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

Abstract

To develop an effective hybrid-mixed element, it is extremely critical as to how to assume the stress field. This research article demonstrates the effect of additional equilibrium stress functions to enhance the numerical performance of the locking-free three-node hybrid-mixed curved beam element, proposed in Saleeb and Chang's previous work. It is exceedingly complicated or even infeasible to determine the stress functions to satisfy fully both the equilibrium conditions and suppression of kinematic deformation modes in the three-node hybrid-mixed formulation. Accordingly, the additional stress functions to satisfy partially or fully equilibrium conditions are incorporated in this study. Several numerical examples for static and dynamic problems confirm that the newly proposed element with these additional stress functions is highly effective regardless of the slenderness ratio and curvature of arches in static and dynamic analyses.

An Explicit Stiffness Matrix for Parabolic Beam Element

“…To overcome this obstacle, the number of nodes and order of functions were increased Ashwell and Sabir (1971) Dawe (1974) Meck (1980). Reduced integration assumed strain function and hybrid-mixed formulation are the other methods for creating locking-free elements Stolarski and Belytschko (1982) Pandian et al (1989) Lim (1993 and Yang and Sin (1995) Kim and Park (2008) Benedetti and Tralli (1989) Kim and Kim (1998) Kim and Lee (2008). Raveendranath and his colleagues (1999) assumed cubic polynomial for radial displacement.…”