.. 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_MBB.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_MBB.py>`
        to download the full example code

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

.. _sphx_glr_examples_topology_optimization_plot_topology_optimization_MBB.py:


Solve a 2D MBB topology optimization problem
============================================

.. GENERATED FROM PYTHON SOURCE LINES 23-33

.. code-block:: Python


    from __future__ import annotations

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

    configure_logger()




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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 34-36

Setup the topology optimization problem
---------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 38-39

Define the target volume fraction:

.. GENERATED FROM PYTHON SOURCE LINES 39-41

.. code-block:: Python

    volume_fraction = 0.3








.. GENERATED FROM PYTHON SOURCE LINES 42-43

Define the problem type:

.. GENERATED FROM PYTHON SOURCE LINES 43-45

.. code-block:: Python

    problem_name = "MBB"








.. GENERATED FROM PYTHON SOURCE LINES 46-47

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

.. GENERATED FROM PYTHON SOURCE LINES 47-50

.. code-block:: Python

    n_x = 50
    n_y = 25








.. GENERATED FROM PYTHON SOURCE LINES 51-52

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

.. GENERATED FROM PYTHON SOURCE LINES 52-55

.. code-block:: Python

    e0 = 1
    nu = 0.3








.. GENERATED FROM PYTHON SOURCE LINES 56-57

Define the penalty of the SIMP approach:

.. GENERATED FROM PYTHON SOURCE LINES 57-59

.. code-block:: Python

    penalty = 3








.. GENERATED FROM PYTHON SOURCE LINES 60-61

Define the minimum member size in the solution:

.. GENERATED FROM PYTHON SOURCE LINES 61-62

.. code-block:: Python

    min_member_size = 1.5







.. GENERATED FROM PYTHON SOURCE LINES 63-64

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

.. GENERATED FROM PYTHON SOURCE LINES 64-75

.. 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 76-79

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

.. GENERATED FROM PYTHON SOURCE LINES 79-86

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 87-88

Add the volume fraction constraint to the scenario:

.. GENERATED FROM PYTHON SOURCE LINES 88-92

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 93-94

Generate the XDSM

.. GENERATED FROM PYTHON SOURCE LINES 94-96

.. code-block:: Python

    scenario.xdsmize()






.. 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"
          },
          {
            "id": "Dis1",
            "name": "DensityFilter",
            "type": "analysis"
          },
          {
            "id": "Dis2",
            "name": "MaterialModelInterpolation",
            "type": "analysis"
          },
          {
            "id": "Dis3",
            "name": "FininiteElementAnalysis",
            "type": "analysis"
          },
          {
            "id": "Dis4",
            "name": "VolumeFraction",
            "type": "analysis"
          }
        ],
        "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": "Optimization problem:\n   minimize compliance(x)\n   with respect to x\n   subject to constraints:\n      volume fraction(x) <= 0.3"
      }
    };
              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 97-98

Execute the scenario

.. GENERATED FROM PYTHON SOURCE LINES 98-100

.. code-block:: Python

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





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

 .. code-block:: none

        INFO - 08:58:36:  
        INFO - 08:58:36: *** Start MDOScenario execution ***
        INFO - 08:58:36: MDOScenario
        INFO - 08:58:36:    Disciplines: DensityFilter FininiteElementAnalysis MaterialModelInterpolation VolumeFraction
        INFO - 08:58:36:    MDO formulation: DisciplinaryOpt
        INFO - 08:58:37: Optimization problem:
        INFO - 08:58:37:    minimize compliance(x)
        INFO - 08:58:37:    with respect to x
        INFO - 08:58:37:    subject to constraints:
        INFO - 08:58:37:       volume fraction(x) <= 0.3
        INFO - 08:58:37: Solving optimization problem with algorithm NLOPT_MMA:
        INFO - 08:58:37:      1%|          | 2/200 [00:00<00:11, 16.73 it/sec, obj=1.79e+3]
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        INFO - 08:58:43:     96%|█████████▋| 193/200 [00:06<00:00, 29.00 it/sec, obj=170]
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        INFO - 08:58:43: Optimization result:
        INFO - 08:58:43:    Optimizer info:
        INFO - 08:58:43:       Status: None
        INFO - 08:58:43:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
        INFO - 08:58:43:       Number of calls to the objective function by the optimizer: 201
        INFO - 08:58:43:    Solution:
        INFO - 08:58:43:       The solution is feasible.
        INFO - 08:58:43:       Objective: 169.89161468983534
        INFO - 08:58:43:       Standardized constraints:
        INFO - 08:58:43:          [volume fraction-0.3] = -4.312432086428508e-07
        INFO - 08:58:43: *** End MDOScenario execution (time: 0:00:06.884067) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 101-104

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

.. GENERATED FROM PYTHON SOURCE LINES 104-108

.. code-block:: Python

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




.. image-sg:: /examples/topology_optimization/images/sphx_glr_plot_topology_optimization_MBB_001.png
   :alt: History plot
   :srcset: /examples/topology_optimization/images/sphx_glr_plot_topology_optimization_MBB_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.basic_history.BasicHistory object at 0x7f1dad8c86d0>



.. GENERATED FROM PYTHON SOURCE LINES 109-110

Plot the solution

.. GENERATED FROM PYTHON SOURCE LINES 110-111

.. code-block:: Python

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



.. image-sg:: /examples/topology_optimization/images/sphx_glr_plot_topology_optimization_MBB_002.png
   :alt: plot topology optimization MBB
   :srcset: /examples/topology_optimization/images/sphx_glr_plot_topology_optimization_MBB_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.topology_view.TopologyView object at 0x7f1da71f3a60>




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

   **Total running time of the script:** (0 minutes 7.203 seconds)


.. _sphx_glr_download_examples_topology_optimization_plot_topology_optimization_MBB.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_MBB.ipynb <plot_topology_optimization_MBB.ipynb>`

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

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


.. only:: html

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

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