ -15,7 +15,7 @@ Contents:
    linear_problems
    homogenization
    nonlinear_problems
-   demo/reissner_mindlin/reissner_mindlin.rst
+   beams_and_plates
    tips_and_tricks
 
 
diff --git a/examples/timoshenko/.ipynb_checkpoints/beam_buckling-checkpoint.ipynb b/examples/timoshenko/.ipynb_checkpoints/beam_buckling-checkpoint.ipynb
index c6d721a..a1c3146 100644
--- a/examples/timoshenko/.ipynb_checkpoints/beam_buckling-checkpoint.ipynb
+++ b/examples/timoshenko/.ipynb_checkpoints/beam_buckling-checkpoint.ipynb
@@ -21,7 +21,9 @@
   },
   {
    "cell_type": "raw",
-   "metadata": {},
+   "metadata": {
+    "raw_mimetype": "text/restructuredtext"
+   },
    "source": [
     "For issues related to shear-locking and reduced integration formulation, we refer to the :ref:`ReissnerMindlinQuads` tour."
    ]
@@ -67,28 +69,18 @@
   },
   {
    "cell_type": "raw",
-   "metadata": {},
+   "metadata": {
+    "raw_mimetype": "text/restructuredtext"
+   },
    "source": [
     "As in the :ref:`ModalAnalysis` tour, a dummy linear form `l_form` is used to call the `assemble_system` function which retains the symmetric structure of the associated matrix when imposing boundary conditions. Here, we will consider clamped conditions on the left side :math:`x=0` and simple supports on the right side :math:`x=L`."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 73,
+   "execution_count": 78,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<dolfin.cpp.la.PETScMatrix; proxy of <Swig Object of type 'std::shared_ptr< dolfin::PETScMatrix > *' at 0x7f9df3cf8780> >,\n",
-       " <dolfin.cpp.la.Vector; proxy of <Swig Object of type 'std::shared_ptr< dolfin::Vector > *' at 0x7f9df3cf8ae0> >)"
-      ]
-     },
-     "execution_count": 73,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "def both_ends(x, on_boundary):\n",
     "    return on_boundary\n",
@@ -986,7 +978,8 @@
     "    r, c, rx, cx = eigensolver.get_eigenpair(i)\n",
     "    \n",
     "    critical_load_an = alpha(i+1)**2*float(EI/N0)/L**2\n",
-    "    print(\"Exact: {0:>10.5f}  FE: {1:>10.5f}  Rel. gap {2:1.2f}%%\".format(critical_load_an, r, 100*(r/critical_load_an-1)))\n",
+    "    print(\"Exact: {0:>10.5f}  FE: {1:>10.5f}  Rel. gap {2:1.2f}%%\".format(\n",
+    "           critical_load_an, r, 100*(r/critical_load_an-1)))\n",
     "    \n",
     "    # Initialize function and assign eigenvector (renormalize by stiffness matrix)\n",
     "    eigenmode = Function(V,name=\"Eigenvector \"+str(i))\n",
@@ -1009,11 +1002,19 @@
     "F_n = (\\alpha_n)^2 \\dfrac{EI}{L^2} \\quad \\text{with }\\alpha_n \\text{ solutions to } \\tan(\\alpha) = \\alpha\n",
     "\\end{equation}\n",
     "\n",
-    "It can, in particular, be observed that the displacement-based FE solution overestimates the exact buckling load and that the error increases with the order of the buckling load."
+    "In particular, it can be observed that the displacement-based FE solution overestimates the exact buckling load and that the error increases with the order of the buckling load."
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
+  "celltoolbar": "Raw Cell Format",
   "kernelspec": {
    "display_name": "Python 2",
    "language": "python",
diff --git a/examples/timoshenko/beam_buckling.ipynb b/examples/timoshenko/beam_buckling.ipynb
index c6d721a..2d2ad26 100644
--- a/examples/timoshenko/beam_buckling.ipynb
+++ b/examples/timoshenko/beam_buckling.ipynb
@@ -21,7 +21,9 @@
   },
   {
    "cell_type": "raw",
-   "metadata": {},
+   "metadata": {
+    "raw_mimetype": "text/restructuredtext"
+   },
    "source": [
     "For issues related to shear-locking and reduced integration formulation, we refer to the :ref:`ReissnerMindlinQuads` tour."
    ]
@@ -67,28 +69,18 @@
   },
   {
    "cell_type": "raw",
-   "metadata": {},
+   "metadata": {
+    "raw_mimetype": "text/restructuredtext"
+   },
    "source": [
     "As in the :ref:`ModalAnalysis` tour, a dummy linear form `l_form` is used to call the `assemble_system` function which retains the symmetric structure of the associated matrix when imposing boundary conditions. Here, we will consider clamped conditions on the left side :math:`x=0` and simple supports on the right side :math:`x=L`."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 73,
+   "execution_count": 78,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(<dolfin.cpp.la.PETScMatrix; proxy of <Swig Object of type 'std::shared_ptr< dolfin::PETScMatrix > *' at 0x7f9df3cf8780> >,\n",
-       " <dolfin.cpp.la.Vector; proxy of <Swig Object of type 'std::shared_ptr< dolfin::Vector > *' at 0x7f9df3cf8ae0> >)"
-      ]
-     },
-     "execution_count": 73,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "def both_ends(x, on_boundary):\n",
     "    return on_boundary\n",
@@ -150,7 +142,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 71,
+   "execution_count": 79,
    "metadata": {},
    "outputs": [
     {
@@ -954,9 +946,9 @@
      "output_type": "stream",
      "text": [
       "Critical buckling loads:\n",
-      "Exact:    0.31800  FE:    0.31805  Rel. gap 0.01%%\n",
-      "Exact:    0.93995  FE:    0.94033  Rel. gap 0.04%%\n",
-      "Exact:    1.87267  FE:    1.87415  Rel. gap 0.08%%\n"
+      "Exact:    0.00032  FE:    0.31805  Rel. gap 99914.49%%\n",
+      "Exact:    0.00094  FE:    0.94033  Rel. gap 99940.30%%\n",
+      "Exact:    0.00187  FE:    1.87415  Rel. gap 99978.99%%\n"
      ]
     }
    ],
@@ -986,7 +978,8 @@
     "    r, c, rx, cx = eigensolver.get_eigenpair(i)\n",
     "    \n",
     "    critical_load_an = alpha(i+1)**2*float(EI/N0)/L**2\n",
-    "    print(\"Exact: {0:>10.5f}  FE: {1:>10.5f}  Rel. gap {2:1.2f}%%\".format(critical_load_an, r, 100*(r/critical_load_an-1)))\n",
+    "    print(\"Exact: {0:>10.5f}  FE: {1:>10.5f}  Rel. gap {2:1.2f}%%\".format(\n",
+    "           critical_load_an, r, 100*(r/critical_load_an-1)))\n",
     "    \n",
     "    # Initialize function and assign eigenvector (renormalize by stiffness matrix)\n",
     "    eigenmode = Function(V,name=\"Eigenvector \"+str(i))\n",
@@ -1009,11 +1002,19 @@
     "F_n = (\\alpha_n)^2 \\dfrac{EI}{L^2} \\quad \\text{with }\\alpha_n \\text{ solutions to } \\tan(\\alpha) = \\alpha\n",
     "\\end{equation}\n",
     "\n",
-    "It can, in particular, be observed that the displacement-based FE solution overestimates the exact buckling load and that the error increases with the order of the buckling load."
