aerosandbox.structures.buckling
===============================

.. py:module:: aerosandbox.structures.buckling


Functions
---------

.. autoapisummary::

   aerosandbox.structures.buckling.column_buckling_critical_load
   aerosandbox.structures.buckling.thin_walled_tube_crippling_buckling_critical_load
   aerosandbox.structures.buckling.plate_buckling_critical_load


Module Contents
---------------

.. py:function:: column_buckling_critical_load(elastic_modulus, moment_of_inertia, length, boundary_condition_type = 'pin-pin', use_recommended_design_values = True)

   Computes the critical load (in N) for a column or tube in compression to buckle via primary buckling. Uses Euler's classical critical
   load formula.

   :param elastic_modulus: The elastic modulus of the material, in Pa.
   :param moment_of_inertia: The moment of inertia of the cross-section, in m^4.
   :param length: The length of the column, in m.
   :param boundary_condition_type: The boundary condition type. Options are:
                                   - "pin-pin"
                                   - "pin-clamp"
                                   - "clamp-clamp"
                                   - "clamp-pin"
                                   - "clamp-free"
                                   - "free-clamp"
   :param use_recommended_design_values: Whether to use the recommended design value of K for a given boundary condition (True)
   :param or to use the less-conservative theoretical value:
                                                             * Recommended values are from Table C.1.8.1 in Steel Construction Manual, 8th edition, 2nd revised
                                                             printing, American Institute of Steel Construction, 1987 via WikiMedia:
                                                             https://commons.wikimedia.org/wiki/File:ColumnEffectiveLength.png
   :type or to use the less-conservative theoretical value: False

   :returns: The critical compressive load (in N) for the column or tube to buckle via primary buckling.


.. py:function:: thin_walled_tube_crippling_buckling_critical_load(elastic_modulus, wall_thickness, radius, use_recommended_design_values = True)

   Computes the critical load for a thin-walled tube in compression to fail in the crippling mode. (Note: you should also check for
   failure by primary buckling using the `column_buckling_critical_load()` function.)

   The crippling mode is a specific instability mode for tubes with thin walls when loaded in compression. It can be
   seen when you step on a soda can and it buckles inwards. The critical load for this mode is given by the
   following formula:

       stress_crippling = crippling_constant * (E * t / r)

   where:

       A recommended value of crippling_constant = 0.3 is given in Raymer: Aircraft Design: A Conceptual Approach,
       5th Edition, Eq. 14.33, pg. 554.

       A theoretically more accurate value of crippling_constant = 0.605 is given in the Air Force Stress Manual,
       Section 2.3.2.1, Eq. 2-20. This value assumes mu = 0.3, which is a good assumption for most metals.

       and E is the elastic modulus, t is the wall thickness, and r is the radius.

   For more info, see the Air Force Stress Manual, Section 2.3.2.1:
   https://engineeringlibrary.org/reference/column-crippling-air-force-stress-manual

   And see Raymer: Aircraft Design: A Conceptual Approach, 5th Edition, pg. 554.

   :param elastic_modulus: The elastic modulus of the material, in Pa.
   :param wall_thickness: The wall thickness of the tube, in m.
   :param radius: The radius of the tube, in m.
   :param use_recommended_design_values: Whether to use the recommended design value of crippling_constant (True)
   :param or to use the less-conservative theoretical value:
   :type or to use the less-conservative theoretical value: False

   :returns: The critical compressive load (in N) for the tube to buckle in the crippling mode.


.. py:function:: plate_buckling_critical_load(length, width, wall_thickness, elastic_modulus, poissons_ratio = 0.33, side_boundary_condition_type = 'clamp-clamp')

   Computes the critical compressive load (in N) for a plate to buckle via plate buckling.

   Assumes a rectangular plate with dimensions:
   - length
   - width
   - wall_thickness

   A compressive force is applied such that it is aligned with the length dimension of the plate.

   Uses constants from NACA TN3781.

   Methdology taken from "Stress Analysis Manual," Air Force Flight Dynamic Laboratory, Oct. 1986.
   Section 6.3: Axial Compression of Flat Plates
   Reproduced at "Engineering Library":
   https://engineeringlibrary.org/reference/analysis-of-plates-axial-compression-air-force-stress-manual

   :param length: The length of the plate, in m.
   :param width: The width of the plate, in m.
   :param wall_thickness: The wall thickness of the plate, in m.
   :param elastic_modulus: The elastic modulus of the material, in Pa.
   :param side_boundary_condition_type: The boundary condition type at the sides of the plate. Options are:
                                        - "clamp-clamp"
                                        - "pin-pin"
                                        - "free-free"

   :returns: The critical compressive load (in N) for the plate to buckle via plate buckling.