Semi‐analytical assessment of free‐edge stress fields in cylindrically curved cross‐ply laminated shells

The present work deals with the semi‐analytical assessment of the three‐dimensional stress fields in cylindrically curved symmetrically and unsymmetrically cross‐ply laminated shells subjected to bending load. The developed approach incorporates a layerwise plane‐strain analysis in the innermost regions of the shell. The closed‐form ‘inner solution’, further on, is upgraded by a displacement‐based approach that enables an adequate depiction of the interlaminar stresses at the free edge. This so‐called ‘free‐edge solution’ employs a discretization scheme of each lamina into a number of numerical plies with respect to the thickness direction. Herein, the displacement field of each layer is specified via a priori unknown displacement‐ and Lagrangian interpolation functions. By applying the principle of minimum elastic potential, the governing equations can be derived in an exact manner and further on can be solved by employing the state space approach. The results of the higher‐order analysis method are verified through comparison with highly detailed finite element simulations and it is found that the semi‐analytical approach works with comparable accuracy, however, only at a fraction of the required computational effort.