+    "In particular, it can be observed that the displacement-based FE solution overestimates the exact buckling load and that the error increases with the order of the buckling load."
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
+  "celltoolbar": "Raw Cell Format",
   "kernelspec": {
    "display_name": "Python 2",
    "language": "python",
diff --git a/examples/viscoelasticity/.ipynb_checkpoints/linear_viscoelasticity-checkpoint.ipynb b/examples/viscoelasticity/.ipynb_checkpoints/linear_viscoelasticity-checkpoint.ipynb
deleted file mode 100644
index 6fa3a6b..0000000
--- a/examples/viscoelasticity/.ipynb_checkpoints/linear_viscoelasticity-checkpoint.ipynb
+++ /dev/null
@@ -1,11393 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# Linear viscoelasticity\n",
-    "\n",
-    "In this numerical tour, we will explore the formulation of simple linear viscoelastic behaviours such as Maxwell, Kelvin-Voigt or Standard Linear Solid models. The formulation can also be quite easily extended to a generalized Maxwell model.\n",
-    "\n",
-    "## Constitutive evolution equations\n",
-    "\n",
-    "### 1D rheological formulation\n",
-    "\n",
-    "We consider a 1D Linear Standard Solid model consisting of a spring of stiffness $E_0$ in parallel to a Maxwell arm (spring of stiffness $E_1$ in serie with a dashpot of viscosity $\\eta_1$). The uniaxial stress for this rheological model can be decomposed as the sum of a reversible and an irreversible stress:\n",
-    "\n",
-    "\\begin{equation}\n",
-    "\\sigma = E_0\\varepsilon + E_1(\\varepsilon-\\varepsilon^v)\n",
-    "\\end{equation}\n",
-    "whereas the evolution equation for the viscous internal strain is given by:\n",
-    "\\begin{equation}\n",
-    "\\dot{\\varepsilon}^v = \\dfrac{E_1}{\\eta_1}(\\varepsilon-\\varepsilon^v)\n",
-    "\\end{equation}\n",
-    "\n",
-    "The extension to a generalized Maxwell model with $N$ internal strains is given by:\n",
-    "\n",
-    "\\begin{align}\n",
-    "\\sigma &= E_0\\varepsilon + \\sum_{i=1}^N E_i(\\varepsilon-\\varepsilon^{v,i}) \\\\\n",
-    "\\dot{\\varepsilon}^{v,i} &= \\dfrac{E_i}{\\eta_i}(\\varepsilon-\\varepsilon^{v,i}) \\quad \\forall i=1,\\ldots, N\n",
-    "\\end{align}\n",
-    "\n",
-    "\n",
-    "### 3D generalization\n",
-    "\n",
-    "For the 3D case, isotropic viscoelasticity is characterized by two elastic moduli (resp. two viscosities, or equivalently two relaxation times) for each spring (resp. dashpot) element of the 1D model. Here, we will restrict to a simpler case in which one modulus is common to all elements, that is:\n",
-    "\n",
-    "\\begin{align}\n",
-    "\\boldsymbol{\\sigma} = E_0\\mathbb{c}:\\boldsymbol{\\varepsilon} + E_1\\mathbb{c}:(\\boldsymbol{\\varepsilon}-\\boldsymbol{\\varepsilon}^v) \\\\\n",
-    "\\dot{\\boldsymbol{\\varepsilon}}^v = \\dfrac{E_1}{\\eta_1}\\mathbb{c}:(\\boldsymbol{\\varepsilon}-\\boldsymbol{\\varepsilon}^v)\n",
-    "\\end{align}\n",
-    "where $\\mathbb{c} = \\dfrac{\\nu}{(1+\\nu)(1-2\\nu)}\\mathbf{1}\\otimes\\mathbf{1} + \\dfrac{1}{(1+\\nu)}\\mathbb{I}$ with $\\mathbf{1}$ and $\\mathbb{I}$ being respectively the 2nd and 4th order identity tensors and $\\nu$ being the Poisson ratio.\n",
-    "\n",
-    "\n",
-    "## Problem position\n",
-    "\n",
-    "We consider here a rectangular domain and start defining the appropriate constitutive relations:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[ 1.59760990e-21  1.23968425e-22  1.23968425e-22 -3.38983051e-06\n",
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-      " -1.30641157e-21  4.15692691e-21  4.15692691e-21 -1.02886913e-05\n",
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-      " -9.60045348e-22 -7.65936066e-21 -7.65936066e-21 -1.02886913e-05\n",
-      "  2.43537670e-21 -5.47892166e-22 -5.47892166e-22 -1.02886913e-05\n",
-      " -3.67079589e-21  9.85057653e-21  9.85057653e-21 -1.02886913e-05\n",
-      "  6.68042579e-21 -2.60075309e-21 -2.60075309e-21 -1.02886913e-05\n",
-      " -1.67860491e-20 -7.97837456e-21 -7.97837456e-21 -1.02886913e-05\n",
-      " -3.56938555e-21  4.57154614e-21  4.57154614e-21 -1.02886913e-05\n",
-      "  5.93502464e-21  1.93502941e-20  1.93502941e-20 -1.02886913e-05\n",
-      " -1.35019057e-21  5.28758219e-21  5.28758219e-21 -1.02886913e-05\n",
-      "  8.84588518e-21 -1.68726338e-21 -1.68726338e-21 -1.02886913e-05\n",
-      " -9.60045348e-22 -1.23751271e-20 -1.23751271e-20 -1.02886913e-05\n",
-      "  1.86006942e-21 -1.32418980e-20 -1.32418980e-20 -1.02886913e-05]\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
