An analytical solution for buckling and vibration of delaminated composite spherical shells

The estimation of the critical buckling loads and eigenfrequencies are among the most common problems of mechanical engineering. These parameters are very important measures to avoid the loss of stability of the designed structures. In this work a progressive analytical model of doubly curved shells will be presented and applied to a delaminated spherical shell. The equations are derived using an improved version of the Sanders shell theory and the System of Exact Kinematic Conditions (SEKC). The solution method is based on the Levy formulation. With this method the governing partial differential equation (PDE) can be reduced to an ordinary differential equation (ODE) with the use of Fourier-series. The resulting set of equations are solved using a variant of the state-space method which is able to solve systems with non-constant system matrix.