Finite element for cylindrical thin shells under harmonic forces

A super-convergent finite element is developed for the steady state analysis of circular cylinders under general harmonic forces based on thin shell theory. Simplifying assumptions in previous thin-shell formulations for straight cylinders are avoided. The resulting model is capable of capturing general in-plane and out-of-plain cross sectional distortions including ovalization, warping, radial extensibility, etc. A series of shape functions are then developed based on the exact solution of the field equations and used to formulate a cylindrical finite element capable of capturing thin shell behaviour with very few degrees of freedom. Through examples, the element is shown to efficiently model cylinders subject to in-phase and out-of phase harmonic loading and support excitation.