Semi‐analytical assessment of free‐edge stress fields in circular cylindrical cross‐ply laminated shells subjected to transverse loads

Abstract

The present work deals with the semi‐analytical assessment of the three‐dimensional stress fields in circular cylindrical symmetrically and unsymmetrically laminated cross‐ply shells undergoing different transverse loads. Starting from a closed‐form plane‐strain analysis in the innermost regions of the laminated shell, the elasticity solution is upgraded by a higher‐order displacement‐based approach which enables the developed method to capture the three‐dimensional stress state due to the free‐edge effect in thick, finite‐length composite laminated shells. In order to realize this, the shell panel is discretized into a number of numerical layers with respect to the thickness direction. By introducing a priori unknown displacement functions in the interfaces of those numerical plies and by making use of the principle of minimum elastic potential, a system of coupled ordinary differential equations is obtained, which, however, can be solved by utilizing the state‐space approach. The results of the developed analysis method are verified through comparison with existing analytical approaches in the literature and finite element simulations and it can be noted that the semi‐analytical approach works with comparable accuracy, however, only at a fraction of the computational effort coming with full‐scale three‐dimensional finite element computations.