Reference problem
=====================


Geometry
---------




.. image:: images/10000000000001D0000001AB8EFE41FE9CF19211.png
    :width: 3.2953in
    :height: 3.0311in


.. _RefImage_10000000000001D0000001AB8EFE41FE9CF19211.png:

**Figure 1.1 Problem Geometry**


Material properties
----------------------

The discrete elements have the following stiffness characteristics in :math:`{\text{N.m}}^{-1}`:

:math:`{R}_{1}={R}_{3}=\left[\begin{array}{cccccc}40& \text{}& \text{}& \text{}& \text{}& \text{}\\ \text{}& 60& \text{}& \text{}& \text{}& \text{}\\ \text{}& \text{}& 500& \text{}& \text{}& \text{}\\ \text{}& \text{}& \text{}& 60& \text{}& \text{}\\ \text{}& \text{}& \text{}& \text{}& 500& \text{}\\ \text{}& \text{}& \text{}& \text{}& \text{}& 650\end{array}\right]`

:math:`{R}_{2}={R}_{4}=\left[\begin{array}{cccccc}40& \text{}& \text{}& \text{}& \text{}& \text{}\\ \text{}& 30& \text{}& \text{}& \text{}& \text{}\\ \text{}& \text{}& 140& \text{}& \text{}& \text{}\\ \text{}& \text{}& \text{}& 30& \text{}& \text{}\\ \text{}& \text{}& \text{}& \text{}& 140& \text{}\\ \text{}& \text{}& \text{}& \text{}& \text{}& 330\end{array}\right]`

The discrete elements have the following mass characteristics in :math:`\text{kg}`:

:math:`{M}_{1}={M}_{2}={M}_{3}={M}_{4}={M}_{5}={M}_{6}=\left[\begin{array}{cccccc}10& \text{}& \text{}& \text{}& \text{}& \text{}\\ \text{}& 10& \text{}& \text{}& \text{}& \text{}\\ \text{}& \text{}& 10& \text{}& \text{}& \text{}\\ \text{}& \text{}& \text{}& 10& \text{}& \text{}\\ \text{}& \text{}& \text{}& \text{}& 10& \text{}\\ \text{}& \text{}& \text{}& \text{}& \text{}& 10\end{array}\right]`


Boundary conditions and loads
-------------------------------------

Imposed displacement:


.. math::
: label: EQ-None

    \ textrm {Embedding at the nodes}
    \ mathit {N2}