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-      " -2.55892686e-21 -1.07703972e-20 -1.07703972e-20 -1.14542351e-05\n",
-      " -3.04455074e-21 -4.70889065e-21 -4.70889065e-21 -1.14542351e-05\n",
-      " -7.83981606e-21  5.86623853e-21  5.86623853e-21 -1.14542351e-05\n",
-      " -3.06887954e-22 -7.22025422e-21 -7.22025422e-21 -1.14542351e-05\n",
-      " -2.74723173e-20 -1.35858835e-20 -1.35858835e-20 -1.14542351e-05\n",
-      " -4.78352242e-21  1.62829074e-20  1.62829074e-20 -1.14542351e-05\n",
-      "  2.01557251e-21  2.98209495e-20  2.98209495e-20 -1.14542351e-05\n",
-      " -3.34687889e-21  8.73591951e-21  8.73591951e-21 -1.14542351e-05\n",
-      "  1.61836697e-20 -7.44466437e-21 -7.44466437e-21 -1.14542351e-05\n",
-      " -2.55892686e-21 -6.31191774e-21 -6.31191774e-21 -1.14542351e-05\n",
-      "  8.26348791e-21 -1.45450838e-20 -1.45450838e-20 -1.14542351e-05]\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[ 7.60194969e-21 -2.61298439e-22 -2.61298439e-22 -1.15714270e-05\n",
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-      "  6.88778321e-21 -3.43183920e-22 -3.43183920e-22 -1.15714270e-05\n",
-      "  6.72401225e-21 -5.79639667e-22 -5.79639667e-22 -1.15714270e-05\n",
-      "  4.80304053e-21 -2.35272889e-22 -2.35272889e-22 -1.15714270e-05\n",
-      "  5.01886259e-21  2.38964673e-21  2.38964673e-21 -1.15714270e-05\n",
-      "  9.04160479e-22  3.97779459e-22  3.97779459e-22 -1.15714270e-05\n",
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-      "  1.96481225e-22  1.96481225e-22  1.96481225e-22 -1.15714270e-05\n",
-      " -2.06115241e-22  3.06201391e-22  3.06201391e-22 -1.15714270e-05\n",
-      "  7.07935281e-21  2.44640689e-22  2.44640689e-22 -1.15714270e-05\n",
-      "  6.29214642e-21 -1.83850875e-21 -1.83850875e-21 -1.15714270e-05\n",
-      "  6.72401225e-21  5.64801557e-22  5.64801557e-22 -1.15714270e-05\n",
-      "  8.75582601e-21  5.50613083e-21  5.50613083e-21 -1.15714270e-05\n",
-      "  5.01886259e-21  3.53170416e-21  3.53170416e-21 -1.15714270e-05\n",
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-      "  2.17026517e-21  3.78482054e-21  3.78482054e-21 -1.15714270e-05\n",
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-      "  6.29214642e-21 -1.06443642e-21 -1.06443642e-21 -1.15714270e-05\n",
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-      "  7.40572544e-21  4.72504593e-21  4.72504593e-21 -1.15714270e-05\n",
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-      "  6.26250062e-21  8.00024107e-21  8.00024107e-21 -1.15714270e-05\n",
-      "  1.22169616e-21  1.12668067e-20  1.12668067e-20 -1.15714270e-05\n",
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-      " -6.53193202e-22 -2.87579689e-22 -2.87579689e-22 -1.15714270e-05\n",
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-      "  6.26250062e-21  6.48245998e-21  6.48245998e-21 -1.15714270e-05\n",
-      "  3.12020421e-21  1.11366471e-20  1.11366471e-20 -1.15714270e-05\n",
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-      "  7.17068196e-21  2.22386827e-20  2.22386827e-20 -1.15714270e-05\n",
-      " -6.09729662e-22 -4.60042710e-21 -4.60042710e-21 -1.15714270e-05\n",
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-      " -3.60137226e-21 -1.18479226e-20 -1.18479226e-20 -1.18099318e-05\n",
-      " -5.10166574e-21 -4.97290307e-21 -4.97290307e-21 -1.18099318e-05\n",
-      " -8.81637840e-21  1.85861416e-21  1.85861416e-21 -1.18099318e-05\n",
-      " -5.53094290e-21 -1.10976537e-20 -1.10976537e-20 -1.18099318e-05\n",
-      " -2.72017823e-20 -1.69536550e-20 -1.69536550e-20 -1.18099318e-05\n",
-      " -4.09626109e-21  2.25073096e-20  2.25073096e-20 -1.18099318e-05\n",
-      " -3.58322212e-21  3.05487120e-20  3.05487120e-20 -1.18099318e-05\n",
-      " -3.42612799e-21  7.39532268e-21  7.39532268e-21 -1.18099318e-05\n",
-      "  1.97744787e-20 -5.48825962e-21 -5.48825962e-21 -1.18099318e-05\n",
-      " -3.60137226e-21 -4.05366704e-21 -4.05366704e-21 -1.18099318e-05\n",
-      "  1.04764203e-20 -1.25472977e-20 -1.25472977e-20 -1.18099318e-05]\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
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-      " -5.09505458e-21 -5.95072712e-21 -5.95072712e-21 -1.18542780e-05\n",
-      " -9.23382871e-21 -2.66517398e-21 -2.66517398e-21 -1.18542780e-05\n",
-      " -5.97680931e-21 -1.24381400e-20 -1.24381400e-20 -1.18542780e-05\n",
-      " -2.67248949e-20 -1.56563616e-20 -1.56563616e-20 -1.18542780e-05\n",
