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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_topology_optimization_plot_topology_optimization_L_shape.py>`
        to download the full example code.

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

.. _sphx_glr_examples_topology_optimization_plot_topology_optimization_L_shape.py:


Solve a 2D L-shape topology optimization problem
================================================

.. GENERATED FROM PYTHON SOURCE LINES 23-31

.. code-block:: Python


    from __future__ import annotations

    from gemseo import create_scenario
    from gemseo.problems.topology_optimization.topopt_initialize import (
        initialize_design_space_and_discipline_to,
    )








.. GENERATED FROM PYTHON SOURCE LINES 32-35

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

.. GENERATED FROM PYTHON SOURCE LINES 35-37

.. code-block:: Python

    volume_fraction = 0.3








.. GENERATED FROM PYTHON SOURCE LINES 38-39

Define the problem type:

.. GENERATED FROM PYTHON SOURCE LINES 39-41

.. code-block:: Python

    problem_name = "L-Shape"








.. GENERATED FROM PYTHON SOURCE LINES 42-43

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

.. GENERATED FROM PYTHON SOURCE LINES 43-46

.. code-block:: Python

    n_x = 25
    n_y = 25








.. GENERATED FROM PYTHON SOURCE LINES 47-48

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

.. GENERATED FROM PYTHON SOURCE LINES 48-51

.. code-block:: Python

    e0 = 1
    nu = 0.3








.. GENERATED FROM PYTHON SOURCE LINES 52-53

Define the penalty of the SIMP approach:

.. GENERATED FROM PYTHON SOURCE LINES 53-55

.. code-block:: Python

    penalty = 3








.. GENERATED FROM PYTHON SOURCE LINES 56-57

Define the minimum member size in the solution:

.. GENERATED FROM PYTHON SOURCE LINES 57-58

.. code-block:: Python

    min_member_size = 1.5







.. GENERATED FROM PYTHON SOURCE LINES 59-60

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

.. GENERATED FROM PYTHON SOURCE LINES 60-72

.. code-block:: Python



    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_member_size,
        vf0=volume_fraction,
    )







.. GENERATED FROM PYTHON SOURCE LINES 73-76

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

.. GENERATED FROM PYTHON SOURCE LINES 76-82

.. code-block:: Python

    scenario = create_scenario(
        disciplines,
        "compliance",
        design_space,
        formulation_name="DisciplinaryOpt",
    )







.. GENERATED FROM PYTHON SOURCE LINES 83-84

Add the volume fraction constraint to the scenario:

.. GENERATED FROM PYTHON SOURCE LINES 84-88

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 89-90

Generate the XDSM

.. GENERATED FROM PYTHON SOURCE LINES 90-92

.. code-block:: Python

    scenario.xdsmize(save_html=False)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">

        <script type="text/javascript">
            document.addEventListener('DOMContentLoaded', () => {
              const mdo = {
      "root": {
        "nodes": [
          {
            "id": "Opt",
            "name": "Optimizer",
            "type": "optimization",
            "status": "DONE"
          },
          {
            "id": "Dis1",
            "name": "DensityFilter",
            "type": "analysis",
            "status": "DONE"
          },
          {
            "id": "Dis2",
            "name": "MaterialModelInterpolation",
            "type": "analysis",
            "status": "DONE"
          },
          {
            "id": "Dis3",
            "name": "FiniteElementAnalysis",
            "type": "analysis",
            "status": "DONE"
          },
          {
            "id": "Dis4",
            "name": "VolumeFraction",
            "type": "analysis",
            "status": "DONE"
          }
        ],
        "edges": [
          {
            "from": "_U_",
            "to": "Opt",
            "name": "x^(0)"
          },
          {
            "from": "Opt",
            "to": "_U_",
            "name": "compliance^*, [volume fraction-0.3]^*"
          },
          {
            "from": "Opt",
            "to": "Dis1",
            "name": "x"
          },
          {
            "from": "Dis3",
            "to": "Opt",
            "name": "compliance"
          },
          {
            "from": "Dis4",
            "to": "Opt",
            "name": "volume fraction"
          },
          {
            "from": "Dis1",
            "to": "_U_",
            "name": "xPhys^*"
          },
          {
            "from": "Dis2",
            "to": "_U_",
            "name": "rho^*, E^*"
          },
          {
            "from": "Dis3",
            "to": "Opt",
            "name": "compliance"
          },
          {
            "from": "Dis4",
            "to": "Opt",
            "name": "volume fraction"
          },
          {
            "from": "Dis1",
            "to": "Dis2",
            "name": "xPhys"
          },
          {
            "from": "Dis2",
            "to": "Dis3",
            "name": "E"
          },
          {
            "from": "Dis2",
            "to": "Dis4",
            "name": "rho"
          }
        ],
        "workflow": [
          "_U_",
          [
            "Opt",
            [
              "Dis1",
              "Dis2",
              "Dis3",
              "Dis4"
            ]
          ]
        ],
        "optpb": ""
      }
    };
              const config = {
                labelizer: {
                    ellipsis: 5,
                    subSupScript: false,
                    showLinkNbOnly: false,
                },
                layout: {
                    origin: { x: 50, y: 20 },
                    cellsize: { w: 150, h: 50 },
                    padding: 10,
                },
                withDefaultDriver: true,
                withTitleTooltip: true,
              };
              xdsmjs.XDSMjs(config).createXdsm(mdo);
            });
        </script>
        <div class='xdsm-toolbar'></div><div class='xdsm2'></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 93-94

