A semi-analytical finite element model for the analysis of laminated 3D axisymmetric shells: Bending, free vibration and buckling

A general semi-analytical finite element model is developed for bending, free vibration and buckling analysis of shells of revolution made of laminated orthotropic elastic material. The 3D elasticity theory is used and the equations of motion are obtained by expanding the displacement field and load in the Fourier series in terms of the circumferential coordinate, θ. The coefficients of the expansion are functions of (r, z), and they are approximated using the finite element method. This leads to a semi-analytical finite element in the (r, z) plane. The element is validated by comparing the present results with the analytical and numerical solutions available in the literature.