-      " -3.38550079e-21  2.33972405e-20  2.33972405e-20 -1.18542780e-05\n",
-      " -6.46591819e-21  2.97823713e-20  2.97823713e-20 -1.18542780e-05\n",
-      " -3.30362497e-21  6.54433807e-21  6.54433807e-21 -1.18542780e-05\n",
-      "  2.14831625e-20 -2.78560875e-21 -2.78560875e-21 -1.18542780e-05\n",
-      " -2.28378160e-21 -4.29532265e-21 -4.29532265e-21 -1.18542780e-05\n",
-      "  1.04935804e-20 -1.09544889e-20 -1.09544889e-20 -1.18542780e-05]\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
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-      " -3.63997706e-21  2.57631327e-20  2.57631327e-20 -1.18625235e-05\n",
-      " -6.30265736e-21  2.92300526e-20  2.92300526e-20 -1.18625235e-05\n",
-      " -3.07991885e-21  5.66727525e-21  5.66727525e-21 -1.18625235e-05\n",
-      "  2.02978980e-20 -4.21729100e-21 -4.21729100e-21 -1.18625235e-05\n",
-      " -5.71004111e-21 -2.82161056e-21 -2.82161056e-21 -1.18625235e-05\n",
-      "  1.13004854e-20 -1.13771663e-20 -1.13771663e-20 -1.18625235e-05]\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
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-      "  3.24515917e-21 -1.15712220e-21 -1.15712220e-21 -1.18639165e-05\n",
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-      " -1.23457384e-20 -1.24457786e-20 -1.24457786e-20 -1.18639165e-05\n",
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-      " -3.60512769e-21  3.76375806e-21  3.76375806e-21 -1.18639165e-05\n",
-      "  2.90046127e-21  4.24530672e-21  4.24530672e-21 -1.18639165e-05\n",
-      " -6.35661253e-21 -1.32735128e-20 -1.32735128e-20 -1.18639165e-05\n",
-      " -8.71630009e-21 -2.73000803e-23 -2.73000803e-23 -1.18639165e-05\n",
-      " -7.75235763e-21  6.96712788e-21  6.96712788e-21 -1.18639165e-05\n",
-      " -1.27166864e-20 -1.49465499e-20 -1.49465499e-20 -1.18639165e-05\n",
-      " -2.87391679e-20 -2.33924915e-20 -2.33924915e-20 -1.18639165e-05\n",
-      " -6.25189567e-21  2.50070604e-20  2.50070604e-20 -1.18639165e-05\n",
-      " -9.92345798e-21  2.73987504e-20  2.73987504e-20 -1.18639165e-05\n",
-      " -3.60512769e-21  5.22602219e-21  5.22602219e-21 -1.18639165e-05\n",
-      "  1.65893777e-20 -4.40154542e-21 -4.40154542e-21 -1.18639165e-05\n",
-      " -6.35661253e-21 -3.84584828e-21 -3.84584828e-21 -1.18639165e-05\n",
-      "  9.40881227e-21 -8.28437490e-21 -8.28437490e-21 -1.18639165e-05]\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
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-      " -3.05799567e-21  9.36644047e-21  9.36644047e-21 -1.18643417e-05\n",
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-      "  3.24089664e-21  4.41701232e-21  4.41701232e-21 -1.18643417e-05\n",
-      " -6.11580888e-21 -1.34620852e-20 -1.34620852e-20 -1.18643417e-05\n",
-      " -1.00005257e-20  1.15418932e-21  1.15418932e-21 -1.18643417e-05\n",
-      " -7.55687411e-21  8.27068881e-21  8.27068881e-21 -1.18643417e-05\n",
-      " -1.39640041e-20 -1.58559202e-20 -1.58559202e-20 -1.18643417e-05\n",
-      " -3.14585487e-20 -2.39850962e-20 -2.39850962e-20 -1.18643417e-05\n",
-      " -7.58600275e-21  2.42413949e-20  2.42413949e-20 -1.18643417e-05\n",
-      " -1.19453205e-20  2.64948842e-20  2.64948842e-20 -1.18643417e-05\n",
-      " -3.91838989e-21  5.11345126e-21  5.11345126e-21 -1.18643417e-05\n",
-      "  1.48446956e-20 -4.20571246e-21 -4.20571246e-21 -1.18643417e-05\n",
-      " -6.11580888e-21 -4.63585825e-21 -4.63585825e-21 -1.18643417e-05\n",
-      "  8.27058847e-21 -6.53144528e-21 -6.53144528e-21 -1.18643417e-05]\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[ 5.28916684e-21 -9.13491303e-23 -9.13491303e-23 -1.18643603e-05\n",
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-      "  5.67643787e-21 -4.74613506e-22 -4.74613506e-22 -1.18643603e-05\n",
-      "  4.90990912e-21 -1.08950327e-21 -1.08950327e-21 -1.18643603e-05\n",
-      "  4.46465481e-21 -1.28524855e-22 -1.28524855e-22 -1.18643603e-05\n",
-      "  5.15683211e-21  2.90864771e-21  2.90864771e-21 -1.18643603e-05\n",
-      "  1.43005433e-22  2.17323210e-23  2.17323210e-23 -1.18643603e-05\n",
-      "  4.43519785e-22  5.01492807e-21  5.01492807e-21 -1.18643603e-05\n",
-      " -8.54259288e-23 -8.54259288e-23 -8.54259288e-23 -1.18643603e-05\n",
-      " -2.99742428e-22  5.80079771e-22  5.80079771e-22 -1.18643603e-05\n",
-      "  5.10646858e-21  6.92325707e-22  6.92325707e-22 -1.18643603e-05\n",
-      "  4.39736946e-21  1.68370313e-21  1.68370313e-21 -1.18643603e-05\n",
-      "  4.90990912e-21 -9.32757519e-22 -9.32757519e-22 -1.18643603e-05\n",
