## 5 Optimization Design for the Framework  
### Optimization Designs for the Portal  
In order to determine the optimum structure of the large-scale moving framework, the portal structure was first optimized based on the FEA method after the sandwich structural parameters optimization. The FEA was carried out to analyze the maximum deformation of the portal under the given operational loads. Boundary conditions are use to describe the interaction of the structure with its environment as shown in Figure 5, where vertical support of the portal is applied as fixed vertical displacement at marked positions, as shown in Figure 5A. Horizontal support of the portal is applied as fixed displacement in \(x\)-direction and fixed displacement in \(y\)-direction at marked positions, as shown in Figure 5B. The weight of the traverse and lifting beam is applied as forces in their center of gravity (COG), as shown in Figure 5C. The acceleration for these two components is also applied at their center of gravity. The COG is rigidly linked to the connection points of the portal. Similarly, the weight of the milling head was considered by a point mass at its mass origin. The point mass was connected to all gravity and acceleration loads, as shown in Figure 5D. The top view of all boundary conditions is shown in Figure 5E. Figure 5: Boundary conditions for composite framework: (**A**) marked positions of vertical support of the portal; (**B**) marked positions of horizontal support of the portal; (**C**) forces direction in the center of gravity (COG) of the traverse and lifting beam; (**D**) forces direction in milling head; (**E**) the top view of all boundary conditions. \begin{table}
\begin{tabular}{c c c c c} \hline
**No** & **Name** & **Operational Loads** & **Description** & **Given Value** \\ \hline \multirow{2}{*}{\(1\)} & \multirow{2}{*}{Load 1} & \multirow{2}{*}{\(G\)} & \(G=mg\) (\(m\) represents mass of the framework, \(g\) represents gravity acceleration) & \multirow{2}{*}{-} \\ \multirow{2}{*}{\(2\)} & \multirow{2}{*}{Load 2} & \multirow{2}{*}{\(G+F_{x}\)} & \(G=mg\) and \(F_{x}=m_{x}\) (\(a_{x}\) represents acceleration in the \(x\)-direction. The maximum \(a_{x}\) is for starting and stopping) & \\ \hline \multirow{2}{*}{\(3\)} & \multirow{2}{*}{Load 3} & \multirow{2}{*}{\(G+F_{y}\)} & \(G=mg\) and \(F_{y}=m_{y}\) (\(a_{y}\) represents acceleration in the \(y\)-direction. The maximum \(a_{y}\) is for starting and stopping) & \\ \hline \multirow{2}{*}{\(4\)} & \multirow{2}{*}{Load 4} & \multirow{2}{*}{\(G+F_{z}\)} & \(G=mg\) and \(F_{z}=m_{z}\) (\(a_{z}\) represents acceleration in the \(z\)-direction. The maximum \(a_{z}\) is for starting and stopping) & \\ \hline \end{tabular}
\end{table} 
Table 5: Operational loads for the milling head in the manufacturing process. A finite element model of the original design of the portal (D0) was first created as shown in Figure 4B. For finite element analysis, aluminum alloy beams were included in the finite element model as beam elements glued to the panel elements. The finite element analysis used small deformations linear-elastic model, in which shell elements adopted four node linear elements Kirchhoff plate theory (in-plane), composite material was with nine node integration trough thickness, beam elements adopted two node linear elements with linear elastic material, and loads (Table 5) and boundary conditions (Figure 5) were used for the simulation analysis. However, the FEA results showed that the displacement of the milling head did not meet the requirements. So, we carried out the structural optimization of the portal. Figure 6 and Table 6 presented a comparison of the portal's performance before and after design optimization. From Table 6, it is observed that compared with the structure of D0 before optimization, although the mass of structure D1 after optimization increased by 6% and the material costs increased by 9%, its stiffness increased by 89%, and the maximum deformation of D1 was much smaller than that of D0. Therefore, the portal structure was optimized as D1.