Execute the scenario

.. GENERATED FROM PYTHON SOURCE LINES 94-96

.. code-block:: Python

    scenario.execute(algo_name="NLOPT_MMA", max_iter=200)





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

 .. code-block:: none

        INFO - 16:24:28: *** Start MDOScenario execution ***
        INFO - 16:24:28: MDOScenario
        INFO - 16:24:28:    Disciplines: DensityFilter FiniteElementAnalysis MaterialModelInterpolation VolumeFraction
        INFO - 16:24:28:    MDO formulation: DisciplinaryOpt
        INFO - 16:24:28: Optimization problem:
        INFO - 16:24:28:    minimize compliance(x)
        INFO - 16:24:28:    with respect to x
        INFO - 16:24:28:    under the inequality constraints
        INFO - 16:24:28:       volume fraction(x) <= 0.3
        INFO - 16:24:28: Solving optimization problem with algorithm NLOPT_MMA:
        INFO - 16:24:28:      1%|          | 2/200 [00:00<00:02, 82.23 it/sec, feas=True, obj=2.23e+3]
        INFO - 16:24:28:      2%|▏         | 3/200 [00:00<00:02, 90.21 it/sec, feas=True, obj=1.96e+3]
        INFO - 16:24:28:      2%|▏         | 4/200 [00:00<00:02, 95.05 it/sec, feas=True, obj=1.75e+3]
        INFO - 16:24:28:      2%|▎         | 5/200 [00:00<00:02, 97.12 it/sec, feas=True, obj=1.57e+3]
        INFO - 16:24:28:      3%|▎         | 6/200 [00:00<00:01, 98.07 it/sec, feas=True, obj=1.2e+3]
        INFO - 16:24:28:      4%|▎         | 7/200 [00:00<00:01, 98.34 it/sec, feas=True, obj=963]
        INFO - 16:24:28:      4%|▍         | 8/200 [00:00<00:01, 98.82 it/sec, feas=True, obj=624]
        INFO - 16:24:28:      4%|▍         | 9/200 [00:00<00:01, 99.18 it/sec, feas=True, obj=497]
        INFO - 16:24:28:      5%|▌         | 10/200 [00:00<00:01, 99.71 it/sec, feas=True, obj=395]
        INFO - 16:24:28:      6%|▌         | 11/200 [00:00<00:01, 99.59 it/sec, feas=True, obj=306]
        INFO - 16:24:28:      6%|▌         | 12/200 [00:00<00:01, 100.22 it/sec, feas=True, obj=251]
        INFO - 16:24:28:      6%|▋         | 13/200 [00:00<00:01, 100.78 it/sec, feas=True, obj=225]
        INFO - 16:24:28:      7%|▋         | 14/200 [00:00<00:01, 101.31 it/sec, feas=True, obj=209]
        INFO - 16:24:28:      8%|▊         | 15/200 [00:00<00:01, 101.95 it/sec, feas=True, obj=201]
        INFO - 16:24:28:      8%|▊         | 16/200 [00:00<00:01, 102.49 it/sec, feas=True, obj=195]
        INFO - 16:24:28:      8%|▊         | 17/200 [00:00<00:01, 102.94 it/sec, feas=True, obj=190]
        INFO - 16:24:28:      9%|▉         | 18/200 [00:00<00:01, 103.63 it/sec, feas=True, obj=186]
        INFO - 16:24:28:     10%|▉         | 19/200 [00:00<00:01, 104.24 it/sec, feas=True, obj=182]
        INFO - 16:24:28:     10%|█         | 20/200 [00:00<00:01, 104.84 it/sec, feas=True, obj=178]
        INFO - 16:24:28:     10%|█         | 21/200 [00:00<00:01, 105.18 it/sec, feas=True, obj=174]
        INFO - 16:24:28:     11%|█         | 22/200 [00:00<00:01, 105.62 it/sec, feas=True, obj=169]
        INFO - 16:24:28:     12%|█▏        | 23/200 [00:00<00:01, 106.03 it/sec, feas=True, obj=164]
        INFO - 16:24:28:     12%|█▏        | 24/200 [00:00<00:01, 106.55 it/sec, feas=True, obj=161]
        INFO - 16:24:28:     12%|█▎        | 25/200 [00:00<00:01, 106.92 it/sec, feas=True, obj=159]
        INFO - 16:24:28:     13%|█▎        | 26/200 [00:00<00:01, 107.38 it/sec, feas=True, obj=157]
        INFO - 16:24:28:     14%|█▎        | 27/200 [00:00<00:01, 107.88 it/sec, feas=True, obj=156]
        INFO - 16:24:28:     14%|█▍        | 28/200 [00:00<00:01, 108.25 it/sec, feas=True, obj=155]
        INFO - 16:24:28:     14%|█▍        | 29/200 [00:00<00:01, 108.43 it/sec, feas=True, obj=154]
        INFO - 16:24:28:     15%|█▌        | 30/200 [00:00<00:01, 108.80 it/sec, feas=True, obj=154]
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        INFO - 16:24:28:     16%|█▋        | 33/200 [00:00<00:01, 109.77 it/sec, feas=True, obj=152]
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        INFO - 16:24:28:     20%|██        | 40/200 [00:00<00:01, 112.03 it/sec, feas=True, obj=152]
        INFO - 16:24:28:     20%|██        | 41/200 [00:00<00:01, 112.36 it/sec, feas=True, obj=152]
        INFO - 16:24:28:     21%|██        | 42/200 [00:00<00:01, 112.68 it/sec, feas=True, obj=152]