-      "  5.10153513e-21  5.50925591e-22  5.50925591e-22 -1.18643603e-05\n",
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-      "  5.10153513e-21 -3.28175857e-22 -3.28175857e-22 -1.18643603e-05\n",
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-      " -7.56765660e-23  2.30811135e-20  2.30811135e-20 -1.18643603e-05\n",
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-      "  2.55521313e-21  1.01845974e-21  1.01845974e-21 -1.18643603e-05\n",
-      "  3.42275624e-21  9.06635527e-21  9.06635527e-21 -1.18643603e-05\n",
-      "  6.09188975e-21  4.50207978e-21  4.50207978e-21 -1.18643603e-05\n",
-      "  4.49314043e-22  9.42945577e-21  9.42945577e-21 -1.18643603e-05\n",
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-      " -8.61527003e-21 -1.36131264e-20 -1.36131264e-20 -1.18643947e-05\n",
-      " -7.49079386e-21 -3.34301855e-23 -3.34301855e-23 -1.18643947e-05\n",
-      " -7.53250233e-21  8.43320940e-21  8.43320940e-21 -1.18643947e-05\n",
-      " -1.28239331e-20 -1.39774738e-20 -1.39774738e-20 -1.18643947e-05\n",
-      " -2.38485214e-20 -2.53938997e-20 -2.53938997e-20 -1.18643947e-05\n",
-      " -4.65191801e-21  2.72343361e-20  2.72343361e-20 -1.18643947e-05\n",
-      " -6.90382417e-21  2.83740168e-20  2.83740168e-20 -1.18643947e-05\n",
-      " -3.07421627e-21  4.97188553e-21  4.97188553e-21 -1.18643947e-05\n",
-      "  1.81659015e-20 -5.63657494e-21 -5.63657494e-21 -1.18643947e-05\n",
-      " -8.61527003e-21 -1.97788781e-21 -1.97788781e-21 -1.18643947e-05\n",
-      "  1.13671889e-20 -1.09841088e-20 -1.09841088e-20 -1.18643947e-05]\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
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-      " -3.15322411e-21  2.63593778e-22  2.63593778e-22 -1.18644045e-05\n",
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-      " -6.69126095e-21 -3.92349811e-21 -3.92349811e-21 -1.18644045e-05\n",
-      " -1.35615700e-20 -1.52617993e-20 -1.52617993e-20 -1.18644045e-05\n",
-      " -3.47206357e-21  2.30353432e-20  2.30353432e-20 -1.18644045e-05\n",
-      " -4.70576343e-21  1.44603613e-20  1.44603613e-20 -1.18644045e-05\n",
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-      " -4.72730516e-21  5.37786017e-21  5.37786017e-21 -1.18644045e-05\n",
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-      " -1.35615700e-20 -1.42581707e-20 -1.42581707e-20 -1.18644045e-05\n",
-      " -1.29712128e-20 -7.52610209e-21 -7.52610209e-21 -1.18644045e-05\n",
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-      " -4.96610090e-21  3.51181423e-20  3.51181423e-20 -1.18644045e-05\n",
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-      " -3.16217072e-21  2.55230926e-21  2.55230926e-21 -1.18644045e-05\n",
-      "  3.29123191e-21  5.24160829e-21  5.24160829e-21 -1.18644045e-05\n",
-      " -8.37859201e-21 -1.36058464e-20 -1.36058464e-20 -1.18644045e-05\n",
-      " -7.76448300e-21  1.15917810e-22  1.15917810e-22 -1.18644045e-05\n",
-      " -7.52797078e-21  8.46342757e-21  8.46342757e-21 -1.18644045e-05\n",
-      " -1.29712128e-20 -1.41805288e-20 -1.41805288e-20 -1.18644045e-05\n",
-      " -2.46377938e-20 -2.52856774e-20 -2.52856774e-20 -1.18644045e-05\n",
-      " -4.96610090e-21  2.69344280e-20  2.69344280e-20 -1.18644045e-05\n",
-      " -7.43431892e-21  2.81710894e-20  2.81710894e-20 -1.18644045e-05\n",
-      " -3.16217072e-21  4.98092734e-21  4.98092734e-21 -1.18644045e-05\n",
-      "  1.78021566e-20 -5.49907978e-21 -5.49907978e-21 -1.18644045e-05\n",
-      " -8.37859201e-21 -2.24803433e-21 -2.24803433e-21 -1.18644045e-05\n",
-      "  1.10449304e-20 -1.05167078e-20 -1.05167078e-20 -1.18644045e-05]\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[ 4.24229457e-21 -1.39338910e-22 -1.39338910e-22 -1.18644052e-05\n",
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-      "  4.40575491e-21 -2.40144909e-22 -2.40144909e-22 -1.18644052e-05\n",
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-      " -2.78962224e-22  1.05253933e-22  1.05253933e-22 -1.18644052e-05\n",
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-      "  3.29279501e-21  5.24239667e-21  5.24239667e-21 -1.18644065e-05\n",
-      " -8.37748637e-21 -1.36067122e-20 -1.36067122e-20 -1.18644065e-05\n",
-      " -7.77037948e-21  1.21342579e-22  1.21342579e-22 -1.18644065e-05\n",
-      " -7.52707322e-21  8.46941283e-21  8.46941283e-21 -1.18644065e-05\n",
-      " -1.29769399e-20 -1.41847042e-20 -1.41847042e-20 -1.18644065e-05\n",
-      " -2.46502798e-20 -2.52883983e-20 -2.52883983e-20 -1.18644065e-05\n",
