Given the background of exceptional specific properties, especially curved composite structures in the form of fibre-reinforced plastics exhibit a significant potential to maximize the efficiency of load-bearing components. However, due to their multilayered character, theoretically weak interlaminar stress singularities in the interfaces at the traction-free edges of composite laminated shells are encountered which pose a significant challenge for the analysis and design of those structures. This contribution tries to make a significant impact on this research field by discussing the computational modelling, global optimization and experimental investigation of stress concentration phenomena in composite laminated shell panels undergoing hygro-thermo-mechanical loads. In this context, a stress function approach is introduced which accounts for the computation of the state variables in thick, infinitely long circular cylindrical composites subjected to uniform edge loads, transverse loads on the inner and outer surfaces of the panel as well as arbitrary through-the-thickness hygro-thermal loads. The presented closed-form analytical solution is further modified by means of a higher-order displacement-based layerwise approach. Based on this semi-analytical solution, the free-edge effect and the free-corner effect in composite laminated shell panels are investigated in detail. Thereafter, the introduced semi-analytical method is combined with a genetic algorithm in order to minimize the delamination tendency of L-shaped CFRP and GFRP cross-ply laminated beams considering a four-point bending load. Moreover, corresponding experimental investigations have been conducted in order to assess the validity and accuracy of the highly efficient approximate analysis methods.