# Research on the Performance of an Aircraft Landing
## 5 Optimization Analysis of the Minimum Unlocking Force  
This section describes the optimization analysis that was conducted to minimize the unlocking force \(F_{Unlock}\) based on the computer-aided engineering software ISIGHT (Dassault, France) combined with MATLAB. On the premise of ensuring an adequate locking ability of the hook lock mechanism (i.e., ensuring that \(\partial_{1}^{c}\) satisfies the specified requirements), a multi-island genetic algorithm (MIGA) is applied to optimize \(F_{Unlock}\) considering the following variables including the spring stiffness \(k\), the original spring length \(lu\), the spring installation position \(c_{2}\) and the spring angle \(\gamma_{2}\).  
The optimization process is illustrated in Figure 13. First, the bifurcation analysis model is established in MATLAB, and the optimization analysis model, ISIGHT, is also constructed. Each optimization iteration is completed in the locked area of the mechanism. Initially, a set of design variables \(\left(k^{i},lu^{i},c_{2}^{i},\gamma_{2}^{i}\right)\) is generated randomly according to the rules of MIGA, which is then passed to MATLAB to determine the motion trajectory and bifurcation position of the lock mechanism using a numerical continuation algorithm with the single parameter of the unlocking force. As a result, it obtains the angle \(\theta_{1}^{ci}\) characterizing the locking ability and the unlocking force \(F_{Unlock}^{i}\) enacted by the limit stopper. Afterwards, \(\theta_{1}^{ci}\) is checked to determine whether it conforms to the locking ability requirement, and \(F_{Unlock}^{i}\) is examined for its validity as a comparison value. If \(F_{Unlock}^{i}\) is an invalid comparison value, a new set of design variables \(\left(k^{i+1},lu^{i+1},c_{2}^{i+1},\gamma_{2}^{i+1}\right)\) is generated directly to enter  
Figure 11: The influence of \(\gamma_{2}\) on \(F_{Unlock}\): (**a**) Unlocking force varies with the \(\gamma_{2}\); (**b**) Projection of the trajectory in the \(F_{Unlock}\)-\(\gamma_{2}\) plane.  
Figure 12: Sensitivity analysis of parameters affecting the unlocking force.  
the next iterative computation. In addition, if \(F_{Unlack}^{i}\) is a valid value, a comparison is made with the previous computational result to check for convergence. When the convergence requirement is met, the optimization computation ends. Otherwise, the next iterative computation is initiated likewise until the convergence requirement is satisfied.  
Here, the optimization problem can be expressed as follows based on the structural constraint and design requirements of the hook lock mechanism:  
Variables: \(k\in[0.5\,kN/mm,6\,kN/mm]\);  
\(lu\in[30\,mm,80\,mm]\);  
\(c_{2}\in[15\,mm,30\,mm]\);  
\(\gamma_{2}\in[28^{\circ},52^{\circ}]\).  
Constraint: \(\theta_{1}^{c}\geq 138^{\circ}\).  
Objective: Min \(F_{Unlock}\).  
The optimization results are shown in Table 2. After optimization, the angle \(\theta_{1}^{c}\) becomes slightly smaller than the initial value of \(138.5^{\circ}\). Nevertheless, it conforms to the specified design requirement of \(138^{\circ}\), which can thus guarantee the locking ability of the hook lock. In contrast, the unlocking force decreases from \(78\) N to \(68.5\) N, showing a reduction of \(12.2\%\).