Example 3¶

This is a $3$ -dimensional example with the ground structure of $27$ nodes $\left(a,b,c\right) \in \R^3$, $a,b,c \in \{1,2,3\}$ measured in meter and $274$ potential bars between every two not fixed nodes – long bars which are located alongside several shorter bars are ignored. The supports are in the nodes $\left(1,a,b\right)$, $a,b \in \{1,2,3\}$ which are fixed in every direction. In the node $\left(3,2,1\right)$ acts a force of $4\cdot10^5 \, \mbox{N}$ in the negative $z$ -direction.

For a perturbation of $10 \, \mbox{\%}$ 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 solutions. In contrast to the optimal solution the robust solution use the third dimension of the space.

Comparison of the volumes¶

	optimal	robust
volume:	6.0000e-03	6.5822e-03

Comparison of the volumes for different redundancies:

redundancy	$\frac{1}{4}$	$\frac{1}{3}$	$\frac{1}{2}$	$1-\frac{1}{2}$	$1-\frac{1}{3}$	$1-\frac{1}{4}$
volume:	8.6667e-03	9.5000e-03	1.2000e-02	1.2000e-02	1.9000e-02	2.6000e-02