A Simplified Bending Analysis of Imperfect Spherical Pressure Vessels

An analytical solution is presented for spherical shells with imperfections in the geometry. The model is based on bending equations of the shell, and the imperfection is considered by an equivalent load approach. Particular expressions for cosine shape imperfections are developed, leading to explicit forms of the equations for displacements and stress resultants. Convergence studies for typical axisymmetric and local imperfections in thin spherical shells are presented, and the limitations of the solution regarding the amplitude of the imperfection are discussed.