.. _linear_elasticity-shell10x_cantilever_interactive: linear_elasticity/shell10x_cantilever_interactive.py ==================================================== **Description** Bending of a long thin cantilever beam, imperative problem description. The example demonstrates use of the :class:`dw_shell10x ` term. Find displacements of the central plane :math:`\ul{u}`, and rotations :math:`\ul{\alpha}` such that: .. math:: \int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}, \ul{\beta}) e_{kl}(\ul{u}, \ul{\alpha}) = - \int_{\Gamma_{right}} \ul{v} \cdot \ul{f} \;, \quad \forall \ul{v} \;, where :math:`D_{ijkl}` is the isotropic elastic tensor, given using the Young's modulus :math:`E` and the Poisson's ratio :math:`\nu`. The variable ``u`` below holds both :math:`\ul{u}` and :math:`\ul{\alpha}` DOFs. For visualization, it is saved as two fields ``u_disp`` and ``u_rot``, corresponding to :math:`\ul{u}` and :math:`\ul{\alpha}`, respectively. The material, loading and discretization parameters can be given using command line options. Besides the default straight beam, two coordinate transformations can be applied (see the ``--transform`` option): - bend: the beam is bent - twist: the beam is twisted For the straight and bent beam a comparison with the analytical solution coming from the Euler-Bernoulli theory is shown. See also :ref:`linear_elasticity-shell10x_cantilever` example. Usage Examples -------------- See all options:: python3 sfepy/examples/linear_elasticity/shell10x_cantilever_interactive.py -h Apply the bending transformation to the beam domain coordinates, plot convergence curves w.r.t. number of elements:: python3 sfepy/examples/linear_elasticity/shell10x_cantilever_interactive.py output -t bend -p Apply the twisting transformation to the beam domain coordinates, change number of cells:: python3 sfepy/examples/linear_elasticity/shell10x_cantilever_interactive.py output -t twist -n 2,51,3 .. image:: /../doc/images/gallery/linear_elasticity-shell10x_cantilever_interactive-shell10x_cantilever_convergence_bent.png .. image:: /../doc/images/gallery/linear_elasticity-shell10x_cantilever_interactive.png :download:`source code ` .. literalinclude:: /../sfepy/examples/linear_elasticity/shell10x_cantilever_interactive.py