.. include:: sub.txt

.. _FixedLocation-BeamIntegration:

===============
 FixedLocation
===============

.. function:: beamIntegration('FixedLocation',tag,N,*secTags,*locs)
   :noindex:

   Create a FixedLocation beamIntegration object.
   This option allows user-specified locations of the integration points. The associated integration
   weights are computed by the method of undetermined coefficients (Vandermonde
   system)

   .. math::

      \sum^N_{i=1}x_i^{j-1}w_i = \int_0^1x^{j-1}dx = \frac{1}{j},\qquad (j=1,...,N)

   Note that :ref:`NewtonCotes-BeamIntegration` integration is recovered when the integration point locations are equally spaced.

   ========================   =============================================================
   ``tag`` |int|              tag of the beam integration
   ``N`` |int|                number of integration points along the element.
   ``secTags`` |listi|        A list previous-defined section objects.
   ``locs`` |listf|           Locations of integration points along the element.
   ========================   =============================================================


   Places ``N`` integration points along the element, whose locations are defined in ``locs``.
   on the natural domain [0, 1]. The force-deformation response at each integration
   point is defined by the ``secs``. Both the ``locs`` and ``secs``
   should be of length ``N``. The order of accuracy for Fixed Location integration is N-1.