Equilibrium-Based Finite Element Formulation for Timoshenko Curved Tapered Beams

Abstract

Due to their excellent mechanical performance and structural efficiency, curved tapered beams have been widely used in many engineering applications, such as, bridge structures, piping systems, biomedical devices, aerospace and aeronautical structures, etc. Their complex geometries pose challenges to the development of robust approaches for the modelling of their mechanical behaviour. Among the various approaches available in the literature for their analysis, those that are based on the finite element method have been the most successful, particularly due to their versatility. Nonetheless, when applied to Timoshenko based structural models, some of these finite element approaches are prone to shear locking when the beam elements become slender and to membrane locking when the curvature of the beam centroid curves increases [1]. The aim of the present contribution is to introduce a novel, simple and effective, finite element formulation for the analysis of two-dimensional Timoshenko curved tapered beams. This formulation relies on a complementary variational approach based on a set of approximations that satisfy in strong form all equilibrium conditions of the boundary-value problem [2], resulting thus in a formulation that is free from both shear and membrane locking phenomena. The effectiveness of the formulation is numerically demonstrated through its application to a circular clamped-clamped beam subjected to a mid-span concentrated load, and the obtained results are analysed and discussed. REFERENCES [1]      H. Stolarski and T. Belytschko, “Shear and membrane locking in curved C0 elements”, Comput. Meth. Appl. Mech. Eng., Vol. 41, pp. 279–296, (1983). [2]      H.A.F.A. Santos, “Complementary-energy methods for geometrically non-linear structural models: an overview and recent developments in the analysis of frames”, Archives of Computational Methods in Engineering, Vol. 18, (2011): 405.