Improvement on the axial force accuracy of the ANCF Euler-Bernoulli beam element with the second-order approximate function of the centerline and precise constraint equations

Miaozi Zheng, Peng Zhang, Binbin Li, Menglan Duan, Jianmin Ma, Jinxin Wang

Abstract: Highlights•Second-order centerline approximate function raises element axial force accuracy.•G2 continuity is satisfied at the node acted by an inclined concentrated force.•Relative rotation of rigid joint is restricted using dot product of gradients.•Partially-clamped end rotation is restricted using zero cross product of gradients.•Second-order elements with derived constraint equations yield correct axial force.