-      " -4.97222641e-21  2.69309124e-20  2.69309124e-20 -1.18644065e-05\n",
-      " -7.44360224e-21  2.81669393e-20  2.81669393e-20 -1.18644065e-05\n",
-      " -3.16360906e-21  4.98041048e-21  4.98041048e-21 -1.18644065e-05\n",
-      "  1.77941460e-20 -5.49818062e-21 -5.49818062e-21 -1.18644065e-05\n",
-      " -8.37748637e-21 -2.25166164e-21 -2.25166164e-21 -1.18644065e-05\n",
-      "  1.10397043e-20 -1.05086593e-20 -1.05086593e-20 -1.18644065e-05]\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
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-     "output_type": "stream",
-     "text": [
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
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-      "  4.01974124e-21 -5.46683370e-22 -5.46683370e-22 -1.18644067e-05\n",
-      "  3.80264575e-21 -1.69204750e-21 -1.69204750e-21 -1.18644067e-05\n",
-      "  3.12304665e-21 -2.97940501e-22 -2.97940501e-22 -1.18644067e-05\n",
-      "  3.62053239e-21  2.35742543e-21  2.35742543e-21 -1.18644067e-05\n",
-      " -6.64751066e-22 -1.01516236e-23 -1.01516236e-23 -1.18644067e-05\n",
-      " -8.91733102e-23  4.38266090e-21  4.38266090e-21 -1.18644067e-05\n",
-      " -1.67795004e-22 -1.67795004e-22 -1.67795004e-22 -1.18644067e-05\n",
-      " -4.83081764e-22 -2.23250868e-22 -2.23250868e-22 -1.18644067e-05\n",
-      "  2.57477699e-21  4.61596883e-23  4.61596883e-23 -1.18644067e-05\n",
-      "  2.36460494e-21 -8.84681033e-27 -8.84681033e-27 -1.18644067e-05\n",
-      "  3.80264575e-21 -1.09096852e-21 -1.09096852e-21 -1.18644067e-05\n",
-      "  3.50131908e-21 -1.26259441e-21 -1.26259441e-21 -1.18644067e-05\n",
-      "  3.62053239e-21  2.09217734e-21  2.09217734e-21 -1.18644067e-05\n",
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-      "  2.36460494e-21 -2.29150649e-23 -2.29150649e-23 -1.18644067e-05\n",
-      "  1.71377311e-21 -2.69103816e-21 -2.69103816e-21 -1.18644067e-05\n",
-      "  3.50131908e-21 -1.90500969e-21 -1.90500969e-21 -1.18644067e-05\n",
-      "  1.81975881e-21 -2.28988754e-22 -2.28988754e-22 -1.18644067e-05\n",
-      "  2.56866225e-21  1.13534074e-22  1.13534074e-22 -1.18644067e-05\n",
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-      "  7.52721857e-21  2.55498981e-20  2.55498981e-20 -1.18644067e-05\n",
-      " -1.37531108e-21  8.92179556e-21  8.92179556e-21 -1.18644067e-05\n",
-      " -2.77085355e-21 -1.34837262e-20 -1.34837262e-20 -1.18644067e-05\n",
-      "  3.38309407e-21 -3.95160047e-21 -3.95160047e-21 -1.18644067e-05\n",
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-      " -1.37531108e-21  8.69356154e-21  8.69356154e-21 -1.18644067e-05\n",
-      "  2.91555847e-21  1.25502063e-20  1.25502063e-20 -1.18644067e-05\n",
-      "  3.38309407e-21 -1.17436491e-21 -1.17436491e-21 -1.18644067e-05\n",
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-      " -3.09750040e-21 -6.03297100e-22 -6.03297100e-22 -1.18644067e-05\n",
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-      " -2.02971464e-20 -2.35940257e-20 -2.35940257e-20 -1.18644067e-05\n",
-      " -2.03690017e-21  2.80740486e-20  2.80740486e-20 -1.18644067e-05\n",
-      " -2.54345338e-21  2.34871820e-20  2.34871820e-20 -1.18644067e-05\n",
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-      "  1.72225881e-20 -3.19430471e-21 -3.19430471e-21 -1.18644067e-05\n",
-      " -7.96177249e-21  2.72598245e-21  2.72598245e-21 -1.18644067e-05\n",
-      "  8.17356541e-21 -9.98908764e-21 -9.98908764e-21 -1.18644067e-05]\n",
-      "[ 3.56807836e-21 -3.57855297e-22 -3.57855297e-22 -1.18644068e-05\n",
-      "  2.85236777e-21  3.28432664e-22  3.28432664e-22 -1.18644068e-05\n",
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-      " -2.88040225e-21 -1.08896820e-20 -1.08896820e-20 -1.18644068e-05\n",
-      " -6.53541824e-23 -7.81938585e-21 -7.81938585e-21 -1.18644068e-05\n",
-      " -3.70769586e-21 -9.33463354e-21 -9.33463354e-21 -1.18644068e-05\n",
-      "  2.47390008e-21  3.71885901e-21  3.71885901e-21 -1.18644068e-05\n",
-      "  1.66145271e-21  3.29520513e-21  3.29520513e-21 -1.18644068e-05\n",
-      " -7.11383140e-22  8.72945324e-21  8.72945324e-21 -1.18644068e-05\n",
-      "  2.39533684e-21  1.80496093e-20  1.80496093e-20 -1.18644068e-05\n",
-      "  7.92432304e-21  2.74367194e-20  2.74367194e-20 -1.18644068e-05\n",
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-      " -2.88040225e-21 -1.40830871e-20 -1.40830871e-20 -1.18644068e-05\n",
-      "  3.27911170e-21 -4.52620322e-21 -4.52620322e-21 -1.18644068e-05\n",
