3D semi-analytical solution of hygro-thermo-mechanical multilayered doubly-curved shells

•3D exact solution of hygro-thermo-mechanical doubly-curved shells is introduced.•The shell unknowns are modelled semi-analytically by the Navier technique.•The continuity conditions is warranted.•The correct load traction condition is considered at the top and bottom of the shell.•Benchmark problem of a shell is proposed.