Example of a mast¶

In this example of a mast are $72$ nodes $\left(a,b,c\right) \in \R^3$ , $a,b \in \{0,\frac{1}{7},\frac{2}{7}\}$ , $c \in \{\frac{x}{7}:x=0,1,\ldots,7\}$ measured in meter and $503$ potential bars between every two not fixed nodes with a maximal distance of $\frac{\sqrt{3}}{7}$ — long bars which are located alongside several shorter bars are ignored. The supports are in the nodes $\left(a,b,0\right)$ , $a,b \in \{0,\frac{2}{7}\}$ which are fixed in every direction. In the node $\left(\frac{1}{7},\frac{1}{7},1\right)$ acts a force of $10^5 \, \mbox{N}$ in the negative $z$ -direction.

The main problem is implemented as a script. The other scripts are linked by the pictures.

For a perturbation of $50 \, \mbox{\%}$ in every direction of the force, and scaling to obtain the same maximal quantities as in the unperturbed case, our robust optimization method produces the robust optimal solution.