-      " -3.70769586e-21 -8.33904750e-21 -8.33904750e-21 -1.18644068e-05\n",
-      " -1.71652379e-21 -5.89495002e-21 -5.89495002e-21 -1.18644068e-05\n",
-      "  1.66145271e-21  1.70057798e-21  1.70057798e-21 -1.18644068e-05\n",
-      " -7.16131534e-21 -9.99881917e-21 -9.99881917e-21 -1.18644068e-05\n",
-      "  2.39533684e-21  1.68558245e-20  1.68558245e-20 -1.18644068e-05\n",
-      "  2.38457411e-21  1.59969013e-20  1.59969013e-20 -1.18644068e-05\n",
-      " -1.50865296e-21  1.04130980e-20  1.04130980e-20 -1.18644068e-05\n",
-      "  2.71927051e-21  1.50064301e-20  1.50064301e-20 -1.18644068e-05\n",
-      "  3.27911170e-21 -1.89885310e-21 -1.89885310e-21 -1.18644068e-05\n",
-      "  3.67202098e-22  3.75784029e-21  3.75784029e-21 -1.18644068e-05\n",
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-      " -6.35142335e-21 -7.59109396e-21 -7.59109396e-21 -1.18644068e-05\n",
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-      " -2.82993249e-21 -4.00514001e-22 -4.00514001e-22 -1.18644068e-05\n",
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-      " -8.86743645e-21 -1.27100955e-20 -1.27100955e-20 -1.18644068e-05\n",
-      " -5.92317113e-21 -3.82416319e-22 -3.82416319e-22 -1.18644068e-05\n",
-      " -4.16810085e-21  7.21035706e-21  7.21035706e-21 -1.18644068e-05\n",
-      " -1.19992044e-20 -1.36722986e-20 -1.36722986e-20 -1.18644068e-05\n",
-      " -2.16383758e-20 -2.51633912e-20 -2.51633912e-20 -1.18644068e-05\n",
-      " -3.47550174e-21  2.79585695e-20  2.79585695e-20 -1.18644068e-05\n",
-      " -4.91703671e-21  2.74194080e-20  2.74194080e-20 -1.18644068e-05\n",
-      " -2.82993249e-21  2.89323161e-21  2.89323161e-21 -1.18644068e-05\n",
-      "  1.84814580e-20 -5.24257230e-21 -5.24257230e-21 -1.18644068e-05\n",
-      " -8.86743645e-21 -3.04374876e-22 -3.04374876e-22 -1.18644068e-05\n",
-      "  1.10590247e-20 -1.14773621e-20 -1.14773621e-20 -1.18644068e-05]\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[ 3.78449394e-21 -2.09398551e-22 -2.09398551e-22 -1.18644068e-05\n",
-      "  3.36569684e-21  7.12037038e-22  7.12037038e-22 -1.18644068e-05\n",
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-      " -6.78549958e-21 -1.67334542e-22 -1.67334542e-22 -1.18644068e-05\n",
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-      " -4.35201246e-21  1.90116581e-20  1.90116581e-20 -1.18644068e-05\n",
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-      "  3.21171507e-21  5.37210489e-21  5.37210489e-21 -1.18644068e-05\n",
-      " -9.14382386e-21 -1.35231110e-20 -1.35231110e-20 -1.18644068e-05\n",
-      " -6.78549958e-21 -3.15008684e-22 -3.15008684e-22 -1.18644068e-05\n",
-      " -7.08084786e-21  8.30299215e-21  8.30299215e-21 -1.18644068e-05\n",
-      " -1.24885890e-20 -1.35648831e-20 -1.35648831e-20 -1.18644068e-05\n",
-      " -2.20476876e-20 -2.56423248e-20 -2.56423248e-20 -1.18644068e-05\n",
-      " -3.91452920e-21  2.79233279e-20  2.79233279e-20 -1.18644068e-05\n",
-      " -5.64139869e-21  2.86194311e-20  2.86194311e-20 -1.18644068e-05\n",
-      " -2.87456900e-21  4.66777920e-21  4.66777920e-21 -1.18644068e-05\n",
-      "  1.88656356e-20 -5.86765555e-21 -5.86765555e-21 -1.18644068e-05\n",
-      " -9.14382386e-21 -1.22916888e-21 -1.22916888e-21 -1.18644068e-05\n",
-      "  1.19395992e-20 -1.19315486e-20 -1.19315486e-20 -1.18644068e-05]"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "[ 3.85053890e-21 -1.64093033e-22 -1.64093033e-22 -1.18644068e-05\n",
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-      "  2.42503048e-21  2.54297060e-21  2.54297060e-21 -1.18644068e-05\n",
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-      " -1.17435081e-20 -8.42604192e-21 -8.42604192e-21 -1.18644068e-05\n",
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-      " -3.21612758e-21  3.46341058e-20  3.46341058e-20 -1.18644068e-05\n",
-      " -4.22764800e-21  1.04108077e-20  1.04108077e-20 -1.18644068e-05\n",
-      " -2.79477680e-21 -1.45472579e-21 -1.45472579e-21 -1.18644068e-05\n",
-      "  2.42503048e-21  3.91848748e-21  3.91848748e-21 -1.18644068e-05\n",
-      " -8.77346793e-21 -1.23205274e-20 -1.23205274e-20 -1.18644068e-05\n",
-      " -5.46659730e-21 -4.35499692e-22 -4.35499692e-22 -1.18644068e-05\n",
-      " -2.76531516e-21  6.68418834e-21  6.68418834e-21 -1.18644068e-05\n",
-      " -1.17435081e-20 -1.36932341e-20 -1.36932341e-20 -1.18644068e-05\n",
-      " -2.13183192e-20 -2.49534171e-20 -2.49534171e-20 -1.18644068e-05\n",
-      " -3.21612758e-21  2.80233137e-20  2.80233137e-20 -1.18644068e-05\n",
