Buckling of composite cylindrical shells with rigid end disks under hydrostatic pressure

An analytical solution of the buckling problem formulated for a composite cylindrical shell with its ends closed by rigid disks and subjected to hydrostatic pressure is presented in the paper. The problem is solved using Fourier decomposition and the Galerkin method. The boundary conditions are assigned in the form accounting for axial displacements of the end disks caused by an axial contraction of the deformed shell. The hoop displacement and deflection of the shell are approximated by the beam function corresponding to the first mode shape of vibration of a clamped-clamped beam. The axial displacement is approximated by the third derivative of the beam function. Based on this solution, a number of analytical formulas enabling calculations of critical hydrostatic pressure for composite orthotropic cylindrical shells are derived. Using these formulas, the critical loads are calculated for the shells with various elastic and geometric properties. The calculations are verified by comparisons with the results of finite-element analyses. The efficiency of analytical solutions in the search for fibre reinforcement arrangements providing maximum resistance to buckling is demonstrated by several examples.