## 4 Illustrative Example  
The example illustrating the proposed algorithm for obtaining a solution set is presented below. As an example, a truss structure is selected for which the system of equations is relatively simple. The essence of the example is to explain the construction of the system of inequalities, which describes the solution set and to show the advantages of the formulation, being aware of its disadvantages. Let us consider a truss composed of three bars, whose geometry and load is presented in Figure 2. The truss consists of three bars and three nodes. It is loaded with two concentrated forces. The extension matrix \(\mathbf{B}\), load vector \(\mathbf{Q}\) and vector of nodal displacements \(\mathbf{q}\) are given by  
\[\mathbf{B}=\left( \begin{array}{cc}1&0\\ \frac{\sqrt{2}}{2}&1\\ 0&\frac{\sqrt{2}}{2}\end{array} \right),\quad\mathbf{Q}=\left( \begin{array}[] {c}Q\\ 2Q\end{array} \right),\quad\mathbf{q}=\left( \begin{array}{c}q_{1}\\ q_{2}\end{array} \right). \tag{35}\]Let the bars be characterized by uncertain Young's moduli. Then, it is possible to decompose elasticity matrix \(\mathbf{E}\) into parts connected and not connected with uncertain parameters, in the form  
\[[\mathbf{E}]=[\mathbf{p}]\,\widehat{\mathbf{E}}=\left( \begin{array}{ccc}[p_{1} ]&0&0\\ 0&[p_{2}]&0\\ 0&0&[p_{3}]\end{array} \right)\left( \begin{array}{ccc}\frac{A_{1}}{L}&0&0\\ 0&\frac{A_{2}}{\sqrt{2}L}&0\\ 0&0&\frac{A_{3}}{L}\end{array} \right), \tag{36}\]  
with uncertain values of bars elasticity \([E_{1}]=[p_{1}]\,A_{1}/L\), \([E_{2}]=[p_{2}]\,A_{2}/(\sqrt{2}L)\), \([E_{3}]=[p_{3}]\,A_{3}/L\). Let us consider the system of inequalities (15). The set \(\mathcal{V}(\mathbf{q})\), defined by (7), is given by  
\[\mathcal{V}(\mathbf{q})=\left( \begin{array}{c}Q\\ 2Q\end{array} \right)-q_{1}\left( \begin{array}{c}1\\ 0\end{array} \right)\ast[E_{1}]-\left(\frac{1}{\sqrt{2}}q_{1}+q_{2}\right) \left( \begin{array}{c}\frac{1}{\sqrt{2}}\\ 1\end{array} \right)\ast[E_{2}]-\frac{1}{\sqrt{2}}q_{2}\left( \begin{array}{c} 0\\ 1\end{array} \right)\ast[E_{3}]\,. \tag{37}\]  
It is worth to note that the decomposition of (37) contains vectors \(\mathbf{B}^{(i)}\)  
\[\mathbf{B}^{(1)}=\left( \begin{array}{c}1\\ 0\end{array} \right),\quad\mathbf{B}^{(2)}=\left( \begin{array}{c}\frac{1}{ \sqrt{2}}\\ 1\end{array} \right),\quad\mathbf{B}^{(3)}=\left( \begin{array}{c}0\\ \frac{1}{\sqrt{2}}\end{array} \right), \tag{38}\]  
which are the rows of matrix \(\mathbf{B}\). Let us define vectors \(\mathbf{u}^{(i)}\) (\(i=1,2,3\)) perpendicular to \(\mathbf{B}^{(i)}\) and in the same time perpendicular to zonotope \(\mathcal{V}(\mathbf{q})\) edges  
\[\mathbf{u}^{(1)}=\left( \begin{array}{c}0\\ 1\end{array} \right),\quad\mathbf{u}^{(2)}=\left( \begin{array}{c}1\\ -\frac{1}{\sqrt{2}}\end{array} \right),\quad\mathbf{u}^{(3)}=\left( \begin{array} []{c}1\\ 0\end{array} \right). \tag{39}\]  
Then the system of inequalities (16) is given by  
\[ \begin{split}\mathbf{u}^{(1)}&\Rightarrow\left|2Q-\left(\frac{1 }{\sqrt{2}}q_{1}+q_{2}\right)E_{2}^{\mathsf{c}}-\frac{1}{\sqrt{2}}q_{2}E_{3} ^{\mathsf{c}}\right|\leq\left|\frac{1}{\sqrt{2}}q_{1}+q_{2}\right|E_{2}^{ \mathsf{A}}+\frac{1}{\sqrt{2}}\left|q_{2}\right|E_{3}^{\mathsf{c}},\\ \mathbf{u}^{(2)}&\Rightarrow\left|Q-\frac{2}{\sqrt{2}}Q-q_{1}E_{1}^{ \mathsf{c}}-\frac{1}{2\sqrt{2}}q_{2}E_{3}^{\mathsf{c}}\right|\leq\left|q_{1} \right|E_{1}^{\mathsf{A}}+\frac{1}{2\sqrt{2}}\left|q_{2}\right|E_{3}^{ \mathsf{c}},\\ \mathbf{u}^{(3)}&\Rightarrow\left|Q-q_{1}E_{1}^{\mathsf{c}}-\left(\frac{1}{2 }q_{1}+\frac{1}{\sqrt{2}}q_{2}\right)E_{2}^{\mathsf{c}}\right|\leq\left|q_{1} \right|E_{1}^{\mathsf{A}}+\left|\frac{1}{2}q_{1}+\frac{1}{\sqrt{2}}q_{2} \right|E_{2}^{\mathsf{A}}.\end{split}