Analysis of locking and stress oscillations in a general curved beam element

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Abstract
In this paper, we have attempted to provide new insights into the phenomenon of shear and membrane locking in a general quadratic curved beam element. Locking is seen to be accompanied by significant quadratic oscillations in the axial force and cubic oscillations in the shear force. The functional reconstitution technique is applied to derive accurate error estimates for the manner in which locking is relieved and for the magnitude of the stress oscillations. The orthogonally correct field‐consistent interpolations are determined for the optimal form of the element using an elegant concept of expanding strain interpolations in terms of Legendre polynomials. The popular two‐point Gaussian integrated version of the element is shown to be non‐orthogonal, resulting in a cubic oscillation in the shear force that curiously vanishes at the Barlow points.

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