Elasticity solution for a laminated orthotropic cylindrical shell subjected to a localized longitudinal shear force

A three-dimensional elasticity solution is presented for the title problem. The solution is in terms of a double Fourier series in the surface-parallel directions and a power series in the thickness direction. On the basis of this solution, it is shown that the classical lamination theory is inadequate for this problem because the steep displacement and stress gradients near the load cannot be captured by it correctly even if the shell is thin.