Stress, Vibration, and Buckling of Multilayered Cylinders

Abstract

An efficient computational procedure is presented for reducing the cost of the stress, free vibration, and buckling analyses of multilayered composite cylinders. The analytical formulation is based on the linear three‐dimensional theory of elasticity. The cylinders are assumed to have simply supported curved edges, and the fibers of the different layers are either in the circumferential or longitudinal direction. The fundamental unknowns consist of the six stress components and the three displacement components of the cylinder. Each of the variables is expressed in terms of a double Fourier series in the longitudinal and circumferential coordinates, and a two‐field mixed finite element model is used for the discretization in the thickness direction. The cylinder response associated with a range of Fourier harmonics in the longitudinal and circumferential directions is approximated by a linear combination of a few global approximation vectors, which are generated at particular values of the Fourier harmonics, within that range. The full equations of the finite element model are solved for only a single pair of Fourier harmonics, and the response corresponding to the other Fourier harmonics is generated using a reduced system of equations with considerably fewer degrees of freedom.