        INFO - 16:24:28:     22%|██▏       | 43/200 [00:00<00:01, 112.95 it/sec, feas=True, obj=152]
        INFO - 16:24:28:     22%|██▏       | 44/200 [00:00<00:01, 113.21 it/sec, feas=True, obj=152]
        INFO - 16:24:28:     22%|██▎       | 45/200 [00:00<00:01, 113.53 it/sec, feas=True, obj=152]
        INFO - 16:24:28:     23%|██▎       | 46/200 [00:00<00:01, 113.76 it/sec, feas=True, obj=152]
        INFO - 16:24:28:     24%|██▎       | 47/200 [00:00<00:01, 114.15 it/sec, feas=True, obj=152]
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        INFO - 16:24:28:     31%|███       | 62/200 [00:00<00:01, 116.72 it/sec, feas=True, obj=152]
        INFO - 16:24:28:     32%|███▏      | 63/200 [00:00<00:01, 116.81 it/sec, feas=True, obj=152]
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        INFO - 16:24:28:     34%|███▎      | 67/200 [00:00<00:01, 117.38 it/sec, feas=True, obj=152]
        INFO - 16:24:28:     34%|███▍      | 68/200 [00:00<00:01, 117.51 it/sec, feas=True, obj=152]
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        INFO - 16:24:28:     40%|████      | 80/200 [00:00<00:01, 118.96 it/sec, feas=True, obj=152]
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        INFO - 16:24:28:     44%|████▍     | 89/200 [00:00<00:00, 120.11 it/sec, feas=True, obj=152]
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        INFO - 16:24:28:     46%|████▌     | 91/200 [00:00<00:00, 120.39 it/sec, feas=True, obj=152]
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        INFO - 16:24:29:     57%|█████▊    | 115/200 [00:00<00:00, 123.11 it/sec, feas=True, obj=152]
        INFO - 16:24:29:     58%|█████▊    | 116/200 [00:00<00:00, 123.21 it/sec, feas=True, obj=152]
        INFO - 16:24:29:     58%|█████▊    | 117/200 [00:00<00:00, 123.31 it/sec, feas=True, obj=152]
        INFO - 16:24:29:     59%|█████▉    | 118/200 [00:00<00:00, 123.41 it/sec, feas=True, obj=152]
        INFO - 16:24:29:     60%|█████▉    | 119/200 [00:00<00:00, 123.52 it/sec, feas=True, obj=152]
        INFO - 16:24:29:     60%|██████    | 120/200 [00:00<00:00, 123.62 it/sec, feas=True, obj=152]
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        INFO - 16:24:29:     63%|██████▎   | 126/200 [00:01<00:00, 124.15 it/sec, feas=True, obj=152]
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        INFO - 16:24:29:     68%|██████▊   | 135/200 [00:01<00:00, 124.81 it/sec, feas=True, obj=152]
        INFO - 16:24:29:     68%|██████▊   | 136/200 [00:01<00:00, 124.86 it/sec, feas=True, obj=152]
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        INFO - 16:24:29:     69%|██████▉   | 138/200 [00:01<00:00, 125.00 it/sec, feas=True, obj=152]
        INFO - 16:24:29:     70%|██████▉   | 139/200 [00:01<00:00, 125.07 it/sec, feas=True, obj=152]
        INFO - 16:24:29:     70%|███████   | 140/200 [00:01<00:00, 125.14 it/sec, feas=True, obj=152]
        INFO - 16:24:29:     70%|███████   | 141/200 [00:01<00:00, 125.21 it/sec, feas=True, obj=152]
        INFO - 16:24:29:     71%|███████   | 142/200 [00:01<00:00, 125.28 it/sec, feas=True, obj=152]
        INFO - 16:24:29:     72%|███████▏  | 143/200 [00:01<00:00, 125.36 it/sec, feas=True, obj=152]
        INFO - 16:24:29:     72%|███████▏  | 144/200 [00:01<00:00, 125.44 it/sec, feas=True, obj=152]
        INFO - 16:24:29:     72%|███████▎  | 145/200 [00:01<00:00, 125.50 it/sec, feas=True, obj=152]
        INFO - 16:24:29:     73%|███████▎  | 146/200 [00:01<00:00, 125.57 it/sec, feas=True, obj=152]
        INFO - 16:24:29:     74%|███████▎  | 147/200 [00:01<00:00, 125.65 it/sec, feas=True, obj=152]
        INFO - 16:24:29: Optimization result:
        INFO - 16:24:29:    Optimizer info:
        INFO - 16:24:29:       Status: None
        INFO - 16:24:29:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
        INFO - 16:24:29:    Solution:
        INFO - 16:24:29:       The solution is feasible.
        INFO - 16:24:29:       Objective: 151.62879223124227
        INFO - 16:24:29:       Standardized constraints:
        INFO - 16:24:29:          [volume fraction-0.3] = 1.0261640776554337e-06
        INFO - 16:24:29: *** End MDOScenario execution ***




