Flexible skin is one of the key technologies for morphing structures in aircraft, requiring not only the ability to undergo large deformations but also the capability to carry significant normal aerodynamic loads. A metal skeleton-enhanced rubber composite flexible skin structure is an effective solution, where the skeleton reinforcement support structure must possess both large deformation and normal load-bearing characteristics. This paper focuses on U-shaped honeycomb skeleton structures, establishing theoretical models for the relationship between the tensile deformation of the skeleton structure and the maximum strain, as well as the deflection of the structure under normal force. By combining the SLSQP optimization algorithm, the geometric dimensions of the skeleton are optimized based on the performance requirements of the skin under specific operating conditions, using out-of-plane deflection as the boundary condition and minimum strain as the optimization objective. The optimization process yielded the optimal geometric dimensions that meet the requirements for deformation and load-bearing capacity. Results show that, regardless of the initial values of the optimization model, the optimization process consistently converges to the same optimal solution, validating the feasibility and effectiveness of the size parameter optimization of U-shaped honeycomb skeleton structures.