:orphan:

.. _ref_vm_examples:

===================
Verification Manual
===================
This section demonstrates a range of Mechanical APDL elements and capabilities
in straightforward problems which have “classical” or readily-obtainable
theoretical solutions using PyMAPDL.

These problems may then serve as the basis for additional validation and
qualification of Mechanical APDL capabilities for specific applications that
may be of interest.


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    <div class="sphx-glr-thumbnails">


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    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - S. Timoshenko, Strength of Materials, Part I, Elementary Theory and    Problems, ...">

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  .. image:: /verif-manual/images/thumb/sphx_glr_vm-001-statically_indeterminate_reaction_force_analysis_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-001-statically_indeterminate_reaction_force_analysis.py`

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      <div class="sphx-glr-thumbnail-title">Statically indeterminate reaction force analysis</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip=" - A standard 30 inch WF beam, with a cross-sectional area A,    is supported as shown below an...">

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  .. image:: /verif-manual/images/thumb/sphx_glr_vm-002-beam_stresses_and_deflections_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-002-beam_stresses_and_deflections.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Beam stresses and deflections</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - S. Timoshenko, Strength of Materials, Part I, Elementary Theory and    Problems, ...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-003-thermally_loaded_support_structure_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-003-thermally_loaded_support_structure.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Thermally loaded support structure</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - S. Timoshenko, Strength of Materials, Part I, Elementary Theory and    Problems, ...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-004-deflection_of_a_hinged_support_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-004-deflection_of_a_hinged_support.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Deflection of a hinged support</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - S. H. Crandall, N. C. Dahl, An Introduction to the Mechanics    of Solids, McGraw...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-005-laterally_loaded_tapered_support_structure_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-005-laterally_loaded_tapered_support_structure.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Laterally Loaded Tapered Support Structure</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - R. D. Cook, Concepts and Applications of Finite Element Analysis, 2nd Edition,   ...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-006-pinched_cylinder_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-006-pinched_cylinder.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Pinched cylinder</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - S. H. Crandall, N. C. Dahl, An Introduction to the Mechanics of Solids,    McGraw...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-007-plastic_compression_of_a_pipe_assembly_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-007-plastic_compression_of_a_pipe_assembly.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Plastic compression of a pipe assembly</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - None.">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-008-parametric_calculation_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-008-parametric_calculation.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Parametric calculation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - G. N. Vanderplaats, Numerical Optimization Techniques for Engineering    Design w...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-009-large_lateral_deflection_of_unequal_stiffness_springs_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-009-large_lateral_deflection_of_unequal_stiffness_springs.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Large lateral deflection of unequal stiffness springs</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - S. H. Crandall, N. C. Dahl, An Introduction to the Mechanics of Solids,    McGraw...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-010-bending_of_a_t-shaped_beam_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-010-bending_of_a_t-shaped_beam.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Bending of a Tee-Shaped Beam</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - S. H. Crandall, N. C. Dahl, An Introduction to the Mechanics of Solids,    McGraw...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-011-residual-stress-problem_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-011-residual-stress-problem.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Residual Stress Problem</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - Timoshenko, Strength of Materials, Part I, Elementary Theory and    Problems, 3rd...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-012-combined-bending-and-torsion_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-012-combined-bending-and-torsion.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Combined bending and torsion</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - S. Timoshenko, Strength of Materials, Part I, Elementary Theory and    Problems, ...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-013_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-013.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Cylindrical Shell Under Pressure</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - S. Timoshenko, Strength of Materials, Part I, Elementary Theory and    Problems, ...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-014_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-014.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Large Deflection Eccentric Compression of Slender Column</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="    Case 1: Uniform loading P, clamped edge.     Case 2: Concentrated center loading F, clamped...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-015_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-015.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Bending of a Circular Plate Using Axisymmetric Shell Elements</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="    Case 1: a moment M.     Case 2: a shear force F.">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-016_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-016.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Bending of a Solid Beam (Plane Elements)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - S. Timoshenko, Strength of Materials, Part I, Elementary Theory and    Problems, ...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-018_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-018.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Out-of-Plane Bending of a Curved Bar</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - S. Timoshenko, Strength of Materials, Part II, Elementary Theory and    Problems,...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-020_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-020.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Cylindrical Membrane Under Pressure</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - S. Timoshenko, Strength of Materials, Part II, Elementary Theory and    Problems,...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-021_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-021.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Tie Rod with Lateral Loading</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - S. Timoshenko, Strength of Materials, Part II, Elementary Theory and    Problems,...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-025_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-025.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Stresses in a Long Cylinder</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - TIMOSHENKO,S.P.,AND J.N.GOODIER,THEORY OF ELASTICITY    MCGRAW-HILL,NEW YORK, PP ...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-291_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-291.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Force on the Boundary of a Semi-Infinite Body (Boussinesq Problem)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - A POINT INTERPOLATION METHOD FOR SIMULATING DISSIPATION PROCESS    OF CONSOLIDATI...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-295_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-295.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">One Dimensional Terzaghi's Consolidation Problem with Permeability as Function of Depth</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reference:  - A.BILLON,J.PICAUT,&#x27;INTRODUCING ATMOSPHERIC ATTENUATION    WITHIN A DIFFUSION MODE...">

.. only:: html

  .. image:: /verif-manual/images/thumb/sphx_glr_vm-299_thumb.png
    :alt:

  :ref:`sphx_glr_verif-manual_vm-299.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Sound Diffusion in a Flat Room</div>
    </div>


.. raw:: html

    </div>


.. toctree::
   :hidden:

   /verif-manual/vm-001-statically_indeterminate_reaction_force_analysis
   /verif-manual/vm-002-beam_stresses_and_deflections
   /verif-manual/vm-003-thermally_loaded_support_structure
   /verif-manual/vm-004-deflection_of_a_hinged_support
   /verif-manual/vm-005-laterally_loaded_tapered_support_structure
   /verif-manual/vm-006-pinched_cylinder
   /verif-manual/vm-007-plastic_compression_of_a_pipe_assembly
   /verif-manual/vm-008-parametric_calculation
   /verif-manual/vm-009-large_lateral_deflection_of_unequal_stiffness_springs
   /verif-manual/vm-010-bending_of_a_t-shaped_beam
   /verif-manual/vm-011-residual-stress-problem
   /verif-manual/vm-012-combined-bending-and-torsion
   /verif-manual/vm-013
   /verif-manual/vm-014
   /verif-manual/vm-015
   /verif-manual/vm-016
   /verif-manual/vm-018
   /verif-manual/vm-020
   /verif-manual/vm-021
   /verif-manual/vm-025
   /verif-manual/vm-291
   /verif-manual/vm-295
   /verif-manual/vm-299



.. only:: html

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

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