## 3 Numerical Validation and Experiments
### Initial Kinematic Boundary Conditions of Panel Components  
To determine the value of boundary conditions prescribed on the edges of stringers and skin, initial variations of points on the surfaces of fixturing boards, stringers I and II, and clamping mechanisms are captured by the measurement device in fuselage panel assembly platform, as shown in Figure 3.  
The variations between the actual and theoretical position and orientation of the skin and stringers edges are the specified kinematic boundary conditions, as depicted in Tables 3 and 4.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Stringer** & \(\alpha\)**/mm** & \(\Delta\)**/mm** & \(\Delta\)**/mm** & \(\Delta\)**/mm** & \(\Delta\)**/mm** & \(\varphi_{\text{x}}\)**/rad** & \(\varphi_{\text{y}}\)**/rad** & \(\varphi_{\text{z}}\)**/rad** \\ \hline I & \(10\) & \(0\) & \(0\) & \(0\) & \(0\) & \(0\) & \(0\) \\ I & \(484.976\) & \(-3.8\times 10^{-6}\) & \(0.781103\) & \(-0.356041\) & \(0.01601\) & \(0.005193\) & \(-0.039305\) \\ \hline II & \(10\) & \(0\) & \(0\) & \(0\) & \(0\) & \(0\) & \(0\) \\  & \(485.013\) & \(3.1\times 10^{-5}\) & \(0.891975\) & \(-0.302205\) & \(-0.01852\) & \(0.00765\) & \(-0.038902\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Actual boundary conditions prescribed on beam with respect to Cartesian coordinate \(O^{b}xyz\).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**R/mm** & \(\alpha\)**/mm** & \(b\)**/mm** & \(h\)**/mm** & \(\mu\) & **\(E\)/GPa** & \(\rho\)**/kg\(\cdot\)m\({}^{-3}\)** & \(\theta_{g}\)**/rad** \\ \hline
2724 & 495.5 & 1794.26 & 2 & 0.33 & 73 & 2780 & 1.2415 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Geometric and material property parameters of skin.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**\(\alpha\)/mm** & \(\Delta\)**\(\tau_{1}\)/mm** & \(\Delta\)**\(\tau_{2}\)/mm** & \(\Delta\)**\(\tau_{3}\)/mm** & \(\varphi_{1}\)**/rad** & \(\varphi_{2}\)**/rad** & \(\varphi_{3}\)**/rad** \\ \hline
495.5 & 494.954 & 0.392835 & \(-0.457491\) & \(-0.004490\) & \(-0.000188\) & \(-0.039646\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Actual boundary conditions prescribed on shell curve edges with respect to Cartesian coordinate \(O_{T1}\tau_{2}\tau_{3}\).  
Figure 3: Experiment platform of aircraft fuselage panel assembly. (**a**) Aircraft assembly platform; (**b**) substructure of fuselage panel.  
The measured variations are converted to the boundary conditions on curve edges of panel \(\alpha=0\) and \(\alpha=495.5\) with respect to curvilinear coordinate as the following expressions:  
\[\begin{array}{l}u\big{|}_{\alpha=0}=v\big{|}_{\alpha=0}=w\big{|}_{\alpha=0}= \varphi_{v}\big{|}_{\alpha=0}=0,\\ u\big{|}_{\alpha=495.5}=\Delta\tau_{1}-\alpha=-0.546,\\ v\big{|}_{\alpha=495.5}=\Delta\tau_{2}\cdot\cos(\beta/R)-\Delta\tau_{3}\cdot \sin(\beta/R),\\ w\big{|}_{\alpha=495.5}=\Delta\tau_{2}\cdot\sin(\beta/R)+\Delta\tau_{3}\cdot \cos(\beta/R),\\ \varphi_{v}\big{|}_{\alpha=495.5}=\text{atan2}(-\textbf{{P}}^{{}^{\prime}}_{31 },\sqrt{(\textbf{{P}}^{{}^{\prime}}_{32})^{2}+(\textbf{{P}}^{{}^{\prime}}_{33} )^{2}}),\end{array} \tag{36}\]  
where  
\[\textbf{{P}}^{{}^{\prime}}=\textbf{{P}}(\beta/R,0,0)\textbf{{P}}(\varphi_{1}, \varphi_{2},\varphi_{3})\textbf{{P}}(-\beta/R,0,0). \tag{37}\]  
In addition to being imposed with the kinematic boundary constraints, the skin and stringers are also subjected to the gravity load. Load components of beam \(q_{x}\), \(q_{y}\) and \(q_{z}\) in the direction of local coordinate axes are \(0\), \(-p^{b}gA\cos(b/2R-\theta_{b})\) and \(\rho^{b}gA\sin(b/2R-\theta_{b})\), and \(q_{rx}=0\). Load components of shell \(q_{1}\), \(q_{2}\) and \(q_{3}\) in the direction of local coordinate axes are \(0\), \(-pght\cos(\beta/R-b/2R)\) and \(-pght\sin(\beta/R-b/2R)\), respectively.