## 1 Introduction  
Stiffened panel structure composed of slender beams and a thin-walled shell is widely applied in the fields of marine and aeronautical engineering since it is lightweight and has high load-bearing capacity. Integrated stiffened panel model, regarded as a single piece structure, is generally exploited for the structural idealization of the built-up construction [1]. An aircraft fuselage panel as the built-up stiffened structure is usually assembled by riveting a skin and the stringers together. Before the riveting operation, the actual position of components (skin and stringer) may differ from the designed dimensions due to deformation resulting from the forces at joining interfaces and clamped boundary conditions with non-zero constraints. Thus, the integrated panel analysis cannot achieve an accurate evaluation of the actual profile. Moreover, numerical computation costs of a large-scale aircraft panel with real boundary conditions are also prohibitive. Therefore, a more efficient substructure model of large built-up panels, taking account of the initial variations, coupled interface force and mixed boundary conditions, should be established to achieve computational cost saving and accurate deformation prediction. Approaches to model the multi-component structures have received attention from aeronautical engineers and mechanical experts, who focus on continuous mechanical descriptions and discrete element modeling of the beam, shell, or their combinations. The integrated one-piece models are mostly utilized in mechanical research to simplify the actual built-up structures. The Euler-Bernoulli beam (EBB) [2], Timoshenko beam [3,4], and nonlinear beam formulation [5] are usually introduced into the deformation analysis of the structures with slender and flexible components. Displacement formulae of these deformation prediction model are expressed or fitted by the Taylor-type expansion [6], Hermite interpolating polynomials [7] and Chebyshev polynomials [8]. The Kirchhoff shell [9], Reissner-Mindlin shell [10], and higher-order approximation shell theory [11] are employed for exploring the intrinsic mechanisms of thin panels. Although the deformation model generated from the single beam theory or shell theory could reduce the computational complexity, it cannot achieve the coupling analysis of structural interaction between multiple adjacent components. To deal with the static analysis of complex thin-walled structures, [PERSON] and [PERSON] [12] built the variable kinematic models using Carrera Unified Formulation, which allows one-, two-, and three-dimensional refined structures to be connected to each other easily. [PERSON] et al. [13] performed a finite element (FE) simulation of the lower lobe fuselage section and also conducted a drop experiment on small components for analyzing the energy absorbing ability of multi-component structures during a crash landing. The grid design for finite element method (FEM) has considerable effects on the time consumption and accuracy of results. [PERSON] et al. [14] proposed a wave finite element method to express the dynamic stiffness matrix of the periodic structures with substructuring techniques that could yield large computational savings. [PERSON] et al. [15] established aerodynamic and structural models of reinforced panels based on the principle of virtual work, which is discretized through the FE method. They found that modeling stiffeners as immovable boundaries would overestimate flutter onset conditions and underestimate post-flutter amplitudes. Thus, considering the flexibility of stiffeners is essential to the nonlinear analysis of complex aircraft configurations. In addition, the solution of boundary value problems for the aforementioned complex mechanical system is another important challenge of multi-component structure analysis. [PERSON] et al. [16] solved the one- and two-dimensional structural mechanics problems by employing the Lagrange multiplier method and double exponential transformation.