.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/topology_optimization/topology_optimization_short_cantilever.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_examples_topology_optimization_topology_optimization_short_cantilever.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_topology_optimization_topology_optimization_short_cantilever.py:


Solve a 2D short cantilever topology optimization problem
=========================================================

.. GENERATED FROM PYTHON SOURCE LINES 23-32

.. code-block:: default

    import matplotlib.pyplot as plt
    from gemseo.api import configure_logger
    from gemseo.api import create_scenario
    from gemseo.problems.topo_opt.topopt_initialize import (
        initialize_design_space_and_discipline_to,
    )
    from matplotlib import colors

    configure_logger()




.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 33-36

Setup the topology optimization problem
---------------------------------------
Define the target volume fraction:

.. GENERATED FROM PYTHON SOURCE LINES 36-38

.. code-block:: default

    volume_fraction = 0.3








.. GENERATED FROM PYTHON SOURCE LINES 39-40

Define the problem type:

.. GENERATED FROM PYTHON SOURCE LINES 40-42

.. code-block:: default

    problem_name = "Short_Cantilever"








.. GENERATED FROM PYTHON SOURCE LINES 43-44

Define the number of elements in the x- and y- directions:

.. GENERATED FROM PYTHON SOURCE LINES 44-47

.. code-block:: default

    n_x = 50
    n_y = 25








.. GENERATED FROM PYTHON SOURCE LINES 48-49

Define the full material Young's modulus and Poisson's ratio:

.. GENERATED FROM PYTHON SOURCE LINES 49-52

.. code-block:: default

    e0 = 1
    nu = 0.3








.. GENERATED FROM PYTHON SOURCE LINES 53-54

Define the penalty of the SIMP approach:

.. GENERATED FROM PYTHON SOURCE LINES 54-56

.. code-block:: default

    penalty = 3








.. GENERATED FROM PYTHON SOURCE LINES 57-58

Define the minimum member size in the solution:

.. GENERATED FROM PYTHON SOURCE LINES 58-60

.. code-block:: default

    min_memeber_size = 1.5








.. GENERATED FROM PYTHON SOURCE LINES 61-62

Instantiate the :class:`.DesignSpace` and the disciplines:

.. GENERATED FROM PYTHON SOURCE LINES 62-74

.. code-block:: default


    design_space, disciplines = initialize_design_space_and_discipline_to(
        problem=problem_name,
        n_x=n_x,
        n_y=n_y,
        e0=e0,
        nu=nu,
        penalty=penalty,
        min_member_size=min_memeber_size,
        vf0=volume_fraction,
    )








.. GENERATED FROM PYTHON SOURCE LINES 75-78

Solve the topology optimization problem
---------------------------------------
Generate a :class:`.MDOScenario`:

.. GENERATED FROM PYTHON SOURCE LINES 78-85

.. code-block:: default

    scenario = create_scenario(
        disciplines,
        formulation="DisciplinaryOpt",
        objective_name="compliance",
        design_space=design_space,
    )








.. GENERATED FROM PYTHON SOURCE LINES 86-87

Add the volume fraction constraint to the scenario:

.. GENERATED FROM PYTHON SOURCE LINES 87-89

.. code-block:: default

    scenario.add_constraint("volume fraction", "ineq", value=volume_fraction)








.. GENERATED FROM PYTHON SOURCE LINES 90-91

Generate the XDSM:

.. GENERATED FROM PYTHON SOURCE LINES 91-93

.. code-block:: default

    scenario.xdsmize()





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

        INFO - 10:03:34: Generating HTML XDSM file in : xdsm.html




.. GENERATED FROM PYTHON SOURCE LINES 94-95

Execute the scenario:

.. GENERATED FROM PYTHON SOURCE LINES 95-97

.. code-block:: default

    scenario.execute(input_data={"max_iter": 200, "algo": "NLOPT_MMA"})





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

        INFO - 10:03:34:  
        INFO - 10:03:34: *** Start MDOScenario execution ***
        INFO - 10:03:34: MDOScenario
        INFO - 10:03:34:    Disciplines: DensityFilter MaterialModelInterpolation FininiteElementAnalysis VolumeFraction
        INFO - 10:03:34:    MDO formulation: DisciplinaryOpt
        INFO - 10:03:34: Optimization problem:
        INFO - 10:03:34:    minimize compliance(x)
        INFO - 10:03:34:    with respect to x
        INFO - 10:03:34:    subject to constraints:
        INFO - 10:03:34:       volume fraction(x) <= 0.3
        INFO - 10:03:34: Solving optimization problem with algorithm NLOPT_MMA:
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        INFO - 10:03:50: Optimization result:
        INFO - 10:03:50:    Optimizer info:
        INFO - 10:03:50:       Status: None
        INFO - 10:03:50:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
        INFO - 10:03:50:       Number of calls to the objective function by the optimizer: 186
        INFO - 10:03:50:    Solution:
        INFO - 10:03:50:       The solution is feasible.
        INFO - 10:03:50:       Objective: 136.56131771172448
        INFO - 10:03:50:       Standardized constraints:
        INFO - 10:03:50:          volume fraction - 0.3 = -1.0460364907594055e-08
        INFO - 10:03:50: *** End MDOScenario execution (time: 0:00:15.619092) ***

    {'max_iter': 200, 'algo': 'NLOPT_MMA'}



.. GENERATED FROM PYTHON SOURCE LINES 98-101

Results
-------
Post-process the optimization history:

.. GENERATED FROM PYTHON SOURCE LINES 101-109

.. code-block:: default

    scenario.post_process(
        "BasicHistory",
        variable_names=["compliance"],
        save=True,
        show=False,
        file_name=problem_name + "_history.png",
    )





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none


    <gemseo.post.basic_history.BasicHistory object at 0x7fdbfb54deb0>



.. GENERATED FROM PYTHON SOURCE LINES 110-111

.. image:: /_images/topology_optimization/Short_Cantilever_history.png

.. GENERATED FROM PYTHON SOURCE LINES 114-115

Plot the solution:

.. GENERATED FROM PYTHON SOURCE LINES 115-128

.. code-block:: default

    plt.ion()  # Ensure that redrawing is possible
    fig, ax = plt.subplots()
    im = ax.imshow(
        -scenario.optimization_result.x_opt.reshape((n_x, n_y)).T,
        cmap="gray",
        interpolation="none",
        norm=colors.Normalize(vmin=-1, vmax=0),
    )
    fig.show()
    im.set_array(-scenario.optimization_result.x_opt.reshape((n_x, n_y)).T)
    fig.canvas.draw()
    plt.savefig(problem_name + "_solution.png")




.. image-sg:: /examples/topology_optimization/images/sphx_glr_topology_optimization_short_cantilever_001.png
   :alt: topology optimization short cantilever
   :srcset: /examples/topology_optimization/images/sphx_glr_topology_optimization_short_cantilever_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 129-130

.. image:: /_images/topology_optimization/Short_Cantilever_solution.png


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  16.226 seconds)


.. _sphx_glr_download_examples_topology_optimization_topology_optimization_short_cantilever.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download sphx-glr-download-python

     :download:`Download Python source code: topology_optimization_short_cantilever.py <topology_optimization_short_cantilever.py>`



  .. container:: sphx-glr-download sphx-glr-download-jupyter

     :download:`Download Jupyter notebook: topology_optimization_short_cantilever.ipynb <topology_optimization_short_cantilever.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_