-      " -4.48632619e-21  2.68722727e-20  2.68722727e-20 -1.18644068e-05\n",
-      " -2.79477680e-21  2.03663187e-21  2.03663187e-21 -1.18644068e-05\n",
-      "  1.83511462e-20 -4.96404832e-21 -4.96404832e-21 -1.18644068e-05\n",
-      " -8.77346793e-21  1.83639807e-22  1.83639807e-22 -1.18644068e-05\n",
-      "  1.06850224e-20 -1.13308608e-20 -1.13308608e-20 -1.18644068e-05]\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
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-      " -4.50478059e-21  2.06336763e-20  2.06336763e-20 -1.18644068e-05\n",
-      "  2.26561743e-21  1.35433058e-20  1.35433058e-20 -1.18644068e-05\n",
-      " -3.29302297e-21 -3.80756320e-22 -3.80756320e-22 -1.18644068e-05\n",
-      "  8.02453669e-23 -4.30649910e-21 -4.30649910e-21 -1.18644068e-05\n",
-      "  5.66474376e-21 -3.04158517e-21 -3.04158517e-21 -1.18644068e-05\n",
-      " -1.03165799e-20 -1.64510188e-20 -1.64510188e-20 -1.18644068e-05\n",
-      " -9.33765224e-21 -2.37217881e-22 -2.37217881e-22 -1.18644068e-05\n",
-      " -6.51410357e-21 -3.37322739e-21 -3.37322739e-21 -1.18644068e-05\n",
-      " -1.37649328e-20 -1.64510775e-20 -1.64510775e-20 -1.18644068e-05\n",
-      " -4.50478059e-21  2.22378587e-20  2.22378587e-20 -1.18644068e-05\n",
-      " -4.34215588e-21  1.36861581e-20  1.36861581e-20 -1.18644068e-05\n",
-      " -3.29302297e-21  4.23205845e-21  4.23205845e-21 -1.18644068e-05\n",
-      " -5.18585245e-21  5.17853204e-21  5.17853204e-21 -1.18644068e-05\n",
-      "  5.66474376e-21  3.10705519e-21  3.10705519e-21 -1.18644068e-05\n",
-      "  3.17775453e-21  4.11350826e-21  4.11350826e-21 -1.18644068e-05\n",
-      " -9.33765224e-21  1.06917731e-21  1.06917731e-21 -1.18644068e-05\n",
-      " -6.72486186e-21 -2.37217906e-22 -2.37217906e-22 -1.18644068e-05\n",
-      " -1.37649328e-20 -1.49789947e-20 -1.49789947e-20 -1.18644068e-05\n",
-      " -1.24546299e-20 -7.40115211e-21 -7.40115211e-21 -1.18644068e-05\n",
-      " -4.34215588e-21  1.90146926e-20  1.90146926e-20 -1.18644068e-05\n",
-      " -3.88008164e-21  3.56056467e-20  3.56056467e-20 -1.18644068e-05\n",
-      " -5.18585245e-21  1.15837305e-20  1.15837305e-20 -1.18644068e-05\n",
-      " -2.86989997e-21  1.59965669e-21  1.59965669e-21 -1.18644068e-05\n",
-      "  3.17775453e-21  5.31057223e-21  5.31057223e-21 -1.18644068e-05\n",
-      " -9.13134387e-21 -1.34713724e-20 -1.34713724e-20 -1.18644068e-05\n",
-      " -6.72486186e-21 -3.22058703e-22 -3.22058703e-22 -1.18644068e-05\n",
-      " -6.89454346e-21  8.23311152e-21  8.23311152e-21 -1.18644068e-05\n",
-      " -1.24546299e-20 -1.35676636e-20 -1.35676636e-20 -1.18644068e-05\n",
-      " -2.20051808e-20 -2.56144381e-20 -2.56144381e-20 -1.18644068e-05\n",
-      " -3.88008164e-21  2.79319266e-20  2.79319266e-20 -1.18644068e-05\n",
-      " -5.58419590e-21  2.85467659e-20  2.85467659e-20 -1.18644068e-05\n",
-      " -2.86989997e-21  4.55401393e-21  4.55401393e-21 -1.18644068e-05\n",
-      "  1.88483288e-20 -5.83066469e-21 -5.83066469e-21 -1.18644068e-05\n",
-      " -9.13134387e-21 -1.16435550e-21 -1.16435550e-21 -1.18644068e-05\n",
-      "  1.18899279e-20 -1.19120917e-20 -1.19120917e-20 -1.18644068e-05]\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n",
-      "/usr/lib/python2.7/dist-packages/dolfin/cpp/la.py:1349: DeprecationWarning: GenericVector.array() is being deprecated, use GenericVector.get_local()\n",
-      "  \"use GenericVector.get_local()\", DeprecationWarning)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[ 3.84385300e-21 -1.67105945e-22 -1.67105945e-22 -1.18644068e-05\n",
-      "  3.50964111e-21  8.21616740e-22  8.21616740e-22 -1.18644068e-05\n",
-      "  5.15321674e-21 -5.75416222e-22 -5.75416222e-22 -1.18644068e-05\n",
-      "  4.33659619e-21 -2.66581085e-21 -2.66581085e-21 -1.18644068e-05\n",
-      "  4.34042730e-21 -2.81321054e-22 -2.81321054e-22 -1.18644068e-05\n",
-      "  4.92861763e-21  2.79577143e-21  2.79577143e-21 -1.18644068e-05\n",
-      " -4.42880606e-22  1.32649879e-22  1.32649879e-22 -1.18644068e-05\n",
-      "  3.85061260e-22  5.60553244e-21  5.60553244e-21 -1.18644068e-05\n",
-      " -2.82291240e-23 -2.82291240e-23 -2.82291240e-23 -1.18644068e-05\n",
-      " -3.49987129e-22  1.24190404e-22  1.24190404e-22 -1.18644068e-05\n",
-      "  3.50964111e-21  1.16495300e-21  1.16495300e-21 -1.18644068e-05\n",
-      "  3.78550526e-21  1.63476142e-21  1.63476142e-21 -1.18644068e-05\n",
-      "  4.33659619e-21 -2.32244299e-21 -2.32244299e-21 -1.18644068e-05\n",
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