Based on a boundary layer theory of shell buckling, the semi-analytical solutions for nonlinear stability analysis of anisotropic laminated composite doubly-curved shells with rectangular planform subjected to lateral pressure are derived. A new shell model of arbitrary constant curvature and fibre stacking sequences but constant thickness is developed. The governing equations are based on an extended higher-order shear deformation shell theory with von Kármán-type of kinematic nonlinearity and including the effect on stiffness couplings. The nonlinear deformation and initial deflection of shells are both taken into account. The boundary layer equations of buckling for doubly-curved shells are introduced to match the asymptotic solutions satisfying the clamped or simply-supported boundary condition. The closed-form solutions for buckling and postbuckling analysis of an anisotropic shear deformable laminated doubly-curved panel are obtained by the two-step perturbation methods and the boundary layer theory for shell buckling, which is employed to determine interactive buckling loads and postbuckling equilibrium paths. At the same time, the internal quantitative relationship in the asymptotic sense between deflection and rotations of the normal to the middle surface is for the first time obtained. The influences of anisotropic lay-up, change in the stacking sequence, temperature variation, different types of elastic foundation and boundary condition on nonlinear stability behaviour are analysed and discussed. The study provides a good theoretical method for the load-carrying capacity design of composite shell structures.

基于壳屈曲边界层理论，推导了矩形平面各向异性层状复合双曲壳在侧压作用下非线性稳定性分析的半解析解。开发了一种具有任意恒定曲率和纤维堆叠序列但厚度恒定的新壳模型。控制方程基于扩展的高阶剪切变形壳理论，具有 von Kármán 型运动学非线性，包括对刚度耦合的影响。壳的非线性变形和初始挠度都被考虑在内。引入双曲壳屈曲边界层方程来匹配满足夹紧或简支边界条件的渐近解。通过两步摄动法和壳屈曲边界层理论，得到了各向异性剪切变形叠层双曲面板屈曲和后屈曲分析的闭式解，用于确定交互屈曲载荷和后屈曲平衡路径. 同时首次得到了中面法线偏转与旋转渐近意义的内定量关系。分析讨论了各向异性铺层、堆叠顺序变化、温度变化、不同类型的弹性基础和边界条件对非线性稳定性行为的影响。该研究为复合壳结构的承载能力设计提供了良好的理论方法。