.. GENERATED FROM PYTHON SOURCE LINES 97-100

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

.. GENERATED FROM PYTHON SOURCE LINES 100-104

.. code-block:: Python

    scenario.post_process(
        post_name="BasicHistory", variable_names=["compliance"], show=True, save=False
    )




.. image-sg:: /examples/topology_optimization/images/sphx_glr_plot_topology_optimization_L_shape_001.png
   :alt: History plot
   :srcset: /examples/topology_optimization/images/sphx_glr_plot_topology_optimization_L_shape_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.basic_history.BasicHistory object at 0x72a4d8a60ec0>



.. GENERATED FROM PYTHON SOURCE LINES 105-106

Plot the solution

.. GENERATED FROM PYTHON SOURCE LINES 106-107

.. code-block:: Python

    scenario.post_process(post_name="TopologyView", n_x=n_x, n_y=n_y, show=True, save=False)



.. image-sg:: /examples/topology_optimization/images/sphx_glr_plot_topology_optimization_L_shape_002.png
   :alt: plot topology optimization L shape
   :srcset: /examples/topology_optimization/images/sphx_glr_plot_topology_optimization_L_shape_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.topology_view.TopologyView object at 0x72a4e03d1d60>




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

   **Total running time of the script:** (0 minutes 1.552 seconds)


.. _sphx_glr_download_examples_topology_optimization_plot_topology_optimization_L_shape.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_topology_optimization_L_shape.zip <plot_topology_optimization_L_shape.zip>`


.. only:: html

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

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