Assessment of Shell Theories for the Static Analysis of Cross-Ply Laminated Circular Cylindrical Shells

This paper examines the accuracy of classical shell theories (CST) according to Flugge, Sanders, Love and Donnell, with respect to the recently available three-dimensional elasticity solution, for cross-ply laminated circular cylindrical shells under static loads. Further, a study has also been made to examine to what extent incorporation of first order shear deformation (FSDT), in aforementioned shell theories, improves the results. In general, all the basic equations (for both CST and FSDT), of aforementioned shell theories, have been presented in a unified form using tracer coefficients. A Navier type solution has been used to analyse both a simply supported circular cylindrical shell of revolution and an all round simply supported circular cylindrical shell panel. A parametric study has been carried out keeping in view the lamination schemes and geometrical parameters of the shell. From the detailed comparisons of the results it has been shown that (i) Donnell's theory (CST and FSDT) could be in error for certain lamination schemes and geometrical parameters and (ii) improved results for stresses and displacements could be obtained by incorporating shear deformation on more accurate theory like Flugge (CST)