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

In this paper, an efficient curved cubic B-spline beam element is developed based on the field consistency principle, for vibration analysis. The form ulation is general in the sense that it includes anisotropy, transverse she ar deformation, in-plane and rotary inertia effects. The element is based o n laminated refined beam theory, which satisfies the interface transverse s hear stress and displacement continuity, and has a vanishing shear stress o n the top and bottom surfaces of the beam. The lack of consistency in the s hear and membrane strain field interpolations in their constrained physical limits causes poor convergence and unacceptable results due to locking. He nce, numerical experimentation is conducted to check these deficiencies wit h a series of assumed shear/membrane strain functions, redistributed in a f ield-consistent manner. The performance of the element is assessed by study ing the free vibration behaviour of a variety of problems ranging from a st raight beam to a circular ring. Copyright (C) 1999 John Wiley & Sons, Ltd.