A p-TYPE SUPERCONVERGENT RECOVERY METHOD FOR FE ELASTIC STABILITY ANALYSIS OF EULER BEAMS1)
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Graphical Abstract
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Abstract
This paper extends the p-type superconvergent recovery method to the finite element elastic stability analysis of Euler beams. Based on the superconvergence properties of the buckling loads and the nodal displacements in the buckling modes in regular FE solutions, a linear ordinary differential boundary value problem (BVP) is set up, which approximately governs the buckling mode in each element. This linear BVP within an element is solved with a higher order element, and a more accurate buckling mode is recovered. Then by substituting the recovered buckling mode into the Rayleigh quotient in analytic form, the buckling load is recovered. This method is simple and clear. It can improve the accuracy and the convergence rate of the buckling loads and the buckling modes significantly with a small amount of computation. Numerical examples demonstrate that this method is reliable and efficient and is worth further extending to other skeletal structures.
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