.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/3_point_bending.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_3_point_bending.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_3_point_bending.py:


Three point bending experiment with a linear elastic constitutive model
=======================================================================

This example demonstrates how to set up a three-point bending beam and access
the displacement data of a specific point using a linear elastic constitutive model.

.. GENERATED FROM PYTHON SOURCE LINES 9-10

To run this example, the following functions need to be imported:

.. GENERATED FROM PYTHON SOURCE LINES 10-16

.. code-block:: Python


    from fenicsxconcrete.experimental_setup.simple_beam import SimpleBeam
    from fenicsxconcrete.finite_element_problem.linear_elasticity import LinearElasticity
    from fenicsxconcrete.sensor_definition.displacement_sensor import DisplacementSensor
    from fenicsxconcrete.util import ureg








.. GENERATED FROM PYTHON SOURCE LINES 17-22

Setting up the Beam
-------------------
First, initialize the setup for the simply supported beam with a distributed load.
Define the geometry, the mesh, and the load. Not defined parameters are set to default values (from class function default_parameters).
Note, all parameters must be pint objects:

.. GENERATED FROM PYTHON SOURCE LINES 22-35

.. code-block:: Python


    parameters = {}
    parameters["length"] = 10 * ureg("m")
    parameters["height"] = 0.5 * ureg("m")
    parameters["width"] = 0.3 * ureg("m")
    parameters["dim"] = 3 * ureg("")
    parameters["num_elements_length"] = 10 * ureg("")
    parameters["num_elements_height"] = 3 * ureg("")
    parameters["num_elements_width"] = 3 * ureg("")
    parameters["load"] = 200 * ureg("kN/m^2")

    beam_setup = SimpleBeam(parameters)








.. GENERATED FROM PYTHON SOURCE LINES 36-40

Initializing the Linear Elasticity Problem
------------------------------------------
Second, initialize the linear elastic problem using the setup object and further material parameters:
Again not defined parameters are set to default values (from class function default_parameters).

.. GENERATED FROM PYTHON SOURCE LINES 40-47

.. code-block:: Python


    parameters["rho"] = 7750 * ureg("kg/m^3")
    parameters["E"] = 210e9 * ureg("N/m^2")
    parameters["nu"] = 0.28 * ureg("")

    problem = LinearElasticity(beam_setup, parameters)








.. GENERATED FROM PYTHON SOURCE LINES 48-51

Setting Up the Sensor
---------------------
Third, set up a sensor and add it to the problem to access results of the FEM simulation:

.. GENERATED FROM PYTHON SOURCE LINES 51-57

.. code-block:: Python


    sensor_location = [parameters["length"].magnitude / 2, parameters["width"].magnitude / 2, 0.0]
    sensor = DisplacementSensor(sensor_location)

    problem.add_sensor(sensor)








.. GENERATED FROM PYTHON SOURCE LINES 58-61

Solving the Problem and Accessing the Results
---------------------------------------------
Finally, solve the problem and access the sensor data:

.. GENERATED FROM PYTHON SOURCE LINES 61-66

.. code-block:: Python

    problem.solve()

    displacement_data = problem.sensors["DisplacementSensor"].data[0]

    print(f"The displacement at the center of the beam in loading direction is {displacement_data[2]:.2f} {sensor.units}.")




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

 .. code-block:: none

    The displacement at the center of the beam in loading direction is -0.01 meter.





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

   **Total running time of the script:** (0 minutes 0.953 seconds)


.. _sphx_glr_download_auto_examples_3_point_bending.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: 3_point_bending.ipynb <3_point_bending.ipynb>`

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

      :download:`Download Python source code: 3_point_bending.py <3_point_bending.py>`

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

      :download:`Download zipped: 3_point_bending.zip <3_point_bending.zip>`