This paper aims at contributing to the field of efficient analysis methods by introducing a semi-analytical approach that enables the investigation of the three-dimensional stress fields in cylindrically curved cross-ply laminated shells subjected to different transverse loadings under consideration of the free-edge effect. The novel analysis method incorporates a closed-form elasticity solution that is superimposed with a layerwise approach, in which the three-dimensional displacement field is discretized with respect to the thickness direction. Lagrangian shape functions of various order are used to interpolate between the a priori unknown displacement functions in the discrete grid points of the numerical layers. Employing the principle of minimum total potential energy, yields a system of coupled ordinary differential equations which is solved by utilizing the state-space approach. The accuracy of the developed method is verified by comparison with existing analytical approaches in the literature and detailed three-dimensional finite element computations. In addition to a study of the out-of-plane stresses in a circular cylindrical fibre metal laminate (GLARE®), the effect of different radius to thickness ratios and length to thickness ratios on the distribution of the interlaminar stress field is investigated.

本文旨在通过引入一种半解析方法来为有效分析方法领域做出贡献，该方法能够在考虑自由边的情况下研究承受不同横向载荷的圆柱弯曲交叉层板壳中的三维应力场。影响。新的分析方法结合了一个封闭形式的弹性解，该解与分层方法叠加，其中三维位移场相对于厚度方向离散化。各种阶的拉格朗日形状函数用于在数值层的离散网格点中的先验未知位移函数之间进行插值。采用总势能最小原则，产生一个耦合常微分方程组，该方程组使用状态空间方法求解。通过与文献中现有的分析方法和详细的三维有限元计算进行比较，验证了所开发方法的准确性。除了研究圆柱形纤维金属层压板 (GLARE®) 中的平面外应力外，还研究了不同半径与厚度比和长度与厚度比对层间应力场分布的影响。