National Aeronautics and Space Administration


Date of this Version



Composite Structures 93 (2011) 2882–2894; doi:10.1016/j.compstruct.2011.05.015


The paper deals with the development and computational assessment of three- and two-node beam finite elements based on the Refined Zigzag Theory (RZT) for the analysis of multilayered composite and sandwich beams. RZT is a recently proposed structural theory that accounts for the stretching, bending, and transverse shear deformations, and which provides substantial improvements over previously developed zigzag and higher-order theories. This new theory is analytically rigorous, variationally consistent, and computationally attractive. The theory is not affected by anomalies of most previous zigzag and higher-order theories, such as the vanishing of transverse shear stress and force at clamped boundaries. In contrast to Timoshenko theory, RZT does not employ shear correction factors to yield accurate results. From the computational mechanics perspective RZT requires C°-continuous shape functions and thus enables the development of efficient displacement-type finite elements. The focus of this paper is to explore several low-order beam finite elements that offer the best compromise between computational efficiency and accuracy. The initial attention is on the choice of shape functions that do not admit shear locking effects in slender beams. For this purpose, anisoparametric (aka interdependent) interpolations are adapted to approximate the four independent kinematic variables that are necessary to model the planar beam deformations. To achieve simple two-node elements, several types of constraint conditions are examined and corresponding deflection shape-functions are derived. It is recognized that the constraint condition requiring a constant variation of the transverse shear force gives rise to a remarkably accurate two-node beam element. The proposed elements and their predictive capabilities are assessed using several elastostatic example problems, where simply supported and cantilevered beams are analyzed over a range of lamination sequences, heterogeneous material properties, and slenderness ratios.