Shear flexible field-consistent curved spline beam element for vibration analysis

In this paper, an e$cient curved cubic B-spline beam element is developed based on the "eld consistency principle, for vibration analysis. The formulation is general in the sense that it includes anisotropy, transverse shear deformation, in-plane and rotary inertia e!ects. The element is based on laminated re"ned beam theory, which satis"es the interface transverse shear stress and displacement continuity, and has a vanishing shear stress on the top and bottom surfaces of the beam. The lack of consistency in the shear and membrane strain "eld interpolations in their constrained physical limits causes poor convergence and unacceptable results due to locking. Hence, numerical experimentation is conducted to check these de"ciencies with a series of assumed shear/membrane strain functions, redistributed in a "eld-consistent manner. The performance of the element is assessed by studying the free vibration behaviour of a variety of problems ranging from a straight beam to a circular ring. Copyrigh