Hybrid-mixed curved beam elements with increased degrees of freedom for static and vibration analyses

Abstract

SUMMARYIn this paper, hybrid-mixed elements for static and vibration analyses of curved beams are presented. The proposed elements based on the Hellinger-Reissner variational principle employ the consistent stress parameters corresponding to the displacement fields with additional internal nodeless degrees of freedom in order to enhance the numerical performance. Elimination of the stress parameters by the stationary condition and condensation of internal nodeless degrees of freedom by Guyan reduction are carried out in the element formulation. This study shows how much the order of internal nodeless displacement functions and the type of mass matrix affect the numerical performance of hybrid-mixed curved beam elements in static and dynamic analyses. Various numerical examples confirm that the proposed elements with increased internal nodeless degrees of freedom generate superior accuracy in the prediction of bending behaviours and high vibration modes.

A mixed stress model for linear elastodynamics of arbitrarily curved beams

“…The Fourier p-elements THICK-2 and THICK-1 seem to have a better behavior when few degrees of freedom are employed, but seem to hardly get the convergence. The 332 element shows a competitive behavior with respect to another hybrid-mixed approach which has been proposed in [22]. In this element, CHM2(n = 2), the displacement description is enriched by a bubble function of degree n + 1.…”

The effect of additional equilibrium stress functions on the three-node hybrid-mixed curved beam element

“…Dorfi and Busby [13] introduced a two-node hybrid-mixed laminated composite curved beam element. Lastly, Kim et al [14,15] enhanced the numerical performance of a two-node hybrid-mixed linear element by employing the nodeless internal degrees of freedom in interpolating the displacement field and field-consistent stress functions. However, additional computational efforts were inevitable to construct the stiffness and mass matrix of a conventional size.…”

“…Due to the numerical problems, such as the locking phenomena and severe disturbance of stress prediction in the earliest attempts, numerous noteworthy elements based on the minimum potential energy principle have been proposed [1][2][3][4][5][6][7][8][9]. As an alternative to these displacementbased elements, considerable efforts have been devoted to the development of mixed or hybrid-mixed finite elements [10][11][12][13][14][15]. Among these, Saleeb and Chang [11] developed well-known two-node and three-node 0 C curved beam elements that satisfy two significant considerations in selecting the stress functions.…”

Geometric nonlinear dynamic analysis of curved beams using curved beam element

“…Leung et al [17] presented Fourier p-elements for in-plane vibration of thin and thick curved beams by introducing additional internal degrees of freedom which are sine functions to Fourier trigonometric functions to avoid membrane and shear locking and to increase the convergence and stability of the curved element. Based on an identical concept, Kim et al [18] added bubble functions to the displacement field interpolation so as to enhance substantially the numerical accuracy, especially in predicting high vibration modes. Although most of the above studies adopted the curved beam element to approximate the curved beam, they focused mainly on the free vibration and static problems, few researchers have considered the rigidflexible coupling dynamics for curved beams.…”