A p-TYPE SUPERCONVERGENT RECOVERY METHOD FOR FE ANALYSIS OF IN-PLANE FREE VIBRATION OF PLANAR CURVED BEAMS

This paper presents a p-type superconvergence recovery method for the finite element analysis of the in-plane free vibration of planar curved beams. Based on the inherent superconvergence properties on frequencies and nodal displacements in modes, a linear ordinary differential boundary value problem (BVP) which approximately governs the mode on each element is set up. This local linear BVP is solved by using a higher order element from which the mode on each element is recovered. Then by substituting the recovered mode into the Rayleigh quotient, the frequency is recovered. This method is a post-processing approach and its recovery computation for each element is handled only on this element domain. It can improve the accuracy and convergence rate of frequencies and modes significantly with a small computation. Numerical examples demonstrate that this method is reliable and efficient and is worth of further exploring.