Free-vibration analysis of arches based on the hybrid-mixed formulation with consistent quadratic stress functions

The well-known two-node hybrid-mixed element with linear displacement interpolation functions and constant stress resultant functions proposed by Saleeb yields locking-free results in static analysis but shows unsatisfactory results in vibration analysis of arches. In this study, we investigate the role of higher-order interpolation functions and consistent stress resultant functions in developing an effective two-node hybrid-mixed finite element for free-vibration analysis of arches with a rectangular cross-section. The present thick element considering shear deformation is based on the Hellinger–Reissner variational principle and introduces additional nodeless degrees of freedom for displacement field interpolation in order to enhance substantially the numerical accuracy especially in predicting high vibration modes. In the performance evaluation of the present hybrid-mixed element, we examine the effect of the nodeless internal displacement functions, the field-consistent stress resultant parameters, the approximation of compliance matrix, and the shear correction factor in curved beam vibrations. Several numerical examples confirm the validity of the present element and also illustrate the dynamic characteristics of arches depending on the curvature, aspect ratio and boundary conditions, etc.