1. Reference problem#

1.1. Geometry#

_images/10000000000001D0000001AB8EFE41FE9CF19211.png

Figure 1.1 Problem Geometry

1.2. Material properties#

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

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

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

The discrete elements have the following mass characteristics in \(\text{kg}\):

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

1.3. Boundary conditions and loads#

Imposed displacement:

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: label: EQ-None

textrm {Embedding at the nodes} mathit {N2}